Testing hierarchical pathway kinetics with residue data on cyantraniliprole

+ + + +

Introduction +

The purpose of this document is to test demonstrate how nonlinear +hierarchical models (NLHM) based on the parent degradation models SFO, +FOMC, DFOP and HS, with serial formation of two or more metabolites can +be fitted with the mkin package.

It was assembled in the course of work package 1.2 of Project Number +173340 (Application of nonlinear hierarchical models to the kinetic +evaluation of chemical degradation data) of the German Environment +Agency carried out in 2022 and 2023.

The mkin package is used in version 1.2.10 which is currently under +development. The newly introduced functionality that is used here is a +simplification of excluding random effects for a set of fits based on a +related set of fits with a reduced model, and the documentation of the +starting parameters of the fit, so that all starting parameters of +saem fits are now listed in the summary. The +saemix package is used as a backend for fitting the NLHM, +but is also loaded to make the convergence plot function available.

This document is processed with the knitr package, which +also provides the kable function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the parallel package is used.

+library(mkin)
+library(knitr)
+library(saemix)
+library(parallel)
+n_cores <- detectCores()
+
+# We need to start a new cluster after defining a compiled model that is
+# saved as a DLL to the user directory, therefore we define a function
+# This is used again after defining the pathway model
+start_cluster <- function(n_cores) {
+  if (Sys.info()["sysname"] == "Windows") {
+    ret <- makePSOCKcluster(n_cores)
+  } else {
+    ret <- makeForkCluster(n_cores)
+  }
+  return(ret)
+}
+cl <- start_cluster(n_cores)

Test data +

The example data are taken from the final addendum to the DAR from +2014 and are distributed with the mkin package. Residue data and time +step normalisation factors are read in using the function +read_spreadsheet from the mkin package. This function also +performs the time step normalisation.

+data_file <- system.file(
+  "testdata", "cyantraniliprole_soil_efsa_2014.xlsx",
+  package = "mkin")
+cyan_ds <- read_spreadsheet(data_file, parent_only = FALSE)

The following tables show the covariate data and the 5 datasets that +were read in from the spreadsheet file.

+pH <- attr(cyan_ds, "covariates")
+kable(pH, caption = "Covariate data")

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Covariate data
	pH
Nambsheim	7.90
Tama	6.20
Gross-Umstadt	7.04
Sassafras	4.62
Lleida	8.05

+for (ds_name in names(cyan_ds)) {
+  print(
+    kable(mkin_long_to_wide(cyan_ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      booktabs = TRUE, row.names = FALSE))
+    cat("\n\\clearpage\n")
+}

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Dataset Nambsheim
time	cyan	JCZ38	J9C38	JSE76	J9Z38
0.000000	105.79	NA	NA	NA	NA
3.210424	77.26	7.92	11.94	5.58	9.12
7.490988	57.13	15.46	16.58	12.59	11.74
17.122259	37.74	15.98	13.36	26.05	10.77
23.543105	31.47	6.05	14.49	34.71	4.96
43.875788	16.74	6.07	7.57	40.38	6.52
67.418893	8.85	10.34	6.39	30.71	8.90
107.014116	5.19	9.61	1.95	20.41	12.93
129.487080	3.45	6.18	1.36	21.78	6.99
195.835832	2.15	9.13	0.95	16.29	7.69
254.693596	1.92	6.92	0.20	13.57	7.16
321.042348	2.26	7.02	NA	11.12	8.66
383.110535	NA	5.05	NA	10.64	5.56
0.000000	105.57	NA	NA	NA	NA
3.210424	78.88	12.77	11.94	5.47	9.12
7.490988	59.94	15.27	16.58	13.60	11.74
17.122259	39.67	14.26	13.36	29.44	10.77
23.543105	30.21	16.07	14.49	35.90	4.96
43.875788	18.06	9.44	7.57	42.30	6.52
67.418893	8.54	5.78	6.39	34.70	8.90
107.014116	7.26	4.54	1.95	23.33	12.93
129.487080	3.60	4.22	1.36	23.56	6.99
195.835832	2.84	3.05	0.95	16.21	7.69
254.693596	2.00	2.90	0.20	15.53	7.16
321.042348	1.79	0.94	NA	9.80	8.66
383.110535	NA	1.82	NA	9.49	5.56

Dataset Tama
time	cyan	JCZ38	J9Z38	JSE76
0.000000	106.14	NA	NA	NA
2.400833	93.47	6.46	2.85	NA
5.601943	88.39	10.86	4.65	3.85
12.804442	72.29	11.97	4.91	11.24
17.606108	65.79	13.11	6.63	13.79
32.811382	53.16	11.24	8.90	23.40
50.417490	44.01	11.34	9.98	29.56
80.027761	33.23	8.82	11.31	35.63
96.833591	40.68	5.94	8.32	29.09
146.450803	20.65	4.49	8.72	36.88
190.466072	17.71	4.66	11.10	40.97
240.083284	14.86	2.27	11.62	40.11
286.499386	12.02	NA	10.73	42.58
0.000000	109.11	NA	NA	NA
2.400833	96.84	5.52	2.04	2.02
5.601943	85.29	9.65	2.99	4.39
12.804442	73.68	12.48	5.05	11.47
17.606108	64.89	12.44	6.29	15.00
32.811382	52.27	10.86	7.65	23.30
50.417490	42.61	10.54	9.37	31.06
80.027761	34.29	10.02	9.04	37.87
96.833591	30.50	6.34	8.14	33.97
146.450803	19.21	6.29	8.52	26.15
190.466072	17.55	5.81	9.89	32.08
240.083284	13.22	5.99	10.79	40.66
286.499386	11.09	6.05	8.82	42.90

Dataset Gross-Umstadt
time	cyan	JCZ38	J9Z38	JSE76
0.0000000	103.03	NA	NA	NA
2.1014681	87.85	4.79	3.26	0.62
4.9034255	77.35	8.05	9.89	1.32
10.5073404	69.33	9.74	12.32	4.74
21.0146807	55.65	14.57	13.59	9.84
31.5220211	49.03	14.66	16.71	12.32
42.0293615	41.86	15.97	13.64	15.53
63.0440422	34.88	18.20	14.12	22.02
84.0587230	28.26	15.64	14.06	25.60
0.0000000	104.05	NA	NA	NA
2.1014681	85.25	2.68	7.32	0.69
4.9034255	77.22	7.28	8.37	1.45
10.5073404	65.23	10.73	10.93	4.74
21.0146807	57.78	12.29	14.80	9.05
31.5220211	54.83	14.05	12.01	11.05
42.0293615	45.17	12.12	17.89	15.71
63.0440422	34.83	12.90	15.86	22.52
84.0587230	26.59	14.28	14.91	28.48
0.0000000	104.62	NA	NA	NA
0.8145225	97.21	NA	4.00	NA
1.9005525	89.64	3.59	5.24	NA
4.0726125	87.90	4.10	9.58	NA
8.1452251	86.90	5.96	9.45	NA
12.2178376	74.74	7.83	15.03	5.33
16.2904502	74.13	8.84	14.41	5.10
24.4356753	65.26	11.84	18.33	6.71
32.5809004	57.70	12.74	19.93	9.74
0.0000000	101.94	NA	NA	NA
0.8145225	99.94	NA	NA	NA
1.9005525	94.87	NA	4.56	NA
4.0726125	86.96	6.75	6.90	NA
8.1452251	80.51	10.68	7.43	2.58
12.2178376	78.38	10.35	9.46	3.69
16.2904502	70.05	13.73	9.27	7.18
24.4356753	61.28	12.57	13.28	13.19
32.5809004	52.85	12.67	12.95	13.69

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Dataset Sassafras
time	cyan	JCZ38	J9Z38	JSE76
0.000000	102.17	NA	NA	NA
2.216719	95.49	1.11	0.10	0.83
5.172343	83.35	6.43	2.89	3.30
11.083593	78.18	10.00	5.59	0.81
22.167186	70.44	17.21	4.23	1.09
33.250779	68.00	20.45	5.86	1.17
44.334371	59.64	24.64	3.17	2.72
66.501557	50.73	27.50	6.19	1.27
88.668742	45.65	32.77	5.69	4.54
0.000000	100.43	NA	NA	NA
2.216719	95.34	3.21	0.14	0.46
5.172343	84.38	5.73	4.75	0.62
11.083593	78.50	11.89	3.99	0.73
22.167186	71.17	17.28	4.39	0.66
33.250779	59.41	18.73	11.85	2.65
44.334371	64.57	22.93	5.13	2.01
66.501557	49.08	33.39	5.67	3.63
88.668742	40.41	39.60	5.93	6.17

Dataset Lleida
time	cyan	JCZ38	J9Z38	JSE76
0.000000	102.71	NA	NA	NA
2.821051	79.11	5.70	8.07	0.97
6.582451	70.03	7.17	11.31	4.72
14.105253	50.93	10.25	14.84	9.95
28.210505	33.43	10.40	14.82	24.06
42.315758	24.69	9.75	16.38	29.38
56.421010	22.99	10.06	15.51	29.25
84.631516	14.63	5.63	14.74	31.04
112.842021	12.43	4.17	13.53	33.28
0.000000	99.31	NA	NA	NA
2.821051	82.07	6.55	5.60	1.12
6.582451	70.65	7.61	8.01	3.21
14.105253	53.52	11.48	10.82	12.24
28.210505	35.60	11.19	15.43	23.53
42.315758	34.26	11.09	13.26	27.42
56.421010	21.79	4.80	18.30	30.20
84.631516	14.06	6.30	16.35	32.32
112.842021	11.51	5.57	12.64	32.51

Parent only evaluations +

As the pathway fits have very long run times, evaluations of the +parent data are performed first, in order to determine for each +hierarchical parent degradation model which random effects on the +degradation model parameters are ill-defined.

+cyan_sep_const <- mmkin(c("SFO", "FOMC", "DFOP", "SFORB", "HS"),
+  cyan_ds, quiet = TRUE, cores = n_cores)
+cyan_sep_tc <- update(cyan_sep_const, error_model = "tc")
+cyan_saem_full <- mhmkin(list(cyan_sep_const, cyan_sep_tc))
+status(cyan_saem_full) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	const	tc
SFO	OK	OK
FOMC	OK	OK
DFOP	OK	OK
SFORB	OK	OK
HS	OK	OK

All fits converged successfully.

+illparms(cyan_saem_full) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	const	tc
SFO	sd(cyan_0)	sd(cyan_0)
FOMC	sd(log_beta)	sd(cyan_0)
DFOP	sd(cyan_0)	sd(cyan_0), sd(log_k1)
SFORB	sd(cyan_free_0)	sd(cyan_free_0), sd(log_k_cyan_free_bound)
HS	sd(cyan_0)	sd(cyan_0)

In almost all models, the random effect for the initial concentration +of the parent compound is ill-defined. For the biexponential models DFOP +and SFORB, the random effect of one additional parameter is ill-defined +when the two-component error model is used.

+anova(cyan_saem_full) |> kable(digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
SFO const	5	833.9	832.0	-412.0
SFO tc	6	831.6	829.3	-409.8
FOMC const	7	709.1	706.4	-347.6
FOMC tc	8	689.2	686.1	-336.6
DFOP const	9	703.0	699.5	-342.5
SFORB const	9	701.3	697.8	-341.7
HS const	9	718.6	715.1	-350.3
DFOP tc	10	703.1	699.2	-341.6
SFORB tc	10	700.0	696.1	-340.0
HS tc	10	716.7	712.8	-348.3

Model comparison based on AIC and BIC indicates that the +two-component error model is preferable for all parent models with the +exception of DFOP. The lowest AIC and BIC values are are obtained with +the FOMC model, followed by SFORB and DFOP.

+stopCluster(cl)

Pathway fits +

Evaluations with pathway established previously +

To test the technical feasibility of coupling the relevant parent +degradation models with different transformation pathway models, a list +of mkinmod models is set up below. As in the EU evaluation, +parallel formation of metabolites JCZ38 and J9Z38 and secondary +formation of metabolite JSE76 from JCZ38 is used.

+if (!dir.exists("cyan_dlls")) dir.create("cyan_dlls")
+cyan_path_1 <- list(
+  sfo_path_1 = mkinmod(
+    cyan = mkinsub("SFO", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "sfo_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  fomc_path_1 = mkinmod(
+    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "fomc_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  dfop_path_1 = mkinmod(
+    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "dfop_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  sforb_path_1 = mkinmod(
+    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "sforb_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  hs_path_1 = mkinmod(
+    cyan = mkinsub("HS", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "hs_path_1", dll_dir = "cyan_dlls", overwrite = TRUE)
+)
+cl_path_1 <- start_cluster(n_cores)

To obtain suitable starting values for the NLHM fits, separate +pathway fits are performed for all datasets.

+f_sep_1_const <- mmkin(
+  cyan_path_1,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_1,
+  quiet = TRUE)
+status(f_sep_1_const) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
sfo_path_1	OK	OK	OK	C	OK
fomc_path_1	OK	OK	OK	OK	OK
dfop_path_1	OK	OK	OK	OK	OK
sforb_path_1	OK	OK	OK	OK	OK
hs_path_1	C	C	C	C	C

+f_sep_1_tc <- update(f_sep_1_const, error_model = "tc")
+status(f_sep_1_tc) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
sfo_path_1	OK	OK	OK	OK	OK
fomc_path_1	OK	OK	OK	OK	OK
dfop_path_1	OK	OK	OK	OK	OK
sforb_path_1	OK	OK	OK	OK	OK
hs_path_1	C	OK	C	OK	C

Most separate fits converged successfully. The biggest convergence +problems are seen when using the HS model with constant variance.

For the hierarchical pathway fits, those random effects that could +not be quantified in the corresponding parent data analyses are +excluded.

In the code below, the output of the illparms function +for the parent only fits is used as an argument +no_random_effect to the mhmkin function. The +possibility to do so was introduced in mkin version 1.2.2 +which is currently under development.

+f_saem_1 <- mhmkin(list(f_sep_1_const, f_sep_1_tc),
+  no_random_effect = illparms(cyan_saem_full),
+  cluster = cl_path_1)

+status(f_saem_1) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	const	tc
sfo_path_1	FO	Fth, FO
fomc_path_1	OK	Fth, FO
dfop_path_1	Fth, FO	Fth, FO
sforb_path_1	Fth, FO	Fth, FO
hs_path_1	FO	E

The status information from the individual fits shows that all fits +completed successfully. The matrix entries Fth and FO indicate that the +Fisher Information Matrix could not be inverted for the fixed effects +(theta) and the random effects (Omega), respectively. For the affected +fits, ill-defined parameters cannot be determined using the +illparms function, because it relies on the Fisher +Information Matrix.

+illparms(f_saem_1) |> kable()

+ +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	const	tc
sfo_path_1	NA	NA
fomc_path_1	sd(log_k_J9Z38), sd(f_cyan_ilr_2), +sd(f_JCZ38_qlogis)	NA
dfop_path_1	NA	NA
sforb_path_1	NA	NA
hs_path_1	NA	E

The model comparisons below suggest that the pathway fits using DFOP +or SFORB for the parent compound provide the best fit.

