Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance

Johannes Ranke

2019-02-26

Introduction

In this document, the example evaluations provided in Attachment 1 to the SOP of US EPA for using the NAFTA guidance (US EPA 2015) are repeated using mkin. The original evaluations reported in the attachment were performed using PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version distributed at the US EPA website today (2019-02-26).

The datasets are now distributed with the mkin package.

Examples where DFOP did not converge with PestDF 0.8.4

In attachment 1, it is reported that the DFOP model does not converge for these datasets when PestDF 0.8.4 was used. For all four datasets, the DFOP model can be fitted with mkin (see below). The negative half-life given by PestDF 0.8.4 for these fits appears to be the result of a bug. The results for the other two models (SFO and IORE) are the same.

Example on page 5, upper panel

p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p5a)

print(p5a)

## Sums of squares:
##       SFO      IORE      DFOP 
## 465.21753  56.27506  32.06401 
## 
## Critical sum of squares for checking the SFO model:
## [1] 64.4304
## 
## Parameters:
## $SFO
##                  Estimate       Pr(>t)        Lower       Upper
## parent_0      95.84012168 1.095639e-21 92.120517864 99.55972549
## k_parent_sink  0.01024015 1.710227e-12  0.008996874  0.01165524
## 
## $IORE
##                         Estimate       Pr(>t)        Lower        Upper
## parent_0            1.007532e+02 2.365797e-26 9.891170e+01 1.025947e+02
## k__iore_parent_sink 1.544192e-05 8.733384e-02 3.482391e-06 6.847393e-05
## N_parent            2.569877e+00 1.140446e-11 2.215298e+00 2.924456e+00
## 
## $DFOP
##              Estimate       Pr(>t) Lower Upper
## parent_0 9.994630e+01 4.330861e-27    NA    NA
## k1       2.674255e-02 3.171390e-05    NA    NA
## k2       2.161318e-12 5.000000e-01    NA    NA
## g        6.465276e-01 2.129114e-05    NA    NA
## 
## 
## DTx values:
##      DT50     DT90 DT50_rep
## SFO  67.7 2.25e+02 6.77e+01
## IORE 58.2 1.07e+03 3.22e+02
## DFOP 55.5 5.84e+11 3.21e+11
## 
## Representative half-life:
## [1] 321.5119

Example on page 5, lower panel

p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p5b)

print(p5b)

## Sums of squares:
##      SFO     IORE     DFOP 
## 94.81123 10.10936  7.55871 
## 
## Critical sum of squares for checking the SFO model:
## [1] 11.77879
## 
## Parameters:
## $SFO
##                   Estimate       Pr(>t)        Lower        Upper
## parent_0      96.497133849 2.623748e-25 94.776528606 98.217739092
## k_parent_sink  0.008002704 1.352275e-14  0.007356108  0.008706135
## 
## $IORE
##                         Estimate       Pr(>t)        Lower        Upper
## parent_0            9.854518e+01 1.019174e-29 9.780760e+01 9.928276e+01
## k__iore_parent_sink 1.532766e-04 1.152046e-02 6.603390e-05 3.557826e-04
## N_parent            1.939125e+00 8.177751e-13 1.741616e+00 2.136633e+00
## 
## $DFOP
##              Estimate       Pr(>t) Lower Upper
## parent_0 9.836323e+01 1.896304e-28    NA    NA
## k1       1.546859e-02 2.833415e-03    NA    NA
## k2       8.172408e-12 5.000000e-01    NA    NA
## g        6.889941e-01 1.306276e-02    NA    NA
## 
## 
## DTx values:
##      DT50     DT90 DT50_rep
## SFO  86.6 2.88e+02 8.66e+01
## IORE 85.5 7.17e+02 2.16e+02
## DFOP 83.6 1.39e+11 8.48e+10
## 
## Representative half-life:
## [1] 215.8655

Example on page 6

p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p6)

print(p6)

