Logistic kinetics

+ +

Function describing exponential decline from a defined starting value, with +an increasing rate constant, supposedly caused by microbial growth

+ +

Usage

logistic.solution(t, parent_0, kmax, k0, r)

+ +

Arguments

+ + +

t: Time.
parent_0: Starting value for the response variable at time zero.
kmax: Maximum rate constant.
k0: Minimum rate constant effective at time zero.
r: Growth rate of the increase in the rate constant.

Value

The value of the response variable at time t.

Note

The solution of the logistic model reduces to the +SFO.solution if k0 is equal to kmax.

References

FOCUS (2006) “Guidance Document on Estimating Persistence +and Degradation Kinetics from Environmental Fate Studies on Pesticides in +EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, +EC Document Reference Sanco/10058/2005 version 2.0, 434 pp, +http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics +FOCUS (2014) “Generic guidance for Estimating Persistence +and Degradation Kinetics from Environmental Fate Studies on Pesticides in +EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, +Version 1.1, 18 December 2014 +http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics

Examples


+  # Reproduce the plot on page 57 of FOCUS (2014)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.2),
+       from = 0, to = 100, ylim = c(0, 100),
+       xlab = "Time", ylab = "Residue")
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.4),
+       from = 0, to = 100, add = TRUE, lty = 2, col = 2)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.8),
+       from = 0, to = 100, add = TRUE, lty = 3, col = 3)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.001, 0.2),
+       from = 0, to = 100, add = TRUE, lty = 4, col = 4)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.08, 0.2),
+       from = 0, to = 100, add = TRUE, lty = 5, col = 5)
+  legend("topright", inset = 0.05,
+         legend = paste0("k0 = ", c(0.0001, 0.0001, 0.0001, 0.001, 0.08),
+                         ", r = ", c(0.2, 0.4, 0.8, 0.2, 0.2)),
+         lty = 1:5, col = 1:5)
+
+
+  # Fit with synthetic data
+  logistic <- mkinmod(parent = mkinsub("logistic"))
+
+  sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+  parms_logistic <- c(kmax = 0.08, k0 = 0.0001, r = 0.2)
+  d_logistic <- mkinpredict(logistic,
+    parms_logistic, c(parent = 100),
+    sampling_times)
+  d_2_1 <- add_err(d_logistic,
+    sdfunc = function(x) sigma_twocomp(x, 0.5, 0.07),
+    n = 1, reps = 2, digits = 5, LOD = 0.1, seed = 123456)[[1]]
+
+  m <- mkinfit("logistic", d_2_1, quiet = TRUE)
+  plot_sep(m)
+
+  summary(m)$bpar
+#>              Estimate   se_notrans   t value       Pr(>t)        Lower
+#> parent_0 1.057896e+02 1.9023449604 55.610120 3.768360e-16 1.016451e+02
+#> kmax     6.398190e-02 0.0143201030  4.467978 3.841828e-04 3.929235e-02
+#> k0       1.612775e-04 0.0005866813  0.274898 3.940351e-01 5.846688e-08
+#> r        2.263946e-01 0.1718110664  1.317695 1.061043e-01 4.335843e-02
+#> sigma    5.332935e+00 0.9145907310  5.830952 4.036926e-05 3.340213e+00
+#>                Upper
+#> parent_0 109.9341588
+#> kmax       0.1041853
+#> k0         0.4448749
+#> r          1.1821120
+#> sigma      7.3256566
+  endpoints(m)$distimes
+#>            DT50     DT90  DT50_k0 DT50_kmax
+#> parent 36.86533 62.41511 4297.853  10.83349
+
+