+anova(f_saem_1[, "const"]) |> kable(digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
sfo_path_1 const	16	2693.0	2686.8	-1330.5
fomc_path_1 const	18	2427.9	2420.9	-1196.0
dfop_path_1 const	20	2403.2	2395.4	-1181.6
sforb_path_1 const	20	2401.4	2393.6	-1180.7
hs_path_1 const	20	2427.2	2419.4	-1193.6

+anova(f_saem_1[1:4, ]) |> kable(digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
sfo_path_1 const	16	2693.0	2686.8	-1330.5
sfo_path_1 tc	17	2657.6	2651.0	-1311.8
fomc_path_1 const	18	2427.9	2420.9	-1196.0
fomc_path_1 tc	19	2423.6	2416.2	-1192.8
dfop_path_1 const	20	2403.2	2395.4	-1181.6
sforb_path_1 const	20	2401.4	2393.6	-1180.7
dfop_path_1 tc	20	2398.0	2390.1	-1179.0
sforb_path_1 tc	20	2399.9	2392.1	-1180.0

For these two parent model, successful fits are shown below. Plots of +the fits with the other parent models are shown in the Appendix.

+plot(f_saem_1[["dfop_path_1", "tc"]])

+DFOP pathway fit with two-component error +

+plot(f_saem_1[["sforb_path_1", "tc"]])

+SFORB pathway fit with two-component error +

A closer graphical analysis of these Figures shows that the residues +of transformation product JCZ38 in the soils Tama and Nambsheim observed +at later time points are strongly and systematically underestimated.

+stopCluster(cl_path_1)

Alternative pathway fits +

To improve the fit for JCZ38, a back-reaction from JSE76 to JCZ38 was +introduced in an alternative version of the transformation pathway, in +analogy to the back-reaction from K5A78 to K5A77. Both pairs of +transformation products are pairs of an organic acid with its +corresponding amide (Addendum 2014, p. 109). As FOMC provided the best +fit for the parent, and the biexponential models DFOP and SFORB provided +the best initial pathway fits, these three parent models are used in the +alternative pathway fits.

+cyan_path_2 <- list(
+  fomc_path_2 = mkinmod(
+    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "fomc_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  ),
+  dfop_path_2 = mkinmod(
+    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "dfop_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  ),
+  sforb_path_2 = mkinmod(
+    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "sforb_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  )
+)
+
+cl_path_2 <- start_cluster(n_cores)
+f_sep_2_const <- mmkin(
+  cyan_path_2,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_2,
+  quiet = TRUE)
+
+status(f_sep_2_const) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
fomc_path_2	OK	OK	OK	C	OK
dfop_path_2	OK	OK	OK	C	OK
sforb_path_2	OK	OK	OK	OK	OK

Using constant variance, separate fits converge with the exception of +the fits to the Sassafras soil data.

+f_sep_2_tc <- update(f_sep_2_const, error_model = "tc")
+status(f_sep_2_tc) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
fomc_path_2	OK	OK	OK	C	OK
dfop_path_2	OK	C	OK	C	OK
sforb_path_2	OK	OK	OK	C	OK

Using the two-component error model, all separate fits converge with +the exception of the alternative pathway fit with DFOP used for the +parent and the Sassafras dataset.

+f_saem_2 <- mhmkin(list(f_sep_2_const, f_sep_2_tc),
+  no_random_effect = illparms(cyan_saem_full[2:4, ]),
+  cluster = cl_path_2)

+status(f_saem_2) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + +

	const	tc
fomc_path_2	E	OK
dfop_path_2	OK	OK
sforb_path_2	OK	OK

The hierarchical fits for the alternative pathway completed +successfully, with the exception of the model using FOMC for the parent +compound and constant variance as the error model.

+illparms(f_saem_2) |> kable()

+ +++++ + + + + + + + + + + + + + + + + + + + + + + +

	const	tc
fomc_path_2	E	sd(f_JSE76_qlogis)
dfop_path_2	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)
sforb_path_2	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)

In all biphasic fits (DFOP or SFORB for the parent compound), the +random effects for the formation fractions for the pathways from JCZ38 +to JSE76, and for the reverse pathway from JSE76 to JCZ38 are +ill-defined.

+anova(f_saem_2[, "tc"]) |> kable(digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
fomc_path_2 tc	21	2249.0	2240.8	-1103.5
dfop_path_2 tc	22	2234.4	2225.8	-1095.2
sforb_path_2 tc	22	2239.7	2231.1	-1097.9

+anova(f_saem_2[2:3,]) |> kable(digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
dfop_path_2 const	22	2288.4	2279.8	-1122.2
sforb_path_2 const	22	2283.3	2274.7	-1119.7
dfop_path_2 tc	22	2234.4	2225.8	-1095.2
sforb_path_2 tc	22	2239.7	2231.1	-1097.9

The variants using the biexponential models DFOP and SFORB for the +parent compound and the two-component error model give the lowest AIC +and BIC values and are plotted below. Compared with the original +pathway, the AIC and BIC values indicate a large improvement. This is +confirmed by the plots, which show that the metabolite JCZ38 is fitted +much better with this model.

+plot(f_saem_2[["fomc_path_2", "tc"]])

+FOMC pathway fit with two-component error, alternative pathway +

+plot(f_saem_2[["dfop_path_2", "tc"]])

+DFOP pathway fit with two-component error, alternative pathway +

+plot(f_saem_2[["sforb_path_2", "tc"]])

+SFORB pathway fit with two-component error, alternative pathway +

+ +

All ill-defined random effects that were identified in the parent +only fits and in the above pathway fits, are excluded for the final +evaluations below. For this purpose, a list of character vectors is +created below that can be indexed by row and column indices, and which +contains the degradation parameter names for which random effects should +be excluded for each of the hierarchical fits contained in +f_saem_2.

+no_ranef <- matrix(list(), nrow = 3, ncol = 2, dimnames = dimnames(f_saem_2))
+no_ranef[["fomc_path_2", "const"]] <- c("log_beta", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["fomc_path_2", "tc"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "const"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "tc"]] <- c("cyan_0", "log_k1", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "const"]] <- c("cyan_free_0",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "tc"]] <- c("cyan_free_0", "log_k_cyan_free_bound",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+clusterExport(cl_path_2, "no_ranef")
+
+f_saem_3 <- update(f_saem_2,
+  no_random_effect = no_ranef,
+  cluster = cl_path_2)

+status(f_saem_3) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + +

	const	tc
fomc_path_2	E	Fth
dfop_path_2	Fth	Fth
sforb_path_2	Fth	Fth

With the exception of the FOMC pathway fit with constant variance, +all updated fits completed successfully. However, the Fisher Information +Matrix for the fixed effects (Fth) could not be inverted, so no +confidence intervals for the optimised parameters are available.

+illparms(f_saem_3) |> kable()

+ + + + + + + + + + + + + + + + + + + + + + + +

	const	tc
fomc_path_2	E
dfop_path_2
sforb_path_2

+anova(f_saem_3[, "tc"]) |> kable(digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
fomc_path_2 tc	19	2249.1	2241.6	-1105.5
dfop_path_2 tc	20	2237.3	2229.5	-1098.6
sforb_path_2 tc	20	2241.3	2233.5	-1100.7

+anova(f_saem_3[2:3,]) |> kable(digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
dfop_path_2 const	20	2282.2	2274.4	-1121.1
sforb_path_2 const	20	2279.7	2271.9	-1119.9
dfop_path_2 tc	20	2237.3	2229.5	-1098.6
sforb_path_2 tc	20	2241.3	2233.5	-1100.7

While the AIC and BIC values of the best fit (DFOP pathway fit with +two-component error) are lower than in the previous fits with the +alternative pathway, the practical value of these refined evaluations is +limited as no confidence intervals are obtained.

+stopCluster(cl_path_2)

Conclusion +

It was demonstrated that a relatively complex transformation pathway +with parallel formation of two primary metabolites and one secondary +metabolite can be fitted even if the data in the individual datasets are +quite different and partly only cover the formation phase.

The run times of the pathway fits were several hours, limiting the +practical feasibility of iterative refinements based on ill-defined +parameters and of alternative checks of parameter identifiability based +on multistart runs.

Acknowledgements +

The helpful comments by Janina Wöltjen of the German Environment +Agency are gratefully acknowledged.

Appendix +

Plots of fits that were not refined further +

+plot(f_saem_1[["sfo_path_1", "tc"]])

+SFO pathway fit with two-component error +

+plot(f_saem_1[["fomc_path_1", "tc"]])

+FOMC pathway fit with two-component error +

+plot(f_saem_1[["sforb_path_1", "tc"]])

+HS pathway fit with two-component error +

Hierarchical fit listings +

Pathway 1 +

+ +Hierarchical SFO path 1 fit with constant variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:42:26 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - k_cyan * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 437.151 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0     log_k_cyan    log_k_JCZ38    log_k_J9Z38    log_k_JSE76 
+       95.3304        -3.8459        -3.1305        -5.0678        -5.3196 
+  f_cyan_ilr_1   f_cyan_ilr_2 f_JCZ38_qlogis 
+        0.8158        23.5335        11.8774 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_0          4.797     0.0000       0.000       0.000      0.0000
+log_k_cyan      0.000     0.9619       0.000       0.000      0.0000
+log_k_JCZ38     0.000     0.0000       2.139       0.000      0.0000
+log_k_J9Z38     0.000     0.0000       0.000       1.639      0.0000
+log_k_JSE76     0.000     0.0000       0.000       0.000      0.7894
+f_cyan_ilr_1    0.000     0.0000       0.000       0.000      0.0000
+f_cyan_ilr_2    0.000     0.0000       0.000       0.000      0.0000
+f_JCZ38_qlogis  0.000     0.0000       0.000       0.000      0.0000
+               f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_0               0.0000        0.000           0.00
+log_k_cyan           0.0000        0.000           0.00
+log_k_JCZ38          0.0000        0.000           0.00
+log_k_J9Z38          0.0000        0.000           0.00
+log_k_JSE76          0.0000        0.000           0.00
+f_cyan_ilr_1         0.7714        0.000           0.00
+f_cyan_ilr_2         0.0000        9.247           0.00
+f_JCZ38_qlogis       0.0000        0.000          16.61
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2693 2687  -1331
+
+Optimised parameters:
+                     est.      lower      upper
+cyan_0            95.1279  9.354e+01  9.671e+01
+log_k_cyan        -3.8527 -4.367e+00 -3.338e+00
+log_k_JCZ38       -3.0381 -4.187e+00 -1.889e+00
+log_k_J9Z38       -5.0095 -5.623e+00 -4.396e+00
+log_k_JSE76       -5.3357 -6.025e+00 -4.646e+00
+f_cyan_ilr_1       0.8050  5.174e-01  1.093e+00
+f_cyan_ilr_2      12.4820 -1.050e+06  1.051e+06
+f_JCZ38_qlogis     1.2912  3.561e-01  2.226e+00
+a.1                4.8393         NA         NA
+SD.log_k_cyan      0.5840         NA         NA
+SD.log_k_JCZ38     1.2740         NA         NA
+SD.log_k_J9Z38     0.3172         NA         NA
+SD.log_k_JSE76     0.5677         NA         NA
+SD.f_cyan_ilr_1    0.2623         NA         NA
+SD.f_cyan_ilr_2    1.3724         NA         NA
+SD.f_JCZ38_qlogis  0.1464         NA         NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5840    NA    NA
+SD.log_k_JCZ38    1.2740    NA    NA
+SD.log_k_J9Z38    0.3172    NA    NA
+SD.log_k_JSE76    0.5677    NA    NA
+SD.f_cyan_ilr_1   0.2623    NA    NA
+SD.f_cyan_ilr_2   1.3724    NA    NA
+SD.f_JCZ38_qlogis 0.1464    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 4.839    NA    NA
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           95.127935 93.542456 96.713413
+k_cyan            0.021221  0.012687  0.035497
+k_JCZ38           0.047924  0.015189  0.151213
+k_J9Z38           0.006674  0.003612  0.012332
+k_JSE76           0.004817  0.002417  0.009601
+f_cyan_to_JCZ38   0.757402        NA        NA
+f_cyan_to_J9Z38   0.242597        NA        NA
+f_JCZ38_to_JSE76  0.784347  0.588098  0.902582
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  7.574e-01
+cyan_J9Z38  2.426e-01
+cyan_sink   9.839e-08
+JCZ38_JSE76 7.843e-01
+JCZ38_sink  2.157e-01
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   32.66 108.50
+JCZ38  14.46  48.05
+J9Z38 103.86 345.00
+JSE76 143.91 478.04
+
+

+ +Hierarchical SFO path 1 fit with two-component error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:42:06 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - k_cyan * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 417.143 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0     log_k_cyan    log_k_JCZ38    log_k_J9Z38    log_k_JSE76 
+       96.0039        -3.8907        -3.1276        -5.0069        -4.9367 
+  f_cyan_ilr_1   f_cyan_ilr_2 f_JCZ38_qlogis 
+        0.7937        22.3422        17.8932 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_0          4.859      0.000        0.00        0.00      0.0000
+log_k_cyan      0.000      0.962        0.00        0.00      0.0000
+log_k_JCZ38     0.000      0.000        2.04        0.00      0.0000
+log_k_J9Z38     0.000      0.000        0.00        1.72      0.0000
+log_k_JSE76     0.000      0.000        0.00        0.00      0.9076
+f_cyan_ilr_1    0.000      0.000        0.00        0.00      0.0000
+f_cyan_ilr_2    0.000      0.000        0.00        0.00      0.0000
+f_JCZ38_qlogis  0.000      0.000        0.00        0.00      0.0000
+               f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_0               0.0000        0.000           0.00
+log_k_cyan           0.0000        0.000           0.00
+log_k_JCZ38          0.0000        0.000           0.00
+log_k_J9Z38          0.0000        0.000           0.00
+log_k_JSE76          0.0000        0.000           0.00
+f_cyan_ilr_1         0.7598        0.000           0.00
+f_cyan_ilr_2         0.0000        8.939           0.00
+f_JCZ38_qlogis       0.0000        0.000          14.49
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2658 2651  -1312
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            94.81681    NA    NA
+log_k_cyan        -3.91558    NA    NA
+log_k_JCZ38       -3.12715    NA    NA
+log_k_J9Z38       -5.04840    NA    NA
+log_k_JSE76       -5.10443    NA    NA
+f_cyan_ilr_1       0.80760    NA    NA
+f_cyan_ilr_2      48.66960    NA    NA
+f_JCZ38_qlogis     3.03397    NA    NA
+a.1                3.93879    NA    NA
+b.1                0.08057    NA    NA
+SD.log_k_cyan      0.58921    NA    NA
+SD.log_k_JCZ38     1.29813    NA    NA
+SD.log_k_J9Z38     0.68372    NA    NA
+SD.log_k_JSE76     0.35128    NA    NA
+SD.f_cyan_ilr_1    0.38352    NA    NA
+SD.f_cyan_ilr_2    4.98884    NA    NA
+SD.f_JCZ38_qlogis  1.75636    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5892    NA    NA
+SD.log_k_JCZ38    1.2981    NA    NA
+SD.log_k_J9Z38    0.6837    NA    NA
+SD.log_k_JSE76    0.3513    NA    NA
+SD.f_cyan_ilr_1   0.3835    NA    NA
+SD.f_cyan_ilr_2   4.9888    NA    NA
+SD.f_JCZ38_qlogis 1.7564    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.93879    NA    NA
+b.1 0.08057    NA    NA
+
+Backtransformed parameters:
+                     est. lower upper
+cyan_0           94.81681    NA    NA
+k_cyan            0.01993    NA    NA
+k_JCZ38           0.04384    NA    NA
+k_J9Z38           0.00642    NA    NA
+k_JSE76           0.00607    NA    NA
+f_cyan_to_JCZ38   0.75807    NA    NA
+f_cyan_to_J9Z38   0.24193    NA    NA
+f_JCZ38_to_JSE76  0.95409    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.75807
+cyan_J9Z38  0.24193
+cyan_sink   0.00000
+JCZ38_JSE76 0.95409
+JCZ38_sink  0.04591
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   34.78 115.54
+JCZ38  15.81  52.52
+J9Z38 107.97 358.68
+JSE76 114.20 379.35
+
+