## Sums of squares:
##       SFO      IORE      DFOP 
## 188.45361  51.00699  42.46931 
## 
## Critical sum of squares for checking the SFO model:
## [1] 58.39888
## 
## Parameters:
## $SFO
##                  Estimate       Pr(>t)       Lower       Upper
## parent_0      94.77587412 1.246335e-24 92.25575879 97.29598945
## k_parent_sink  0.01794259 2.347664e-16  0.01660595  0.01938682
## 
## $IORE
##                         Estimate       Pr(>t)        Lower        Upper
## parent_0            97.124460863 5.616271e-27 95.493434421 98.755487305
## k__iore_parent_sink  0.002517728 3.535472e-03  0.001263771  0.005015906
## N_parent             1.495871465 6.129227e-13  1.323799338  1.667943591
## 
## $DFOP
##              Estimate       Pr(>t) Lower Upper
## parent_0 9.662275e+01 4.174516e-26    NA    NA
## k1       2.547327e-02 2.115246e-05    NA    NA
## k2       3.087623e-11 5.000000e-01    NA    NA
## g        8.613785e-01 2.097173e-05    NA    NA
## 
## 
## DTx values:
##      DT50     DT90 DT50_rep
## SFO  38.6 1.28e+02 3.86e+01
## IORE 34.0 1.77e+02 5.32e+01
## DFOP 34.1 1.06e+10 2.24e+10
## 
## Representative half-life:
## [1] 53.16582

Example on page 7

p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p7)

print(p7)

## Sums of squares:
##      SFO     IORE     DFOP 
## 3661.661 3195.030 3174.145 
## 
## Critical sum of squares for checking the SFO model:
## [1] 3334.194
## 
## Parameters:
## $SFO
##                   Estimate       Pr(>t)        Lower        Upper
## parent_0      96.417960406 1.520951e-53 93.295541980 99.540378832
## k_parent_sink  0.007350054 3.592731e-21  0.006413446  0.008423441
## 
## $IORE
##                         Estimate       Pr(>t)        Lower        Upper
## parent_0            9.915322e+01 7.332574e-49 9.534934e+01 1.029571e+02
## k__iore_parent_sink 1.600884e-05 3.472978e-01 9.982484e-08 2.567328e-03
## N_parent            2.446000e+00 6.141482e-05 1.260173e+00 3.631827e+00
## 
## $DFOP
##              Estimate       Pr(>t) Lower Upper
## parent_0 9.886065e+01 8.134302e-48    NA    NA
## k1       1.805928e-02 2.198367e-01    NA    NA
## k2       3.279731e-10 5.000000e-01    NA    NA
## g        6.063177e-01 2.601365e-01    NA    NA
## 
## 
## DTx values:
##      DT50     DT90 DT50_rep
## SFO  94.3 3.13e+02 9.43e+01
## IORE 96.7 1.51e+03 4.55e+02
## DFOP 96.4 4.18e+09 2.11e+09
## 
## Representative half-life:
## [1] 454.5528

Examples where the representative half-life deviates from the observed DT50

Example on page 8

For this dataset, the IORE fit does not converge when the default starting values used by mkin for the IORE model are used. Therefore, a lower value for the rate constant is used here.

p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent_sink = 1e-3))

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p8)

print(p8)

## Sums of squares:
##       SFO      IORE      DFOP 
## 1996.9408  444.9237  547.5616 
## 
## Critical sum of squares for checking the SFO model:
## [1] 477.4924
## 
## Parameters:
## $SFO
##                         Estimate Pr(>t) Lower Upper
## parent_0            88.165489334     NA    NA    NA
## k__iore_parent_sink  0.001000000     NA    NA    NA
## k_parent_sink        0.008032303     NA    NA    NA
## 
## $IORE
##                         Estimate       Pr(>t)        Lower        Upper
## parent_0            9.771060e+01 1.048016e-35 9.442778e+01 1.009934e+02
## k__iore_parent_sink 6.141041e-05 2.763666e-02 2.205805e-05 1.709688e-04
## N_parent            2.271648e+00 5.996684e-19 2.015215e+00 2.528080e+00
## 
## $DFOP
##                         Estimate Pr(>t) Lower Upper
## parent_0            95.706193520     NA    NA    NA
## k__iore_parent_sink  0.001000000     NA    NA    NA
## k1                   0.024995243     NA    NA    NA
## k2                   0.002734623     NA    NA    NA
## g                    0.588349874     NA    NA    NA
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO  86.3  287     86.3
## IORE 53.4  668    201.0
## DFOP 55.6  517    253.0
## 
## Representative half-life:
## [1] 201.0316