+ +Hierarchical FOMC path 1 fit with constant variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:42:57 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 468.609 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.2314        -3.3680        -5.1108        -5.9416         0.7144 
+  f_cyan_ilr_2 f_JCZ38_qlogis      log_alpha       log_beta 
+        7.0229        14.9234        -0.1791         2.9811 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.416       0.000         0.0       0.000       0.0000
+log_k_JCZ38     0.000       2.439         0.0       0.000       0.0000
+log_k_J9Z38     0.000       0.000         1.7       0.000       0.0000
+log_k_JSE76     0.000       0.000         0.0       1.856       0.0000
+f_cyan_ilr_1    0.000       0.000         0.0       0.000       0.7164
+f_cyan_ilr_2    0.000       0.000         0.0       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000         0.0       0.000       0.0000
+log_alpha       0.000       0.000         0.0       0.000       0.0000
+log_beta        0.000       0.000         0.0       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          11.57           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          18.81    0.0000   0.0000
+log_alpha              0.00           0.00    0.4144   0.0000
+log_beta               0.00           0.00    0.0000   0.5077
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2428 2421  -1196
+
+Optimised parameters:
+                      est.    lower    upper
+cyan_0            101.1664 98.51265 103.8202
+log_k_JCZ38        -3.3883 -4.78250  -1.9941
+log_k_J9Z38        -5.3087 -5.91564  -4.7017
+log_k_JSE76        -6.1313 -7.30061  -4.9619
+f_cyan_ilr_1        0.7456  0.43782   1.0534
+f_cyan_ilr_2        0.8181  0.24956   1.3866
+f_JCZ38_qlogis      2.0467  0.61165   3.4817
+log_alpha          -0.2391 -0.62806   0.1499
+log_beta            2.8739  2.67664   3.0711
+a.1                 3.4160  3.17960   3.6525
+SD.cyan_0           2.4355  0.40399   4.4671
+SD.log_k_JCZ38      1.5654  0.57311   2.5576
+SD.log_k_J9Z38      0.4645 -0.06533   0.9943
+SD.log_k_JSE76      0.9841  0.10738   1.8609
+SD.f_cyan_ilr_1     0.3285  0.10546   0.5515
+SD.f_cyan_ilr_2     0.2276 -0.38711   0.8424
+SD.f_JCZ38_qlogis   0.8340 -0.20970   1.8777
+SD.log_alpha        0.4250  0.16017   0.6898
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph
+log_k_JCZ38    -0.0159                                                        
+log_k_J9Z38    -0.0546  0.0080                                                
+log_k_JSE76    -0.0337  0.0016  0.0074                                        
+f_cyan_ilr_1   -0.0095  0.0194 -0.1573  0.0003                                
+f_cyan_ilr_2   -0.2733  0.0799  0.3059  0.0263  0.0125                        
+f_JCZ38_qlogis  0.0755 -0.0783 -0.0516  0.1222 -0.1155 -0.5231                
+log_alpha      -0.0567  0.0120  0.0351  0.0189  0.0040  0.0829 -0.0502        
+log_beta       -0.2980  0.0461  0.1382  0.0758  0.0209  0.4079 -0.2053  0.2759
+
+Random effects:
+                    est.    lower  upper
+SD.cyan_0         2.4355  0.40399 4.4671
+SD.log_k_JCZ38    1.5654  0.57311 2.5576
+SD.log_k_J9Z38    0.4645 -0.06533 0.9943
+SD.log_k_JSE76    0.9841  0.10738 1.8609
+SD.f_cyan_ilr_1   0.3285  0.10546 0.5515
+SD.f_cyan_ilr_2   0.2276 -0.38711 0.8424
+SD.f_JCZ38_qlogis 0.8340 -0.20970 1.8777
+SD.log_alpha      0.4250  0.16017 0.6898
+
+Variance model:
+     est. lower upper
+a.1 3.416  3.18 3.652
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.012e+02 9.851e+01 103.82023
+k_JCZ38          3.377e-02 8.375e-03   0.13614
+k_J9Z38          4.948e-03 2.697e-03   0.00908
+k_JSE76          2.174e-03 6.751e-04   0.00700
+f_cyan_to_JCZ38  6.389e-01        NA        NA
+f_cyan_to_J9Z38  2.226e-01        NA        NA
+f_JCZ38_to_JSE76 8.856e-01 6.483e-01   0.97016
+alpha            7.873e-01 5.336e-01   1.16166
+beta             1.771e+01 1.454e+01  21.56509
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6389
+cyan_J9Z38  0.2226
+cyan_sink   0.1385
+JCZ38_JSE76 0.8856
+JCZ38_sink  0.1144
+
+Estimated disappearance times:
+        DT50    DT90 DT50back
+cyan   25.00  312.06    93.94
+JCZ38  20.53   68.19       NA
+J9Z38 140.07  465.32       NA
+JSE76 318.86 1059.22       NA
+
+

+ +Hierarchical FOMC path 1 fit with two-component error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:42:50 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 460.309 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+     101.13294       -3.32499       -5.09097       -5.93566        0.71359 
+  f_cyan_ilr_2 f_JCZ38_qlogis      log_alpha       log_beta 
+      10.30315       14.62272       -0.09633        3.10634 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.649       0.000        0.00        0.00       0.0000
+log_k_JCZ38     0.000       2.319        0.00        0.00       0.0000
+log_k_J9Z38     0.000       0.000        1.73        0.00       0.0000
+log_k_JSE76     0.000       0.000        0.00        1.86       0.0000
+f_cyan_ilr_1    0.000       0.000        0.00        0.00       0.7183
+f_cyan_ilr_2    0.000       0.000        0.00        0.00       0.0000
+f_JCZ38_qlogis  0.000       0.000        0.00        0.00       0.0000
+log_alpha       0.000       0.000        0.00        0.00       0.0000
+log_beta        0.000       0.000        0.00        0.00       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          12.85           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          18.54    0.0000   0.0000
+log_alpha              0.00           0.00    0.3142   0.0000
+log_beta               0.00           0.00    0.0000   0.7333
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2424 2416  -1193
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            100.65667    NA    NA
+log_k_JCZ38        -3.45782    NA    NA
+log_k_J9Z38        -5.23476    NA    NA
+log_k_JSE76        -5.71827    NA    NA
+f_cyan_ilr_1        0.68389    NA    NA
+f_cyan_ilr_2        0.61027    NA    NA
+f_JCZ38_qlogis    116.27482    NA    NA
+log_alpha          -0.14484    NA    NA
+log_beta            3.03220    NA    NA
+a.1                 3.11051    NA    NA
+b.1                 0.04508    NA    NA
+SD.log_k_JCZ38      1.39961    NA    NA
+SD.log_k_J9Z38      0.57920    NA    NA
+SD.log_k_JSE76      0.68364    NA    NA
+SD.f_cyan_ilr_1     0.31477    NA    NA
+SD.f_cyan_ilr_2     0.37716    NA    NA
+SD.f_JCZ38_qlogis   5.52695    NA    NA
+SD.log_alpha        0.22823    NA    NA
+SD.log_beta         0.39161    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.3996    NA    NA
+SD.log_k_J9Z38    0.5792    NA    NA
+SD.log_k_JSE76    0.6836    NA    NA
+SD.f_cyan_ilr_1   0.3148    NA    NA
+SD.f_cyan_ilr_2   0.3772    NA    NA
+SD.f_JCZ38_qlogis 5.5270    NA    NA
+SD.log_alpha      0.2282    NA    NA
+SD.log_beta       0.3916    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.11051    NA    NA
+b.1 0.04508    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.007e+02    NA    NA
+k_JCZ38          3.150e-02    NA    NA
+k_J9Z38          5.328e-03    NA    NA
+k_JSE76          3.285e-03    NA    NA
+f_cyan_to_JCZ38  5.980e-01    NA    NA
+f_cyan_to_J9Z38  2.273e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+alpha            8.652e-01    NA    NA
+beta             2.074e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5980
+cyan_J9Z38  0.2273
+cyan_sink   0.1746
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50  DT90 DT50back
+cyan   25.48 276.2    83.15
+JCZ38  22.01  73.1       NA
+J9Z38 130.09 432.2       NA
+JSE76 210.98 700.9       NA
+
+

+ +Hierarchical DFOP path 1 fit with constant variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:43:33 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 504.014 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.0643        -3.4008        -5.0024        -5.8612         0.6855 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2       g_qlogis 
+        1.2366        13.6901        -1.8641        -4.5063        -0.6468 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.466       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.382       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.595       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       1.245       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6852
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_k1          0.000       0.000       0.000       0.000       0.0000
+log_k2          0.000       0.000       0.000       0.000       0.0000
+g_qlogis        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis
+cyan_0                 0.00           0.00 0.0000 0.0000    0.000
+log_k_JCZ38            0.00           0.00 0.0000 0.0000    0.000
+log_k_J9Z38            0.00           0.00 0.0000 0.0000    0.000
+log_k_JSE76            0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_1           0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_2           1.28           0.00 0.0000 0.0000    0.000
+f_JCZ38_qlogis         0.00          16.08 0.0000 0.0000    0.000
+log_k1                 0.00           0.00 0.9866 0.0000    0.000
+log_k2                 0.00           0.00 0.0000 0.5953    0.000
+g_qlogis               0.00           0.00 0.0000 0.0000    1.583
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2403 2395  -1182
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            102.5565    NA    NA
+log_k_JCZ38        -3.4729    NA    NA
+log_k_J9Z38        -5.1533    NA    NA
+log_k_JSE76        -5.6669    NA    NA
+f_cyan_ilr_1        0.6665    NA    NA
+f_cyan_ilr_2        0.5191    NA    NA
+f_JCZ38_qlogis     37.0113    NA    NA
+log_k1             -1.8497    NA    NA
+log_k2             -4.4931    NA    NA
+g_qlogis           -0.6383    NA    NA
+a.1                 3.2397    NA    NA
+SD.log_k_JCZ38      1.4286    NA    NA
+SD.log_k_J9Z38      0.5312    NA    NA
+SD.log_k_JSE76      0.6627    NA    NA
+SD.f_cyan_ilr_1     0.3013    NA    NA
+SD.f_cyan_ilr_2     0.2980    NA    NA
+SD.f_JCZ38_qlogis   0.1637    NA    NA
+SD.log_k1           0.5069    NA    NA
+SD.log_k2           0.3828    NA    NA
+SD.g_qlogis         0.8641    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4286    NA    NA
+SD.log_k_J9Z38    0.5312    NA    NA
+SD.log_k_JSE76    0.6627    NA    NA
+SD.f_cyan_ilr_1   0.3013    NA    NA
+SD.f_cyan_ilr_2   0.2980    NA    NA
+SD.f_JCZ38_qlogis 0.1637    NA    NA
+SD.log_k1         0.5069    NA    NA
+SD.log_k2         0.3828    NA    NA
+SD.g_qlogis       0.8641    NA    NA
+
+Variance model:
+    est. lower upper
+a.1 3.24    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.026e+02    NA    NA
+k_JCZ38          3.103e-02    NA    NA
+k_J9Z38          5.780e-03    NA    NA
+k_JSE76          3.459e-03    NA    NA
+f_cyan_to_JCZ38  5.813e-01    NA    NA
+f_cyan_to_J9Z38  2.265e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.573e-01    NA    NA
+k2               1.119e-02    NA    NA
+g                3.456e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5813
+cyan_J9Z38  0.2265
+cyan_sink   0.1922
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   25.23 167.94    50.55   4.407   61.97
+JCZ38  22.34  74.22       NA      NA      NA
+J9Z38 119.92 398.36       NA      NA      NA
+JSE76 200.41 665.76       NA      NA      NA
+
+

+ +Hierarchical DFOP path 1 fit with two-component error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:46:07 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 658.043 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.3964        -3.3626        -4.9792        -5.8727         0.6814 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2       g_qlogis 
+        6.8713        13.6901        -1.9222        -4.5035        -0.7172 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.317       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.272       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.633       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       1.271       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6839
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_k1          0.000       0.000       0.000       0.000       0.0000
+log_k2          0.000       0.000       0.000       0.000       0.0000
+g_qlogis        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis
+cyan_0                 0.00           0.00 0.0000 0.0000    0.000
+log_k_JCZ38            0.00           0.00 0.0000 0.0000    0.000
+log_k_J9Z38            0.00           0.00 0.0000 0.0000    0.000
+log_k_JSE76            0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_1           0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_2          11.95           0.00 0.0000 0.0000    0.000
+f_JCZ38_qlogis         0.00          16.08 0.0000 0.0000    0.000
+log_k1                 0.00           0.00 0.9496 0.0000    0.000
+log_k2                 0.00           0.00 0.0000 0.5846    0.000
+g_qlogis               0.00           0.00 0.0000 0.0000    1.719
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2398 2390  -1179
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            100.69709    NA    NA
+log_k_JCZ38        -3.46669    NA    NA
+log_k_J9Z38        -5.05076    NA    NA
+log_k_JSE76        -5.55558    NA    NA
+f_cyan_ilr_1        0.66045    NA    NA
+f_cyan_ilr_2        0.84275    NA    NA
+f_JCZ38_qlogis     64.22404    NA    NA
+log_k1             -2.17715    NA    NA
+log_k2             -4.55002    NA    NA
+g_qlogis           -0.55920    NA    NA
+a.1                 2.95785    NA    NA
+b.1                 0.04456    NA    NA
+SD.log_k_JCZ38      1.39881    NA    NA
+SD.log_k_J9Z38      0.67788    NA    NA
+SD.log_k_JSE76      0.52603    NA    NA
+SD.f_cyan_ilr_1     0.32490    NA    NA
+SD.f_cyan_ilr_2     0.53923    NA    NA
+SD.f_JCZ38_qlogis   2.75576    NA    NA
+SD.log_k2           0.30694    NA    NA
+SD.g_qlogis         0.83619    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.3988    NA    NA
+SD.log_k_J9Z38    0.6779    NA    NA
+SD.log_k_JSE76    0.5260    NA    NA
+SD.f_cyan_ilr_1   0.3249    NA    NA
+SD.f_cyan_ilr_2   0.5392    NA    NA
+SD.f_JCZ38_qlogis 2.7558    NA    NA
+SD.log_k2         0.3069    NA    NA
+SD.g_qlogis       0.8362    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.95785    NA    NA
+b.1 0.04456    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.007e+02    NA    NA
+k_JCZ38          3.122e-02    NA    NA
+k_J9Z38          6.404e-03    NA    NA
+k_JSE76          3.866e-03    NA    NA
+f_cyan_to_JCZ38  6.187e-01    NA    NA
+f_cyan_to_J9Z38  2.431e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.134e-01    NA    NA
+k2               1.057e-02    NA    NA
+g                3.637e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6187
+cyan_J9Z38  0.2431
+cyan_sink   0.1382
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   26.35 175.12    52.72   6.114    65.6
+JCZ38  22.20  73.75       NA      NA      NA
+J9Z38 108.23 359.53       NA      NA      NA
+JSE76 179.30 595.62       NA      NA      NA
+
+

+ +Hierarchical SFORB path 1 fit with constant variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:43:36 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 507.042 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.0643               -2.8987               -2.7077 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.4717               -3.4008               -5.0024 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -5.8613                0.6855                1.2366 
+       f_JCZ38_qlogis 
+              13.7395 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.466          0.0000                 0.000
+log_k_cyan_free             0.000          0.6158                 0.000
+log_k_cyan_free_bound       0.000          0.0000                 1.463
+log_k_cyan_bound_free       0.000          0.0000                 0.000
+log_k_JCZ38                 0.000          0.0000                 0.000
+log_k_J9Z38                 0.000          0.0000                 0.000
+log_k_JSE76                 0.000          0.0000                 0.000
+f_cyan_ilr_1                0.000          0.0000                 0.000
+f_cyan_ilr_2                0.000          0.0000                 0.000
+f_JCZ38_qlogis              0.000          0.0000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000       0.000       0.000       0.000
+log_k_cyan_free                       0.000       0.000       0.000       0.000
+log_k_cyan_free_bound                 0.000       0.000       0.000       0.000
+log_k_cyan_bound_free                 1.058       0.000       0.000       0.000
+log_k_JCZ38                           0.000       2.382       0.000       0.000
+log_k_J9Z38                           0.000       0.000       1.595       0.000
+log_k_JSE76                           0.000       0.000       0.000       1.245
+f_cyan_ilr_1                          0.000       0.000       0.000       0.000
+f_cyan_ilr_2                          0.000       0.000       0.000       0.000
+f_JCZ38_qlogis                        0.000       0.000       0.000       0.000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_free_0                 0.0000         0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00
+f_cyan_ilr_1                0.6852         0.00           0.00
+f_cyan_ilr_2                0.0000         1.28           0.00
+f_JCZ38_qlogis              0.0000         0.00          16.13
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2401 2394  -1181
+
+Optimised parameters:
+                             est. lower upper
+cyan_free_0              102.8136    NA    NA
+log_k_cyan_free           -2.7935    NA    NA
+log_k_cyan_free_bound     -2.5440    NA    NA
+log_k_cyan_bound_free     -3.4303    NA    NA
+log_k_JCZ38               -3.5010    NA    NA
+log_k_J9Z38               -5.1226    NA    NA
+log_k_JSE76               -5.6314    NA    NA
+f_cyan_ilr_1               0.6609    NA    NA
+f_cyan_ilr_2               0.5085    NA    NA
+f_JCZ38_qlogis            44.0153    NA    NA
+a.1                        3.2318    NA    NA
+SD.log_k_cyan_free         0.3211    NA    NA
+SD.log_k_cyan_free_bound   0.8408    NA    NA
+SD.log_k_cyan_bound_free   0.5724    NA    NA
+SD.log_k_JCZ38             1.4925    NA    NA
+SD.log_k_J9Z38             0.5816    NA    NA
+SD.log_k_JSE76             0.6037    NA    NA
+SD.f_cyan_ilr_1            0.3115    NA    NA
+SD.f_cyan_ilr_2            0.3436    NA    NA
+SD.f_JCZ38_qlogis          4.8937    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.3211    NA    NA
+SD.log_k_cyan_free_bound 0.8408    NA    NA
+SD.log_k_cyan_bound_free 0.5724    NA    NA
+SD.log_k_JCZ38           1.4925    NA    NA
+SD.log_k_J9Z38           0.5816    NA    NA
+SD.log_k_JSE76           0.6037    NA    NA
+SD.f_cyan_ilr_1          0.3115    NA    NA
+SD.f_cyan_ilr_2          0.3436    NA    NA
+SD.f_JCZ38_qlogis        4.8937    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.232    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.028e+02    NA    NA
+k_cyan_free          6.120e-02    NA    NA
+k_cyan_free_bound    7.855e-02    NA    NA
+k_cyan_bound_free    3.238e-02    NA    NA
+k_JCZ38              3.017e-02    NA    NA
+k_J9Z38              5.961e-03    NA    NA
+k_JSE76              3.584e-03    NA    NA
+f_cyan_free_to_JCZ38 5.784e-01    NA    NA
+f_cyan_free_to_J9Z38 2.271e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.15973 0.01241 0.33124 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.5784
+cyan_free_J9Z38 0.2271
+cyan_free_sink  0.1945
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   24.51 153.18    46.11         4.34        55.87
+JCZ38  22.98  76.33       NA           NA           NA
+J9Z38 116.28 386.29       NA           NA           NA
+JSE76 193.42 642.53       NA           NA           NA
+
+

+ +Hierarchical SFORB path 1 fit with two-component error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:46:14 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 664.11 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             101.3964               -2.9881               -2.7949 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.4376               -3.3626               -4.9792 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -5.8727                0.6814                6.7399 
+       f_JCZ38_qlogis 
+              13.7395 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.317          0.0000                 0.000
+log_k_cyan_free             0.000          0.7301                 0.000
+log_k_cyan_free_bound       0.000          0.0000                 1.384
+log_k_cyan_bound_free       0.000          0.0000                 0.000
+log_k_JCZ38                 0.000          0.0000                 0.000
+log_k_J9Z38                 0.000          0.0000                 0.000
+log_k_JSE76                 0.000          0.0000                 0.000
+f_cyan_ilr_1                0.000          0.0000                 0.000
+f_cyan_ilr_2                0.000          0.0000                 0.000
+f_JCZ38_qlogis              0.000          0.0000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000       0.000       0.000       0.000
+log_k_cyan_free                       0.000       0.000       0.000       0.000
+log_k_cyan_free_bound                 0.000       0.000       0.000       0.000
+log_k_cyan_bound_free                 1.109       0.000       0.000       0.000
+log_k_JCZ38                           0.000       2.272       0.000       0.000
+log_k_J9Z38                           0.000       0.000       1.633       0.000
+log_k_JSE76                           0.000       0.000       0.000       1.271
+f_cyan_ilr_1                          0.000       0.000       0.000       0.000
+f_cyan_ilr_2                          0.000       0.000       0.000       0.000
+f_JCZ38_qlogis                        0.000       0.000       0.000       0.000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_free_0                 0.0000         0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00
+f_cyan_ilr_1                0.6838         0.00           0.00
+f_cyan_ilr_2                0.0000        11.69           0.00
+f_JCZ38_qlogis              0.0000         0.00          16.13
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2400 2392  -1180
+
+Optimised parameters:
+                              est. lower upper
+cyan_free_0              100.56004    NA    NA
+log_k_cyan_free           -3.12657    NA    NA
+log_k_cyan_free_bound     -3.16825    NA    NA
+log_k_cyan_bound_free     -3.66003    NA    NA
+log_k_JCZ38               -3.47278    NA    NA
+log_k_J9Z38               -5.06823    NA    NA
+log_k_JSE76               -5.54327    NA    NA
+f_cyan_ilr_1               0.66631    NA    NA
+f_cyan_ilr_2               0.82898    NA    NA
+f_JCZ38_qlogis            38.31115    NA    NA
+a.1                        2.98352    NA    NA
+b.1                        0.04388    NA    NA
+SD.log_k_cyan_free         0.49145    NA    NA
+SD.log_k_cyan_bound_free   0.27347    NA    NA
+SD.log_k_JCZ38             1.41193    NA    NA
+SD.log_k_J9Z38             0.66073    NA    NA
+SD.log_k_JSE76             0.55885    NA    NA
+SD.f_cyan_ilr_1            0.33020    NA    NA
+SD.f_cyan_ilr_2            0.51367    NA    NA
+SD.f_JCZ38_qlogis          5.52122    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.4914    NA    NA
+SD.log_k_cyan_bound_free 0.2735    NA    NA
+SD.log_k_JCZ38           1.4119    NA    NA
+SD.log_k_J9Z38           0.6607    NA    NA
+SD.log_k_JSE76           0.5589    NA    NA
+SD.f_cyan_ilr_1          0.3302    NA    NA
+SD.f_cyan_ilr_2          0.5137    NA    NA
+SD.f_JCZ38_qlogis        5.5212    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.98352    NA    NA
+b.1 0.04388    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.006e+02    NA    NA
+k_cyan_free          4.387e-02    NA    NA
+k_cyan_free_bound    4.208e-02    NA    NA
+k_cyan_bound_free    2.573e-02    NA    NA
+k_JCZ38              3.103e-02    NA    NA
+k_J9Z38              6.294e-03    NA    NA
+k_JSE76              3.914e-03    NA    NA
+f_cyan_free_to_JCZ38 6.188e-01    NA    NA
+f_cyan_free_to_J9Z38 2.412e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.10044 0.01124 0.36580 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.6188
+cyan_free_J9Z38 0.2412
+cyan_free_sink  0.1400
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+
+Estimated disappearance times:
+        DT50  DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   26.05 164.4    49.48        6.901        61.67
+JCZ38  22.34  74.2       NA           NA           NA
+J9Z38 110.14 365.9       NA           NA           NA
+JSE76 177.11 588.3       NA           NA           NA
+
+

+ +Hierarchical HS path 1 fit with constant variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:43:42 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ifelse(time <= tb, k1, k2) * cyan -
+           k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ifelse(time <= tb, k1, k2) * cyan -
+           k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 512.818 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.8845        -3.4495        -4.9355        -5.6040         0.6468 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2         log_tb 
+        1.2396         9.7220        -2.9079        -4.1810         1.7813 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.406        0.00        0.00       0.000       0.0000
+log_k_JCZ38     0.000        2.33        0.00       0.000       0.0000
+log_k_J9Z38     0.000        0.00        1.59       0.000       0.0000
+log_k_JSE76     0.000        0.00        0.00       1.013       0.0000
+f_cyan_ilr_1    0.000        0.00        0.00       0.000       0.6367
+f_cyan_ilr_2    0.000        0.00        0.00       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00        0.00       0.000       0.0000
+log_k1          0.000        0.00        0.00       0.000       0.0000
+log_k2          0.000        0.00        0.00       0.000       0.0000
+log_tb          0.000        0.00        0.00       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb
+cyan_0                0.000           0.00 0.0000 0.0000 0.0000
+log_k_JCZ38           0.000           0.00 0.0000 0.0000 0.0000
+log_k_J9Z38           0.000           0.00 0.0000 0.0000 0.0000
+log_k_JSE76           0.000           0.00 0.0000 0.0000 0.0000
+f_cyan_ilr_1          0.000           0.00 0.0000 0.0000 0.0000
+f_cyan_ilr_2          2.038           0.00 0.0000 0.0000 0.0000
+f_JCZ38_qlogis        0.000          10.33 0.0000 0.0000 0.0000
+log_k1                0.000           0.00 0.7006 0.0000 0.0000
+log_k2                0.000           0.00 0.0000 0.8928 0.0000
+log_tb                0.000           0.00 0.0000 0.0000 0.6773
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2427 2419  -1194
+
+Optimised parameters:
+                      est.      lower      upper
+cyan_0            101.9660  1.005e+02  1.035e+02
+log_k_JCZ38        -3.4698 -4.716e+00 -2.224e+00
+log_k_J9Z38        -5.0947 -5.740e+00 -4.450e+00
+log_k_JSE76        -5.5977 -6.321e+00 -4.875e+00
+f_cyan_ilr_1        0.6595  3.734e-01  9.456e-01
+f_cyan_ilr_2        0.5905  1.664e-01  1.015e+00
+f_JCZ38_qlogis     25.8627 -4.224e+05  4.225e+05
+log_k1             -3.0884 -3.453e+00 -2.723e+00
+log_k2             -4.3877 -4.778e+00 -3.998e+00
+log_tb              2.3057  1.715e+00  2.896e+00
+a.1                 3.3228         NA         NA
+SD.log_k_JCZ38      1.4071         NA         NA
+SD.log_k_J9Z38      0.5774         NA         NA
+SD.log_k_JSE76      0.6214         NA         NA
+SD.f_cyan_ilr_1     0.3058         NA         NA
+SD.f_cyan_ilr_2     0.3470         NA         NA
+SD.f_JCZ38_qlogis   0.0644         NA         NA
+SD.log_k1           0.3994         NA         NA
+SD.log_k2           0.4373         NA         NA
+SD.log_tb           0.6419         NA         NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4071    NA    NA
+SD.log_k_J9Z38    0.5774    NA    NA
+SD.log_k_JSE76    0.6214    NA    NA
+SD.f_cyan_ilr_1   0.3058    NA    NA
+SD.f_cyan_ilr_2   0.3470    NA    NA
+SD.f_JCZ38_qlogis 0.0644    NA    NA
+SD.log_k1         0.3994    NA    NA
+SD.log_k2         0.4373    NA    NA
+SD.log_tb         0.6419    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.323    NA    NA
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.020e+02 1.005e+02 1.035e+02
+k_JCZ38          3.112e-02 8.951e-03 1.082e-01
+k_J9Z38          6.129e-03 3.216e-03 1.168e-02
+k_JSE76          3.706e-03 1.798e-03 7.639e-03
+f_cyan_to_JCZ38  5.890e-01        NA        NA
+f_cyan_to_J9Z38  2.318e-01        NA        NA
+f_JCZ38_to_JSE76 1.000e+00 0.000e+00 1.000e+00
+k1               4.558e-02 3.164e-02 6.565e-02
+k2               1.243e-02 8.417e-03 1.835e-02
+tb               1.003e+01 5.557e+00 1.811e+01
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  5.890e-01
+cyan_J9Z38  2.318e-01
+cyan_sink   1.793e-01
+JCZ38_JSE76 1.000e+00
+JCZ38_sink  5.861e-12
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   29.02 158.51    47.72   15.21   55.77
+JCZ38  22.27  73.98       NA      NA      NA
+J9Z38 113.09 375.69       NA      NA      NA
+JSE76 187.01 621.23       NA      NA      NA
+
+

Pathway 2 +

+ +Hierarchical FOMC path 2 fit with two-component error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:54:36 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 491.928 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4477        -1.8631        -5.1087        -2.5114         0.6826 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.7944        15.9616        13.1566        -0.1564         2.9781 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          7.701       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.448       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.724       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.659       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6356
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_alpha       0.000       0.000       0.000       0.000       0.0000
+log_beta        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          10.32           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.23           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          14.99    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3924   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5639
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2249 2241  -1104
+
+Optimised parameters:
+                       est.      lower     upper
+cyan_0            101.55265  9.920e+01  103.9059
+log_k_JCZ38        -2.32302 -2.832e+00   -1.8142
+log_k_J9Z38        -5.13082 -5.942e+00   -4.3199
+log_k_JSE76        -3.01756 -4.262e+00   -1.7736
+f_cyan_ilr_1        0.70850  3.657e-01    1.0513
+f_cyan_ilr_2        0.95775  2.612e-01    1.6543
+f_JCZ38_qlogis      3.86105  9.248e-01    6.7973
+f_JSE76_qlogis      7.51583 -1.120e+02  127.0392
+log_alpha          -0.15308 -4.508e-01    0.1446
+log_beta            2.99165  2.711e+00    3.2720
+a.1                 2.04034  1.843e+00    2.2382
+b.1                 0.06924  5.749e-02    0.0810
+SD.log_k_JCZ38      0.50818  1.390e-01    0.8774
+SD.log_k_J9Z38      0.86597  2.652e-01    1.4667
+SD.log_k_JSE76      1.38092  4.864e-01    2.2754
+SD.f_cyan_ilr_1     0.38204  1.354e-01    0.6286
+SD.f_cyan_ilr_2     0.55129  7.198e-02    1.0306
+SD.f_JCZ38_qlogis   1.88457  1.711e-02    3.7520
+SD.f_JSE76_qlogis   2.64018 -2.450e+03 2454.9447
+SD.log_alpha        0.31860  1.047e-01    0.5325
+SD.log_beta         0.24195  1.273e-02    0.4712
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0235                                                        
+log_k_J9Z38    -0.0442  0.0047                                                
+log_k_JSE76    -0.0023  0.0966  0.0006                                        
+f_cyan_ilr_1   -0.0032  0.0070 -0.0536 -0.0001                                
+f_cyan_ilr_2   -0.5189  0.0452  0.1152  0.0013 -0.0304                        
+f_JCZ38_qlogis  0.1088 -0.0848 -0.0240  0.0040 -0.0384 -0.2303                
+f_JSE76_qlogis -0.0545  0.1315  0.0195  0.0020  0.0252  0.1737 -0.5939        
+log_alpha      -0.0445  0.0056  0.0261  0.0019 -0.0055  0.0586 -0.0239 -0.0284
+log_beta       -0.2388  0.0163  0.0566  0.0040 -0.0078  0.2183 -0.0714 -0.0332
+               log_lph
+log_k_JCZ38           
+log_k_J9Z38           
+log_k_JSE76           
+f_cyan_ilr_1          
+f_cyan_ilr_2          
+f_JCZ38_qlogis        
+f_JSE76_qlogis        
+log_alpha             
+log_beta        0.2135
+
+Random effects:
+                    est.      lower     upper
+SD.log_k_JCZ38    0.5082  1.390e-01    0.8774
+SD.log_k_J9Z38    0.8660  2.652e-01    1.4667
+SD.log_k_JSE76    1.3809  4.864e-01    2.2754
+SD.f_cyan_ilr_1   0.3820  1.354e-01    0.6286
+SD.f_cyan_ilr_2   0.5513  7.198e-02    1.0306
+SD.f_JCZ38_qlogis 1.8846  1.711e-02    3.7520
+SD.f_JSE76_qlogis 2.6402 -2.450e+03 2454.9447
+SD.log_alpha      0.3186  1.047e-01    0.5325
+SD.log_beta       0.2420  1.273e-02    0.4712
+
+Variance model:
+       est.   lower upper
+a.1 2.04034 1.84252 2.238
+b.1 0.06924 0.05749 0.081
+
+Backtransformed parameters:
+                      est.     lower    upper
+cyan_0           1.016e+02 9.920e+01 103.9059
+k_JCZ38          9.798e-02 5.890e-02   0.1630
+k_J9Z38          5.912e-03 2.627e-03   0.0133
+k_JSE76          4.892e-02 1.410e-02   0.1697
+f_cyan_to_JCZ38  6.432e-01        NA       NA
+f_cyan_to_J9Z38  2.362e-01        NA       NA
+f_JCZ38_to_JSE76 9.794e-01 7.160e-01   0.9989
+f_JSE76_to_JCZ38 9.995e-01 2.268e-49   1.0000
+alpha            8.581e-01 6.371e-01   1.1556
+beta             1.992e+01 1.505e+01  26.3646
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  0.6432301
+cyan_J9Z38  0.2361657
+cyan_sink   0.1206042
+JCZ38_JSE76 0.9793879
+JCZ38_sink  0.0206121
+JSE76_JCZ38 0.9994559
+JSE76_sink  0.0005441
+
+Estimated disappearance times:
+         DT50   DT90 DT50back
+cyan   24.759 271.61    81.76
+JCZ38   7.075  23.50       NA
+J9Z38 117.249 389.49       NA
+JSE76  14.169  47.07       NA
+
+

+ +Hierarchical DFOP path 2 fit with constant variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:55:32 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 548.554 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4380        -2.3107        -5.3123        -3.7120         0.6757 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1439        13.1194        12.3492        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5644 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.591      0.0000       0.000         0.0       0.0000
+log_k_JCZ38     0.000      0.7966       0.000         0.0       0.0000
+log_k_J9Z38     0.000      0.0000       1.561         0.0       0.0000
+log_k_JSE76     0.000      0.0000       0.000         0.8       0.0000
+f_cyan_ilr_1    0.000      0.0000       0.000         0.0       0.6349
+f_cyan_ilr_2    0.000      0.0000       0.000         0.0       0.0000
+f_JCZ38_qlogis  0.000      0.0000       0.000         0.0       0.0000
+f_JSE76_qlogis  0.000      0.0000       0.000         0.0       0.0000
+log_k1          0.000      0.0000       0.000         0.0       0.0000
+log_k2          0.000      0.0000       0.000         0.0       0.0000
+g_qlogis        0.000      0.0000       0.000         0.0       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                0.000           0.00           0.00  0.000 0.0000
+log_k_JCZ38           0.000           0.00           0.00  0.000 0.0000
+log_k_J9Z38           0.000           0.00           0.00  0.000 0.0000
+log_k_JSE76           0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00           0.00  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.86           0.00  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00          13.91  0.000 0.0000
+log_k1                0.000           0.00           0.00  1.106 0.0000
+log_k2                0.000           0.00           0.00  0.000 0.6141
+g_qlogis              0.000           0.00           0.00  0.000 0.0000
+               g_qlogis
+cyan_0            0.000
+log_k_JCZ38       0.000
+log_k_J9Z38       0.000
+log_k_JSE76       0.000
+f_cyan_ilr_1      0.000
+f_cyan_ilr_2      0.000
+f_JCZ38_qlogis    0.000
+f_JSE76_qlogis    0.000
+log_k1            0.000
+log_k2            0.000
+g_qlogis          1.595
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2288 2280  -1122
+
+Optimised parameters:
+                      est.      lower      upper
+cyan_0            102.7204  1.014e+02  1.040e+02
+log_k_JCZ38        -2.8925 -4.044e+00 -1.741e+00
+log_k_J9Z38        -5.1430 -5.828e+00 -4.457e+00
+log_k_JSE76        -3.5577 -4.174e+00 -2.941e+00
+f_cyan_ilr_1        0.6929  3.788e-01  1.007e+00
+f_cyan_ilr_2        0.6066  5.342e-02  1.160e+00
+f_JCZ38_qlogis      9.8071 -2.819e+03  2.838e+03
+f_JSE76_qlogis      2.2229  5.684e-01  3.877e+00
+log_k1             -1.9339 -2.609e+00 -1.258e+00
+log_k2             -4.4709 -4.935e+00 -4.007e+00
+g_qlogis           -0.4987 -1.373e+00  3.757e-01
+a.1                 2.7368  2.545e+00  2.928e+00
+SD.log_k_JCZ38      1.2747  4.577e-01  2.092e+00
+SD.log_k_J9Z38      0.6758  1.418e-01  1.210e+00
+SD.log_k_JSE76      0.5869  1.169e-01  1.057e+00
+SD.f_cyan_ilr_1     0.3392  1.161e-01  5.622e-01
+SD.f_cyan_ilr_2     0.4200  8.501e-02  7.550e-01
+SD.f_JCZ38_qlogis   0.8511 -1.137e+06  1.137e+06
+SD.f_JSE76_qlogis   0.3767 -5.238e-01  1.277e+00
+SD.log_k1           0.7475  2.601e-01  1.235e+00
+SD.log_k2           0.5179  1.837e-01  8.521e-01
+SD.g_qlogis         0.9817  3.553e-01  1.608e+00
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0351                                                        
+log_k_J9Z38    -0.0541  0.0043                                                
+log_k_JSE76    -0.0078  0.0900 -0.0014                                        
+f_cyan_ilr_1   -0.0249  0.0268 -0.0962  0.0000                                
+f_cyan_ilr_2   -0.3560  0.0848  0.1545 -0.0022  0.0463                        
+f_JCZ38_qlogis  0.2005 -0.1226 -0.0347  0.0514 -0.1840 -0.5906                
+f_JSE76_qlogis -0.1638  0.1307  0.0266  0.0001  0.1645  0.5181 -0.9297        
+log_k1          0.0881 -0.0071  0.0005 -0.0070 -0.0064 -0.0346  0.0316 -0.0341
+log_k2          0.0238 -0.0003  0.0082 -0.0022 -0.0017 -0.0017 -0.0002 -0.0076
+g_qlogis        0.0198 -0.0002 -0.0109  0.0034  0.0017 -0.0176  0.0044  0.0051
+               log_k1  log_k2 
+log_k_JCZ38                   
+log_k_J9Z38                   
+log_k_JSE76                   
+f_cyan_ilr_1                  
+f_cyan_ilr_2                  
+f_JCZ38_qlogis                
+f_JSE76_qlogis                
+log_k1                        
+log_k2          0.0276        
+g_qlogis       -0.0283 -0.0309
+
+Random effects:
+                    est.      lower     upper
+SD.log_k_JCZ38    1.2747  4.577e-01 2.092e+00
+SD.log_k_J9Z38    0.6758  1.418e-01 1.210e+00
+SD.log_k_JSE76    0.5869  1.169e-01 1.057e+00
+SD.f_cyan_ilr_1   0.3392  1.161e-01 5.622e-01
+SD.f_cyan_ilr_2   0.4200  8.501e-02 7.550e-01
+SD.f_JCZ38_qlogis 0.8511 -1.137e+06 1.137e+06
+SD.f_JSE76_qlogis 0.3767 -5.238e-01 1.277e+00
+SD.log_k1         0.7475  2.601e-01 1.235e+00
+SD.log_k2         0.5179  1.837e-01 8.521e-01
+SD.g_qlogis       0.9817  3.553e-01 1.608e+00
+
+Variance model:
+     est. lower upper
+a.1 2.737 2.545 2.928
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           102.72037 1.014e+02 104.00464
+k_JCZ38            0.05544 1.752e-02   0.17539
+k_J9Z38            0.00584 2.942e-03   0.01159
+k_JSE76            0.02850 1.539e-02   0.05279
+f_cyan_to_JCZ38    0.59995        NA        NA
+f_cyan_to_J9Z38    0.22519        NA        NA
+f_JCZ38_to_JSE76   0.99994 0.000e+00   1.00000
+f_JSE76_to_JCZ38   0.90229 6.384e-01   0.97971
+k1                 0.14459 7.357e-02   0.28414
+k2                 0.01144 7.192e-03   0.01819
+g                  0.37784 2.021e-01   0.59284
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  5.999e-01
+cyan_J9Z38  2.252e-01
+cyan_sink   1.749e-01
+JCZ38_JSE76 9.999e-01
+JCZ38_sink  5.506e-05
+JSE76_JCZ38 9.023e-01
+JSE76_sink  9.771e-02
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   21.93 159.83    48.11   4.794    60.6
+JCZ38  12.50  41.53       NA      NA      NA
+J9Z38 118.69 394.27       NA      NA      NA
+JSE76  24.32  80.78       NA      NA      NA
+
+

+ +Hierarchical DFOP path 2 fit with two-component error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:57:56 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 691.67 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.7393        -1.4493        -5.0118        -2.1269         0.6720 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        7.3362        13.4423        13.2659        -2.0061        -4.5527 
+      g_qlogis 
+       -0.5806 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.604        0.00       0.000       0.000       0.0000
+log_k_JCZ38     0.000        2.77       0.000       0.000       0.0000
+log_k_J9Z38     0.000        0.00       1.662       0.000       0.0000
+log_k_JSE76     0.000        0.00       0.000       5.021       0.0000
+f_cyan_ilr_1    0.000        0.00       0.000       0.000       0.6519
+f_cyan_ilr_2    0.000        0.00       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000        0.00       0.000       0.000       0.0000
+log_k1          0.000        0.00       0.000       0.000       0.0000
+log_k2          0.000        0.00       0.000       0.000       0.0000
+g_qlogis        0.000        0.00       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                 0.00           0.00           0.00 0.0000 0.0000
+log_k_JCZ38            0.00           0.00           0.00 0.0000 0.0000
+log_k_J9Z38            0.00           0.00           0.00 0.0000 0.0000
+log_k_JSE76            0.00           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_1           0.00           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_2          13.37           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis         0.00          14.21           0.00 0.0000 0.0000
+f_JSE76_qlogis         0.00           0.00          14.58 0.0000 0.0000
+log_k1                 0.00           0.00           0.00 0.8453 0.0000
+log_k2                 0.00           0.00           0.00 0.0000 0.5969
+g_qlogis               0.00           0.00           0.00 0.0000 0.0000
+               g_qlogis
+cyan_0             0.00
+log_k_JCZ38        0.00
+log_k_J9Z38        0.00
+log_k_JSE76        0.00
+f_cyan_ilr_1       0.00
+f_cyan_ilr_2       0.00
+f_JCZ38_qlogis     0.00
+f_JSE76_qlogis     0.00
+log_k1             0.00
+log_k2             0.00
+g_qlogis           1.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2234 2226  -1095
+
+Optimised parameters:
+                       est.     lower     upper
+cyan_0            101.25496  99.14662 103.36331
+log_k_JCZ38        -2.55593  -3.32972  -1.78215
+log_k_J9Z38        -5.07103  -5.85423  -4.28783
+log_k_JSE76        -3.25468  -4.17577  -2.33360
+f_cyan_ilr_1        0.70139   0.35924   1.04355
+f_cyan_ilr_2        1.07712   0.17789   1.97636
+f_JCZ38_qlogis      3.57483   0.05990   7.08976
+f_JSE76_qlogis      4.54884  -7.25628  16.35395
+log_k1             -2.38201  -2.51639  -2.24763
+log_k2             -4.66741  -4.91865  -4.41617
+g_qlogis           -0.28446  -1.14192   0.57300
+a.1                 2.05925   1.86481   2.25369
+b.1                 0.06172   0.05062   0.07282
+SD.log_k_JCZ38      0.81137   0.25296   1.36977
+SD.log_k_J9Z38      0.83542   0.25395   1.41689
+SD.log_k_JSE76      0.97903   0.30100   1.65707
+SD.f_cyan_ilr_1     0.37878   0.13374   0.62382
+SD.f_cyan_ilr_2     0.67274   0.10102   1.24446
+SD.f_JCZ38_qlogis   1.35327  -0.42359   3.13012
+SD.f_JSE76_qlogis   1.43956 -19.14972  22.02884
+SD.log_k2           0.25329   0.07521   0.43138
+SD.g_qlogis         0.95167   0.35149   1.55184
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0265                                                        
+log_k_J9Z38    -0.0392  0.0024                                                
+log_k_JSE76     0.0011  0.1220 -0.0016                                        
+f_cyan_ilr_1   -0.0161  0.0217 -0.0552  0.0034                                
+f_cyan_ilr_2   -0.4718  0.0829  0.1102  0.0042  0.0095                        
+f_JCZ38_qlogis  0.1609 -0.1318 -0.0277  0.0081 -0.1040 -0.4559                
+f_JSE76_qlogis -0.1289  0.1494  0.0219  0.0012  0.1004  0.4309 -0.8543        
+log_k1          0.2618 -0.0739 -0.0167 -0.0148 -0.0444 -0.2768  0.3518 -0.3818
+log_k2          0.0603 -0.0217  0.0174 -0.0058 -0.0197 -0.0533  0.0923 -0.1281
+g_qlogis        0.0362  0.0115 -0.0111  0.0040  0.0095 -0.0116 -0.0439  0.0651
+               log_k1  log_k2 
+log_k_JCZ38                   
+log_k_J9Z38                   
+log_k_JSE76                   
+f_cyan_ilr_1                  
+f_cyan_ilr_2                  
+f_JCZ38_qlogis                
+f_JSE76_qlogis                
+log_k1                        
+log_k2          0.3269        
+g_qlogis       -0.1656 -0.0928
+
+Random effects:
+                    est.     lower   upper
+SD.log_k_JCZ38    0.8114   0.25296  1.3698
+SD.log_k_J9Z38    0.8354   0.25395  1.4169
+SD.log_k_JSE76    0.9790   0.30100  1.6571
+SD.f_cyan_ilr_1   0.3788   0.13374  0.6238
+SD.f_cyan_ilr_2   0.6727   0.10102  1.2445
+SD.f_JCZ38_qlogis 1.3533  -0.42359  3.1301
+SD.f_JSE76_qlogis 1.4396 -19.14972 22.0288
+SD.log_k2         0.2533   0.07521  0.4314
+SD.g_qlogis       0.9517   0.35149  1.5518
+
+Variance model:
+       est.   lower   upper
+a.1 2.05925 1.86481 2.25369
+b.1 0.06172 0.05062 0.07282
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.013e+02 9.915e+01 103.36331
+k_JCZ38          7.762e-02 3.580e-02   0.16828
+k_J9Z38          6.276e-03 2.868e-03   0.01373
+k_JSE76          3.859e-02 1.536e-02   0.09695
+f_cyan_to_JCZ38  6.520e-01        NA        NA
+f_cyan_to_J9Z38  2.418e-01        NA        NA
+f_JCZ38_to_JSE76 9.727e-01 5.150e-01   0.99917
+f_JSE76_to_JCZ38 9.895e-01 7.052e-04   1.00000
+k1               9.236e-02 8.075e-02   0.10565
+k2               9.397e-03 7.309e-03   0.01208
+g                4.294e-01 2.420e-01   0.63945
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.65203
+cyan_J9Z38  0.24181
+cyan_sink   0.10616
+JCZ38_JSE76 0.97274
+JCZ38_sink  0.02726
+JSE76_JCZ38 0.98953
+JSE76_sink  0.01047
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   24.26 185.34    55.79   7.504   73.77
+JCZ38   8.93  29.66       NA      NA      NA
+J9Z38 110.45 366.89       NA      NA      NA
+JSE76  17.96  59.66       NA      NA      NA
+
+

+ +Hierarchical SFORB path 2 fit with constant variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:55:26 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 542.162 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.4395               -2.7673               -2.8942 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6201               -2.3107               -5.3123 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.7120                0.6754                1.1448 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              14.8408               15.4734 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.589          0.0000                  0.00
+log_k_cyan_free             0.000          0.4849                  0.00
+log_k_cyan_free_bound       0.000          0.0000                  1.62
+log_k_cyan_bound_free       0.000          0.0000                  0.00
+log_k_JCZ38                 0.000          0.0000                  0.00
+log_k_J9Z38                 0.000          0.0000                  0.00
+log_k_JSE76                 0.000          0.0000                  0.00
+f_cyan_ilr_1                0.000          0.0000                  0.00
+f_cyan_ilr_2                0.000          0.0000                  0.00
+f_JCZ38_qlogis              0.000          0.0000                  0.00
+f_JSE76_qlogis              0.000          0.0000                  0.00
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000         0.0
+log_k_cyan_free                       0.000      0.0000       0.000         0.0
+log_k_cyan_free_bound                 0.000      0.0000       0.000         0.0
+log_k_cyan_bound_free                 1.197      0.0000       0.000         0.0
+log_k_JCZ38                           0.000      0.7966       0.000         0.0
+log_k_J9Z38                           0.000      0.0000       1.561         0.0
+log_k_JSE76                           0.000      0.0000       0.000         0.8
+f_cyan_ilr_1                          0.000      0.0000       0.000         0.0
+f_cyan_ilr_2                          0.000      0.0000       0.000         0.0
+f_JCZ38_qlogis                        0.000      0.0000       0.000         0.0
+f_JSE76_qlogis                        0.000      0.0000       0.000         0.0
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000            0.0           0.00
+log_k_cyan_free             0.0000        0.000            0.0           0.00
+log_k_cyan_free_bound       0.0000        0.000            0.0           0.00
+log_k_cyan_bound_free       0.0000        0.000            0.0           0.00
+log_k_JCZ38                 0.0000        0.000            0.0           0.00
+log_k_J9Z38                 0.0000        0.000            0.0           0.00
+log_k_JSE76                 0.0000        0.000            0.0           0.00
+f_cyan_ilr_1                0.6349        0.000            0.0           0.00
+f_cyan_ilr_2                0.0000        1.797            0.0           0.00
+f_JCZ38_qlogis              0.0000        0.000           15.6           0.00
+f_JSE76_qlogis              0.0000        0.000            0.0          17.52
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2283 2275  -1120
+
+Optimised parameters:
+                             est.     lower    upper
+cyan_free_0              102.6517 101.40815 103.8952
+log_k_cyan_free           -2.8729  -3.18649  -2.5593
+log_k_cyan_free_bound     -2.7803  -3.60525  -1.9552
+log_k_cyan_bound_free     -3.5845  -4.16644  -3.0026
+log_k_JCZ38               -2.3411  -2.89698  -1.7852
+log_k_J9Z38               -5.2487  -6.01271  -4.4847
+log_k_JSE76               -3.0259  -4.28274  -1.7690
+f_cyan_ilr_1               0.7289   0.38214   1.0756
+f_cyan_ilr_2               0.6891   0.18277   1.1954
+f_JCZ38_qlogis             4.2162   0.47015   7.9622
+f_JSE76_qlogis             5.8911 -20.19088  31.9730
+a.1                        2.7159   2.52587   2.9060
+SD.log_k_cyan_free         0.3354   0.10979   0.5610
+SD.log_k_cyan_free_bound   0.9061   0.30969   1.5025
+SD.log_k_cyan_bound_free   0.6376   0.21229   1.0628
+SD.log_k_JCZ38             0.5499   0.14533   0.9545
+SD.log_k_J9Z38             0.7457   0.15106   1.3404
+SD.log_k_JSE76             1.3822   0.47329   2.2912
+SD.f_cyan_ilr_1            0.3820   0.13280   0.6313
+SD.f_cyan_ilr_2            0.4317   0.06803   0.7953
+SD.f_JCZ38_qlogis          1.8258  -0.25423   3.9059
+SD.f_JSE76_qlogis          2.2348 -83.33679  87.8065
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.1944                                                
+log_k_cyan_free_bound  0.0815  0.0814                                        
+log_k_cyan_bound_free  0.0106  0.0426  0.0585                                
+log_k_JCZ38           -0.0231 -0.0106 -0.0089     -0.0051                    
+log_k_J9Z38           -0.0457 -0.0108  0.0019      0.0129      0.0032        
+log_k_JSE76           -0.0054 -0.0024 -0.0017     -0.0005      0.1108  0.0009
+f_cyan_ilr_1           0.0051 -0.0005 -0.0035     -0.0056      0.0131 -0.0967
+f_cyan_ilr_2          -0.3182 -0.0771 -0.0309     -0.0038      0.0680  0.1643
+f_JCZ38_qlogis         0.0834  0.0369  0.0302      0.0172     -0.1145 -0.0204
+f_JSE76_qlogis        -0.0553 -0.0365 -0.0441     -0.0414      0.1579  0.0175
+                      l__JSE7 f_cy__1 f_cy__2 f_JCZ38
+log_k_cyan_free                                      
+log_k_cyan_free_bound                                
+log_k_cyan_bound_free                                
+log_k_JCZ38                                          
+log_k_J9Z38                                          
+log_k_JSE76                                          
+f_cyan_ilr_1          -0.0002                        
+f_cyan_ilr_2           0.0020 -0.0415                
+f_JCZ38_qlogis         0.0052 -0.0665 -0.3437        
+f_JSE76_qlogis         0.0066  0.0635  0.3491 -0.7487
+
+Random effects:
+                           est.     lower   upper
+SD.log_k_cyan_free       0.3354   0.10979  0.5610
+SD.log_k_cyan_free_bound 0.9061   0.30969  1.5025
+SD.log_k_cyan_bound_free 0.6376   0.21229  1.0628
+SD.log_k_JCZ38           0.5499   0.14533  0.9545
+SD.log_k_J9Z38           0.7457   0.15106  1.3404
+SD.log_k_JSE76           1.3822   0.47329  2.2912
+SD.f_cyan_ilr_1          0.3820   0.13280  0.6313
+SD.f_cyan_ilr_2          0.4317   0.06803  0.7953
+SD.f_JCZ38_qlogis        1.8258  -0.25423  3.9059
+SD.f_JSE76_qlogis        2.2348 -83.33679 87.8065
+
+Variance model:
+     est. lower upper
+a.1 2.716 2.526 2.906
+
+Backtransformed parameters:
+                          est.     lower     upper
+cyan_free_0          1.027e+02 1.014e+02 103.89517
+k_cyan_free          5.654e-02 4.132e-02   0.07736
+k_cyan_free_bound    6.202e-02 2.718e-02   0.14153
+k_cyan_bound_free    2.775e-02 1.551e-02   0.04966
+k_JCZ38              9.622e-02 5.519e-02   0.16777
+k_J9Z38              5.254e-03 2.447e-03   0.01128
+k_JSE76              4.852e-02 1.380e-02   0.17051
+f_cyan_free_to_JCZ38 6.197e-01 5.643e-01   0.84429
+f_cyan_free_to_J9Z38 2.211e-01 5.643e-01   0.84429
+f_JCZ38_to_JSE76     9.855e-01 6.154e-01   0.99965
+f_JSE76_to_JCZ38     9.972e-01 1.703e-09   1.00000
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.13466 0.01165 0.36490 
+
+Resulting formation fractions:
+                      ff
+cyan_free_JCZ38 0.619745
+cyan_free_J9Z38 0.221083
+cyan_free_sink  0.159172
+cyan_free       1.000000
+JCZ38_JSE76     0.985460
+JCZ38_sink      0.014540
+JSE76_JCZ38     0.997244
+JSE76_sink      0.002756
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.293 158.67    47.77        5.147         59.5
+JCZ38   7.203  23.93       NA           NA           NA
+J9Z38 131.918 438.22       NA           NA           NA
+JSE76  14.287  47.46       NA           NA           NA
+
+

+ +Hierarchical SFORB path 2 fit with two-component error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 07:58:06 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 701.582 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             101.7511               -2.8370               -3.0162 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6600               -2.2988               -5.3129 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.6991                0.6722                4.8596 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              13.4678               14.2149 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.629           0.000                 0.000
+log_k_cyan_free             0.000           0.446                 0.000
+log_k_cyan_free_bound       0.000           0.000                 1.449
+log_k_cyan_bound_free       0.000           0.000                 0.000
+log_k_JCZ38                 0.000           0.000                 0.000
+log_k_J9Z38                 0.000           0.000                 0.000
+log_k_JSE76                 0.000           0.000                 0.000
+f_cyan_ilr_1                0.000           0.000                 0.000
+f_cyan_ilr_2                0.000           0.000                 0.000
+f_JCZ38_qlogis              0.000           0.000                 0.000
+f_JSE76_qlogis              0.000           0.000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000      0.0000
+log_k_cyan_free                       0.000      0.0000       0.000      0.0000
+log_k_cyan_free_bound                 0.000      0.0000       0.000      0.0000
+log_k_cyan_bound_free                 1.213      0.0000       0.000      0.0000
+log_k_JCZ38                           0.000      0.7801       0.000      0.0000
+log_k_J9Z38                           0.000      0.0000       1.575      0.0000
+log_k_JSE76                           0.000      0.0000       0.000      0.8078
+f_cyan_ilr_1                          0.000      0.0000       0.000      0.0000
+f_cyan_ilr_2                          0.000      0.0000       0.000      0.0000
+f_JCZ38_qlogis                        0.000      0.0000       0.000      0.0000
+f_JSE76_qlogis                        0.000      0.0000       0.000      0.0000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000           0.00           0.00
+log_k_cyan_free             0.0000        0.000           0.00           0.00
+log_k_cyan_free_bound       0.0000        0.000           0.00           0.00
+log_k_cyan_bound_free       0.0000        0.000           0.00           0.00
+log_k_JCZ38                 0.0000        0.000           0.00           0.00
+log_k_J9Z38                 0.0000        0.000           0.00           0.00
+log_k_JSE76                 0.0000        0.000           0.00           0.00
+f_cyan_ilr_1                0.6518        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        9.981           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          14.26           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          16.17
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2240 2231  -1098
+
+Optimised parameters:
+                              est.      lower      upper
+cyan_free_0              100.73014  9.873e+01  1.027e+02
+log_k_cyan_free           -3.19634 -3.641e+00 -2.752e+00
+log_k_cyan_free_bound     -3.43533 -3.674e+00 -3.197e+00
+log_k_cyan_bound_free     -3.83282 -4.163e+00 -3.503e+00
+log_k_JCZ38               -2.51065 -3.225e+00 -1.796e+00
+log_k_J9Z38               -5.02539 -5.825e+00 -4.226e+00
+log_k_JSE76               -3.24777 -4.163e+00 -2.333e+00
+f_cyan_ilr_1               0.70640  3.562e-01  1.057e+00
+f_cyan_ilr_2               1.42704  3.170e-01  2.537e+00
+f_JCZ38_qlogis             2.84779  1.042e+00  4.654e+00
+f_JSE76_qlogis             8.63674 -6.407e+02  6.580e+02
+a.1                        2.07082  1.877e+00  2.265e+00
+b.1                        0.06227  5.098e-02  7.355e-02
+SD.log_k_cyan_free         0.49674  1.865e-01  8.069e-01
+SD.log_k_cyan_bound_free   0.28537  6.809e-02  5.027e-01
+SD.log_k_JCZ38             0.74846  2.305e-01  1.266e+00
+SD.log_k_J9Z38             0.86077  2.713e-01  1.450e+00
+SD.log_k_JSE76             0.97613  3.030e-01  1.649e+00
+SD.f_cyan_ilr_1            0.38994  1.382e-01  6.417e-01
+SD.f_cyan_ilr_2            0.82869  3.917e-02  1.618e+00
+SD.f_JCZ38_qlogis          1.05000 -2.808e-02  2.128e+00
+SD.f_JSE76_qlogis          0.44681 -3.985e+05  3.985e+05
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.0936                                                
+log_k_cyan_free_bound  0.1302  0.1627                                        
+log_k_cyan_bound_free  0.0029  0.0525  0.5181                                
+log_k_JCZ38           -0.0116 -0.0077 -0.0430     -0.0236                    
+log_k_J9Z38           -0.0192 -0.0077 -0.0048      0.0229     -0.0005        
+log_k_JSE76            0.0007 -0.0020 -0.0134     -0.0072      0.1225 -0.0016
+f_cyan_ilr_1          -0.0118 -0.0027 -0.0132     -0.0118      0.0127 -0.0505
+f_cyan_ilr_2          -0.4643 -0.0762 -0.1245      0.0137      0.0497  0.1003
+f_JCZ38_qlogis         0.0710  0.0371  0.1826      0.0925     -0.0869 -0.0130
+f_JSE76_qlogis        -0.0367 -0.0270 -0.2274     -0.1865      0.1244  0.0098
+                      l__JSE7 f_cy__1 f_cy__2 f_JCZ38
+log_k_cyan_free                                      
+log_k_cyan_free_bound                                
+log_k_cyan_bound_free                                
+log_k_JCZ38                                          
+log_k_J9Z38                                          
+log_k_JSE76                                          
+f_cyan_ilr_1           0.0036                        
+f_cyan_ilr_2           0.0050 -0.0201                
+f_JCZ38_qlogis         0.0142 -0.0529 -0.2698        
+f_JSE76_qlogis         0.0064  0.0345  0.2015 -0.7058
+
+Random effects:
+                           est.      lower     upper
+SD.log_k_cyan_free       0.4967  1.865e-01 8.069e-01
+SD.log_k_cyan_bound_free 0.2854  6.809e-02 5.027e-01
+SD.log_k_JCZ38           0.7485  2.305e-01 1.266e+00
+SD.log_k_J9Z38           0.8608  2.713e-01 1.450e+00
+SD.log_k_JSE76           0.9761  3.030e-01 1.649e+00
+SD.f_cyan_ilr_1          0.3899  1.382e-01 6.417e-01
+SD.f_cyan_ilr_2          0.8287  3.917e-02 1.618e+00
+SD.f_JCZ38_qlogis        1.0500 -2.808e-02 2.128e+00
+SD.f_JSE76_qlogis        0.4468 -3.985e+05 3.985e+05
+
+Variance model:
+       est.   lower   upper
+a.1 2.07082 1.87680 2.26483
+b.1 0.06227 0.05098 0.07355
+
+Backtransformed parameters:
+                          est.      lower     upper
+cyan_free_0          1.007e+02  9.873e+01 102.72898
+k_cyan_free          4.091e-02  2.623e-02   0.06382
+k_cyan_free_bound    3.221e-02  2.537e-02   0.04090
+k_cyan_bound_free    2.165e-02  1.557e-02   0.03011
+k_JCZ38              8.122e-02  3.975e-02   0.16594
+k_J9Z38              6.569e-03  2.954e-03   0.01461
+k_JSE76              3.886e-02  1.556e-02   0.09703
+f_cyan_free_to_JCZ38 6.785e-01  6.102e-01   0.97309
+f_cyan_free_to_J9Z38 2.498e-01  6.102e-01   0.97309
+f_JCZ38_to_JSE76     9.452e-01  7.392e-01   0.99056
+f_JSE76_to_JCZ38     9.998e-01 5.580e-279   1.00000
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08426 0.01051 0.41220 
+
+Resulting formation fractions:
+                       ff
+cyan_free_JCZ38 0.6784541
+cyan_free_J9Z38 0.2498405
+cyan_free_sink  0.0717054
+cyan_free       1.0000000
+JCZ38_JSE76     0.9452043
+JCZ38_sink      0.0547957
+JSE76_JCZ38     0.9998226
+JSE76_sink      0.0001774
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.237 168.51    50.73        8.226        65.95
+JCZ38   8.535  28.35       NA           NA           NA
+J9Z38 105.517 350.52       NA           NA           NA
+JSE76  17.837  59.25       NA           NA           NA
+
+

Pathway 2, refined fits +

+ +Hierarchical FOMC path 2 fit with reduced random effects, two-component +error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:11:01 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 773.693 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4477        -1.8631        -5.1087        -2.5114         0.6826 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.7944        15.9616        13.1566        -0.1564         2.9781 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          7.701       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.448       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.724       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.659       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6356
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_alpha       0.000       0.000       0.000       0.000       0.0000
+log_beta        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          10.32           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.23           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          14.99    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3924   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5639
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2249 2242  -1106
+
+Optimised parameters:
+                     est.   lower  upper
+cyan_0          101.24524      NA     NA
+log_k_JCZ38      -2.85375      NA     NA
+log_k_J9Z38      -5.07729      NA     NA
+log_k_JSE76      -3.53511      NA     NA
+f_cyan_ilr_1      0.67478      NA     NA
+f_cyan_ilr_2      0.97152      NA     NA
+f_JCZ38_qlogis  213.48001      NA     NA
+f_JSE76_qlogis    2.02040      NA     NA
+log_alpha        -0.11041      NA     NA
+log_beta          3.06575      NA     NA
+a.1               2.05279 1.85495 2.2506
+b.1               0.07116 0.05912 0.0832
+SD.log_k_JCZ38    1.21713 0.44160 1.9927
+SD.log_k_J9Z38    0.88268 0.27541 1.4900
+SD.log_k_JSE76    0.59452 0.15005 1.0390
+SD.f_cyan_ilr_1   0.35370 0.12409 0.5833
+SD.f_cyan_ilr_2   0.78186 0.18547 1.3782
+SD.log_alpha      0.27781 0.08168 0.4739
+SD.log_beta       0.32608 0.06490 0.5873
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.2171 0.44160 1.9927
+SD.log_k_J9Z38  0.8827 0.27541 1.4900
+SD.log_k_JSE76  0.5945 0.15005 1.0390
+SD.f_cyan_ilr_1 0.3537 0.12409 0.5833
+SD.f_cyan_ilr_2 0.7819 0.18547 1.3782
+SD.log_alpha    0.2778 0.08168 0.4739
+SD.log_beta     0.3261 0.06490 0.5873
+
+Variance model:
+       est.   lower  upper
+a.1 2.05279 1.85495 2.2506
+b.1 0.07116 0.05912 0.0832
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.012e+02    NA    NA
+k_JCZ38          5.763e-02    NA    NA
+k_J9Z38          6.237e-03    NA    NA
+k_JSE76          2.916e-02    NA    NA
+f_cyan_to_JCZ38  6.354e-01    NA    NA
+f_cyan_to_J9Z38  2.447e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.829e-01    NA    NA
+alpha            8.955e-01    NA    NA
+beta             2.145e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6354
+cyan_J9Z38  0.2447
+cyan_sink   0.1200
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8829
+JSE76_sink  0.1171
+
+Estimated disappearance times:
+        DT50   DT90 DT50back
+cyan   25.07 259.21    78.03
+JCZ38  12.03  39.96       NA
+J9Z38 111.14 369.19       NA
+JSE76  23.77  78.98       NA
+
+

+ +Hierarchical DFOP path 2 fit with reduced random effects, constant +variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:12:27 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 859.906 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4380        -2.3107        -5.3123        -3.7120         0.6757 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1439        13.1194        12.3492        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5644 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.591      0.0000       0.000         0.0       0.0000
+log_k_JCZ38     0.000      0.7966       0.000         0.0       0.0000
+log_k_J9Z38     0.000      0.0000       1.561         0.0       0.0000
+log_k_JSE76     0.000      0.0000       0.000         0.8       0.0000
+f_cyan_ilr_1    0.000      0.0000       0.000         0.0       0.6349
+f_cyan_ilr_2    0.000      0.0000       0.000         0.0       0.0000
+f_JCZ38_qlogis  0.000      0.0000       0.000         0.0       0.0000
+f_JSE76_qlogis  0.000      0.0000       0.000         0.0       0.0000
+log_k1          0.000      0.0000       0.000         0.0       0.0000
+log_k2          0.000      0.0000       0.000         0.0       0.0000
+g_qlogis        0.000      0.0000       0.000         0.0       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                0.000           0.00           0.00  0.000 0.0000
+log_k_JCZ38           0.000           0.00           0.00  0.000 0.0000
+log_k_J9Z38           0.000           0.00           0.00  0.000 0.0000
+log_k_JSE76           0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00           0.00  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.86           0.00  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00          13.91  0.000 0.0000
+log_k1                0.000           0.00           0.00  1.106 0.0000
+log_k2                0.000           0.00           0.00  0.000 0.6141
+g_qlogis              0.000           0.00           0.00  0.000 0.0000
+               g_qlogis
+cyan_0            0.000
+log_k_JCZ38       0.000
+log_k_J9Z38       0.000
+log_k_JSE76       0.000
+f_cyan_ilr_1      0.000
+f_cyan_ilr_2      0.000
+f_JCZ38_qlogis    0.000
+f_JSE76_qlogis    0.000
+log_k1            0.000
+log_k2            0.000
+g_qlogis          1.595
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2282 2274  -1121
+
+Optimised parameters:
+                     est.   lower  upper
+cyan_0           102.6036      NA     NA
+log_k_JCZ38       -2.9348      NA     NA
+log_k_J9Z38       -5.1617      NA     NA
+log_k_JSE76       -3.6396      NA     NA
+f_cyan_ilr_1       0.6991      NA     NA
+f_cyan_ilr_2       0.6341      NA     NA
+f_JCZ38_qlogis  4232.3011      NA     NA
+f_JSE76_qlogis     1.9658      NA     NA
+log_k1            -1.9503      NA     NA
+log_k2            -4.4745      NA     NA
+g_qlogis          -0.4967      NA     NA
+a.1                2.7461 2.59274 2.8994
+SD.log_k_JCZ38     1.3178 0.47602 2.1596
+SD.log_k_J9Z38     0.7022 0.15061 1.2538
+SD.log_k_JSE76     0.6566 0.15613 1.1570
+SD.f_cyan_ilr_1    0.3409 0.11666 0.5652
+SD.f_cyan_ilr_2    0.4385 0.09482 0.7821
+SD.log_k1          0.7381 0.25599 1.2202
+SD.log_k2          0.5133 0.18152 0.8450
+SD.g_qlogis        0.9866 0.35681 1.6164
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.3178 0.47602 2.1596
+SD.log_k_J9Z38  0.7022 0.15061 1.2538
+SD.log_k_JSE76  0.6566 0.15613 1.1570
+SD.f_cyan_ilr_1 0.3409 0.11666 0.5652
+SD.f_cyan_ilr_2 0.4385 0.09482 0.7821
+SD.log_k1       0.7381 0.25599 1.2202
+SD.log_k2       0.5133 0.18152 0.8450
+SD.g_qlogis     0.9866 0.35681 1.6164
+
+Variance model:
+     est. lower upper
+a.1 2.746 2.593 2.899
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.026e+02    NA    NA
+k_JCZ38          5.314e-02    NA    NA
+k_J9Z38          5.732e-03    NA    NA
+k_JSE76          2.626e-02    NA    NA
+f_cyan_to_JCZ38  6.051e-01    NA    NA
+f_cyan_to_J9Z38  2.251e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.772e-01    NA    NA
+k1               1.422e-01    NA    NA
+k2               1.140e-02    NA    NA
+g                3.783e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6051
+cyan_J9Z38  0.2251
+cyan_sink   0.1698
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8772
+JSE76_sink  0.1228
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   22.05 160.35    48.27   4.873   60.83
+JCZ38  13.04  43.33       NA      NA      NA
+J9Z38 120.93 401.73       NA      NA      NA
+JSE76  26.39  87.68       NA      NA      NA
+
+

+ +Hierarchical DFOP path 2 fit with reduced random effects, two-component +error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:12:54 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 886.298 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.7393        -1.4493        -5.0118        -2.1269         0.6720 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        7.3362        13.4423        13.2659        -2.0061        -4.5527 
+      g_qlogis 
+       -0.5806 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.604        0.00       0.000       0.000       0.0000
+log_k_JCZ38     0.000        2.77       0.000       0.000       0.0000
+log_k_J9Z38     0.000        0.00       1.662       0.000       0.0000
+log_k_JSE76     0.000        0.00       0.000       5.021       0.0000
+f_cyan_ilr_1    0.000        0.00       0.000       0.000       0.6519
+f_cyan_ilr_2    0.000        0.00       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000        0.00       0.000       0.000       0.0000
+log_k1          0.000        0.00       0.000       0.000       0.0000
+log_k2          0.000        0.00       0.000       0.000       0.0000
+g_qlogis        0.000        0.00       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                 0.00           0.00           0.00 0.0000 0.0000
+log_k_JCZ38            0.00           0.00           0.00 0.0000 0.0000
+log_k_J9Z38            0.00           0.00           0.00 0.0000 0.0000
+log_k_JSE76            0.00           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_1           0.00           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_2          13.37           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis         0.00          14.21           0.00 0.0000 0.0000
+f_JSE76_qlogis         0.00           0.00          14.58 0.0000 0.0000
+log_k1                 0.00           0.00           0.00 0.8453 0.0000
+log_k2                 0.00           0.00           0.00 0.0000 0.5969
+g_qlogis               0.00           0.00           0.00 0.0000 0.0000
+               g_qlogis
+cyan_0             0.00
+log_k_JCZ38        0.00
+log_k_J9Z38        0.00
+log_k_JSE76        0.00
+f_cyan_ilr_1       0.00
+f_cyan_ilr_2       0.00
+f_JCZ38_qlogis     0.00
+f_JSE76_qlogis     0.00
+log_k1             0.00
+log_k2             0.00
+g_qlogis           1.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2237 2229  -1099
+
+Optimised parameters:
+                     est.   lower   upper
+cyan_0          101.00243      NA      NA
+log_k_JCZ38      -2.80828      NA      NA
+log_k_J9Z38      -5.04449      NA      NA
+log_k_JSE76      -3.66981      NA      NA
+f_cyan_ilr_1      0.72564      NA      NA
+f_cyan_ilr_2      1.37978      NA      NA
+f_JCZ38_qlogis    1.98726      NA      NA
+f_JSE76_qlogis  414.80884      NA      NA
+log_k1           -2.38601      NA      NA
+log_k2           -4.63632      NA      NA
+g_qlogis         -0.33920      NA      NA
+a.1               2.10837 1.91261 2.30413
+b.1               0.06223 0.05085 0.07361
+SD.log_k_JCZ38    1.30902 0.48128 2.13675
+SD.log_k_J9Z38    0.83882 0.25790 1.41974
+SD.log_k_JSE76    0.58104 0.14201 1.02008
+SD.f_cyan_ilr_1   0.35421 0.12398 0.58443
+SD.f_cyan_ilr_2   0.79373 0.12007 1.46739
+SD.log_k2         0.27476 0.08557 0.46394
+SD.g_qlogis       0.96170 0.35463 1.56878
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.3090 0.48128 2.1367
+SD.log_k_J9Z38  0.8388 0.25790 1.4197
+SD.log_k_JSE76  0.5810 0.14201 1.0201
+SD.f_cyan_ilr_1 0.3542 0.12398 0.5844
+SD.f_cyan_ilr_2 0.7937 0.12007 1.4674
+SD.log_k2       0.2748 0.08557 0.4639
+SD.g_qlogis     0.9617 0.35463 1.5688
+
+Variance model:
+       est.   lower   upper
+a.1 2.10837 1.91261 2.30413
+b.1 0.06223 0.05085 0.07361
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.010e+02    NA    NA
+k_JCZ38          6.031e-02    NA    NA
+k_J9Z38          6.445e-03    NA    NA
+k_JSE76          2.548e-02    NA    NA
+f_cyan_to_JCZ38  6.808e-01    NA    NA
+f_cyan_to_J9Z38  2.440e-01    NA    NA
+f_JCZ38_to_JSE76 8.795e-01    NA    NA
+f_JSE76_to_JCZ38 1.000e+00    NA    NA
+k1               9.200e-02    NA    NA
+k2               9.693e-03    NA    NA
+g                4.160e-01    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.68081
+cyan_J9Z38  0.24398
+cyan_sink   0.07521
+JCZ38_JSE76 0.87945
+JCZ38_sink  0.12055
+JSE76_JCZ38 1.00000
+JSE76_sink  0.00000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   25.00 182.05     54.8   7.535   71.51
+JCZ38  11.49  38.18       NA      NA      NA
+J9Z38 107.55 357.28       NA      NA      NA
+JSE76  27.20  90.36       NA      NA      NA
+
+

+ +Hierarchical SFORB path 2 fit with reduced random effects, constant +variance + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:12:32 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 865.121 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.4395               -2.7673               -2.8942 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6201               -2.3107               -5.3123 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.7120                0.6754                1.1448 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              14.8408               15.4734 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.589          0.0000                  0.00
+log_k_cyan_free             0.000          0.4849                  0.00
+log_k_cyan_free_bound       0.000          0.0000                  1.62
+log_k_cyan_bound_free       0.000          0.0000                  0.00
+log_k_JCZ38                 0.000          0.0000                  0.00
+log_k_J9Z38                 0.000          0.0000                  0.00
+log_k_JSE76                 0.000          0.0000                  0.00
+f_cyan_ilr_1                0.000          0.0000                  0.00
+f_cyan_ilr_2                0.000          0.0000                  0.00
+f_JCZ38_qlogis              0.000          0.0000                  0.00
+f_JSE76_qlogis              0.000          0.0000                  0.00
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000         0.0
+log_k_cyan_free                       0.000      0.0000       0.000         0.0
+log_k_cyan_free_bound                 0.000      0.0000       0.000         0.0
+log_k_cyan_bound_free                 1.197      0.0000       0.000         0.0
+log_k_JCZ38                           0.000      0.7966       0.000         0.0
+log_k_J9Z38                           0.000      0.0000       1.561         0.0
+log_k_JSE76                           0.000      0.0000       0.000         0.8
+f_cyan_ilr_1                          0.000      0.0000       0.000         0.0
+f_cyan_ilr_2                          0.000      0.0000       0.000         0.0
+f_JCZ38_qlogis                        0.000      0.0000       0.000         0.0
+f_JSE76_qlogis                        0.000      0.0000       0.000         0.0
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000            0.0           0.00
+log_k_cyan_free             0.0000        0.000            0.0           0.00
+log_k_cyan_free_bound       0.0000        0.000            0.0           0.00
+log_k_cyan_bound_free       0.0000        0.000            0.0           0.00
+log_k_JCZ38                 0.0000        0.000            0.0           0.00
+log_k_J9Z38                 0.0000        0.000            0.0           0.00
+log_k_JSE76                 0.0000        0.000            0.0           0.00
+f_cyan_ilr_1                0.6349        0.000            0.0           0.00
+f_cyan_ilr_2                0.0000        1.797            0.0           0.00
+f_JCZ38_qlogis              0.0000        0.000           15.6           0.00
+f_JSE76_qlogis              0.0000        0.000            0.0          17.52
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2280 2272  -1120
+
+Optimised parameters:
+                              est.   lower  upper
+cyan_free_0               102.6532      NA     NA
+log_k_cyan_free            -2.8547      NA     NA
+log_k_cyan_free_bound      -2.7004      NA     NA
+log_k_cyan_bound_free      -3.5078      NA     NA
+log_k_JCZ38                -2.9255      NA     NA
+log_k_J9Z38                -5.1089      NA     NA
+log_k_JSE76                -3.6263      NA     NA
+f_cyan_ilr_1                0.6873      NA     NA
+f_cyan_ilr_2                0.6498      NA     NA
+f_JCZ38_qlogis           3624.2149      NA     NA
+f_JSE76_qlogis              1.9991      NA     NA
+a.1                         2.7472 2.55559 2.9388
+SD.log_k_cyan_free          0.3227 0.10296 0.5423
+SD.log_k_cyan_free_bound    0.8757 0.29525 1.4562
+SD.log_k_cyan_bound_free    0.6128 0.20220 1.0233
+SD.log_k_JCZ38              1.3431 0.48474 2.2014
+SD.log_k_J9Z38              0.6881 0.14714 1.2291
+SD.log_k_JSE76              0.6461 0.15321 1.1390
+SD.f_cyan_ilr_1             0.3361 0.11376 0.5585
+SD.f_cyan_ilr_2             0.4286 0.08419 0.7730
+
+Correlation is not available
+
+Random effects:
+                           est.   lower  upper
+SD.log_k_cyan_free       0.3227 0.10296 0.5423
+SD.log_k_cyan_free_bound 0.8757 0.29525 1.4562
+SD.log_k_cyan_bound_free 0.6128 0.20220 1.0233
+SD.log_k_JCZ38           1.3431 0.48474 2.2014
+SD.log_k_J9Z38           0.6881 0.14714 1.2291
+SD.log_k_JSE76           0.6461 0.15321 1.1390
+SD.f_cyan_ilr_1          0.3361 0.11376 0.5585
+SD.f_cyan_ilr_2          0.4286 0.08419 0.7730
+
+Variance model:
+     est. lower upper
+a.1 2.747 2.556 2.939
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.027e+02    NA    NA
+k_cyan_free          5.758e-02    NA    NA
+k_cyan_free_bound    6.718e-02    NA    NA
+k_cyan_bound_free    2.996e-02    NA    NA
+k_JCZ38              5.364e-02    NA    NA
+k_J9Z38              6.042e-03    NA    NA
+k_JSE76              2.662e-02    NA    NA
+f_cyan_free_to_JCZ38 6.039e-01    NA    NA
+f_cyan_free_to_J9Z38 2.285e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+f_JSE76_to_JCZ38     8.807e-01    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+ 0.1426  0.0121  0.3484 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.6039
+cyan_free_J9Z38 0.2285
+cyan_free_sink  0.1676
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+JSE76_JCZ38     0.8807
+JSE76_sink      0.1193
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.84 154.95    46.65         4.86        57.31
+JCZ38  12.92  42.93       NA           NA           NA
+J9Z38 114.71 381.07       NA           NA           NA
+JSE76  26.04  86.51       NA           NA           NA
+
+

+ +Hierarchical SFORB path 2 fit with reduced random effects, two-component +error + +


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.4.2 
+Date of fit:     Fri Feb 14 08:12:36 2025 
+Date of summary: Fri Feb 14 08:12:55 2025 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 868.952 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             101.7511               -2.8370               -3.0162 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6600               -2.2988               -5.3129 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.6991                0.6722                4.8596 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              13.4678               14.2149 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.629           0.000                 0.000
+log_k_cyan_free             0.000           0.446                 0.000
+log_k_cyan_free_bound       0.000           0.000                 1.449
+log_k_cyan_bound_free       0.000           0.000                 0.000
+log_k_JCZ38                 0.000           0.000                 0.000
+log_k_J9Z38                 0.000           0.000                 0.000
+log_k_JSE76                 0.000           0.000                 0.000
+f_cyan_ilr_1                0.000           0.000                 0.000
+f_cyan_ilr_2                0.000           0.000                 0.000
+f_JCZ38_qlogis              0.000           0.000                 0.000
+f_JSE76_qlogis              0.000           0.000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000      0.0000
+log_k_cyan_free                       0.000      0.0000       0.000      0.0000
+log_k_cyan_free_bound                 0.000      0.0000       0.000      0.0000
+log_k_cyan_bound_free                 1.213      0.0000       0.000      0.0000
+log_k_JCZ38                           0.000      0.7801       0.000      0.0000
+log_k_J9Z38                           0.000      0.0000       1.575      0.0000
+log_k_JSE76                           0.000      0.0000       0.000      0.8078
+f_cyan_ilr_1                          0.000      0.0000       0.000      0.0000
+f_cyan_ilr_2                          0.000      0.0000       0.000      0.0000
+f_JCZ38_qlogis                        0.000      0.0000       0.000      0.0000
+f_JSE76_qlogis                        0.000      0.0000       0.000      0.0000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000           0.00           0.00
+log_k_cyan_free             0.0000        0.000           0.00           0.00
+log_k_cyan_free_bound       0.0000        0.000           0.00           0.00
+log_k_cyan_bound_free       0.0000        0.000           0.00           0.00
+log_k_JCZ38                 0.0000        0.000           0.00           0.00
+log_k_J9Z38                 0.0000        0.000           0.00           0.00
+log_k_JSE76                 0.0000        0.000           0.00           0.00
+f_cyan_ilr_1                0.6518        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        9.981           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          14.26           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          16.17
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2241 2233  -1101
+
+Optimised parameters:
+                              est.   lower   upper
+cyan_free_0              100.95469      NA      NA
+log_k_cyan_free           -3.18706      NA      NA
+log_k_cyan_free_bound     -3.38455      NA      NA
+log_k_cyan_bound_free     -3.75788      NA      NA
+log_k_JCZ38               -2.77024      NA      NA
+log_k_J9Z38               -5.03665      NA      NA
+log_k_JSE76               -3.60289      NA      NA
+f_cyan_ilr_1               0.72263      NA      NA
+f_cyan_ilr_2               1.45352      NA      NA
+f_JCZ38_qlogis             2.00778      NA      NA
+f_JSE76_qlogis           941.58570      NA      NA
+a.1                        2.11130 1.91479 2.30780
+b.1                        0.06299 0.05152 0.07445
+SD.log_k_cyan_free         0.50098 0.18805 0.81390
+SD.log_k_cyan_bound_free   0.31671 0.08467 0.54875
+SD.log_k_JCZ38             1.25865 0.45932 2.05798
+SD.log_k_J9Z38             0.86833 0.27222 1.46444
+SD.log_k_JSE76             0.59325 0.14711 1.03940
+SD.f_cyan_ilr_1            0.35705 0.12521 0.58890
+SD.f_cyan_ilr_2            0.88541 0.13797 1.63286
+
+Correlation is not available
+
+Random effects:
+                           est.   lower  upper
+SD.log_k_cyan_free       0.5010 0.18805 0.8139
+SD.log_k_cyan_bound_free 0.3167 0.08467 0.5487
+SD.log_k_JCZ38           1.2587 0.45932 2.0580
+SD.log_k_J9Z38           0.8683 0.27222 1.4644
+SD.log_k_JSE76           0.5933 0.14711 1.0394
+SD.f_cyan_ilr_1          0.3571 0.12521 0.5889
+SD.f_cyan_ilr_2          0.8854 0.13797 1.6329
+
+Variance model:
+       est.   lower   upper
+a.1 2.11130 1.91479 2.30780
+b.1 0.06299 0.05152 0.07445
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.010e+02    NA    NA
+k_cyan_free          4.129e-02    NA    NA
+k_cyan_free_bound    3.389e-02    NA    NA
+k_cyan_bound_free    2.333e-02    NA    NA
+k_JCZ38              6.265e-02    NA    NA
+k_J9Z38              6.495e-03    NA    NA
+k_JSE76              2.724e-02    NA    NA
+f_cyan_free_to_JCZ38 6.844e-01    NA    NA
+f_cyan_free_to_J9Z38 2.463e-01    NA    NA
+f_JCZ38_to_JSE76     8.816e-01    NA    NA
+f_JSE76_to_JCZ38     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08751 0.01101 0.39586 
+
+Resulting formation fractions:
+                     ff
+cyan_free_JCZ38 0.68444
+cyan_free_J9Z38 0.24633
+cyan_free_sink  0.06923
+cyan_free       1.00000
+JCZ38_JSE76     0.88161
+JCZ38_sink      0.11839
+JSE76_JCZ38     1.00000
+JSE76_sink      0.00000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.36 163.36    49.18        7.921        62.95
+JCZ38  11.06  36.75       NA           NA           NA
+J9Z38 106.71 354.49       NA           NA           NA
+JSE76  25.44  84.51       NA           NA           NA
+
+

Session info +

R version 4.4.2 (2024-10-31)
+Platform: x86_64-pc-linux-gnu
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+
+locale:
+ [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
+ [3] LC_TIME=de_DE.UTF-8        LC_COLLATE=de_DE.UTF-8    
+ [5] LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=de_DE.UTF-8   
+ [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                 
+ [9] LC_ADDRESS=C               LC_TELEPHONE=C            
+[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       
+
+time zone: Europe/Berlin
+tzcode source: system (glibc)
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
+
+loaded via a namespace (and not attached):
+ [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
+ [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
+ [9] fastmap_1.2.0     cellranger_1.1.0  jsonlite_1.8.9    processx_3.8.4   
+[13] pkgbuild_1.4.5    deSolve_1.40      mclust_6.1.1      ps_1.8.1         
+[17] gridExtra_2.3     fansi_1.0.6       scales_1.3.0      codetools_0.2-20 
+[21] textshaping_0.4.1 jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4      
+[25] munsell_0.5.1     cachem_1.1.0      yaml_2.3.10       inline_0.3.20    
+[29] tools_4.4.2       dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1    
+[33] vctrs_0.6.5       R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4  
+[37] fs_1.6.5          htmlwidgets_1.6.4 MASS_7.3-61       ragg_1.3.3       
+[41] callr_3.7.6       pkgconfig_2.0.3   desc_1.4.3        pkgdown_2.1.1    
+[45] pillar_1.9.0      bslib_0.8.0       gtable_0.3.6      glue_1.8.0       
+[49] systemfonts_1.1.0 xfun_0.49         tibble_3.2.1      lmtest_0.9-40    
+[53] tidyselect_1.2.1  htmltools_0.5.8.1 nlme_3.1-166      compiler_4.4.2   
+[57] readxl_1.4.3

Hardware info +

CPU model: AMD Ryzen 9 7950X 16-Core Processor

MemTotal:       64927788 kB

Johannes +Ranke

Last change on 13 February +2023, last compiled on 14 Februar 2025

Introduction +

Test data +

Parent only evaluations +

Pathway fits +

Evaluations with pathway established previously +

Alternative pathway fits +

Refinement of alternative pathway fits +

Conclusion +

Acknowledgements +

Appendix +

Plots of fits that were not refined further +

Hierarchical fit listings +

Pathway 1 +

Pathway 2 +

Pathway 2, refined fits +

Session info +

Hardware info +