Examples where SFO was not selected for an abiotic study

Example on page 9, upper panel

p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p9a)

print(p9a)

## Sums of squares:
##       SFO      IORE      DFOP 
## 839.35238  88.57064   9.93363 
## 
## Critical sum of squares for checking the SFO model:
## [1] 105.5678
## 
## Parameters:
## $SFO
##                 Estimate       Pr(>t)       Lower       Upper
## parent_0      88.1933161 1.117569e-12 79.76708923 96.61954288
## k_parent_sink  0.0409019 9.501453e-08  0.03258829  0.05133639
## 
## $IORE
##                         Estimate       Pr(>t)        Lower        Upper
## parent_0            9.891481e+01 5.163566e-17 9.497891e+01 1.028507e+02
## k__iore_parent_sink 1.927824e-05 1.480158e-01 2.650455e-06 1.402214e-04
## N_parent            2.910027e+00 3.738041e-09 2.428904e+00 3.391151e+00
## 
## $DFOP
##              Estimate       Pr(>t) Lower Upper
## parent_0 9.853112e+01 1.308505e-21    NA    NA
## k1       1.382145e-01 3.630589e-09    NA    NA
## k2       6.019228e-13 5.000000e-01    NA    NA
## g        6.518659e-01 1.502543e-10    NA    NA
## 
## 
## DTx values:
##      DT50     DT90 DT50_rep
## SFO  16.9 5.63e+01 1.69e+01
## IORE 11.6 3.37e+02 1.01e+02
## DFOP 10.5 2.07e+12 1.15e+12
## 
## Representative half-life:
## [1] 101.4264

In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.

Example on page 9, lower panel

p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p9b)

print(p9b)

## Sums of squares:
##      SFO     IORE     DFOP 
## 35.64867 23.22334 35.64867 
## 
## Critical sum of squares for checking the SFO model:
## [1] 28.54188
## 
## Parameters:
## $SFO
##                  Estimate       Pr(>t)      Lower       Upper
## parent_0      94.71226787 2.207090e-20 93.0673253 96.35721040
## k_parent_sink  0.03887215 1.482921e-14  0.0368549  0.04099981
## 
## $IORE
##                       Estimate       Pr(>t)       Lower      Upper
## parent_0            93.8626223 2.911881e-19 92.29955547 95.4256890
## k__iore_parent_sink  0.1271399 2.725876e-02  0.04570569  0.3536663
## N_parent             0.7108771 3.130915e-05  0.46052920  0.9612249
## 
## $DFOP
##             Estimate Pr(>t) Lower Upper
## parent_0 94.71226786     NA    NA    NA
## k1        0.03887215     NA    NA    NA
## k2        0.03887215     NA    NA    NA
## g         0.77417779     NA    NA    NA
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO  17.8 59.2     17.8
## IORE 18.4 49.2     14.8
## DFOP 17.8 59.2     17.8
## 
## Representative half-life:
## [1] 14.80013

Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) than PestDF (13.5 days). Presumably, this is related to the fact that PestDF gives a negative value for the proportion of the fast degradation which should be between 0 and 1, inclusive. This parameter is called f in PestDF and g in mkin. In mkin, it is restricted to the interval from 0 to 1.

Example on page 10

p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p10)

print(p10)

## Sums of squares:
##      SFO     IORE     DFOP 
## 899.4089 336.4348 899.4089 
## 
## Critical sum of squares for checking the SFO model:
## [1] 413.4841
## 
## Parameters:
## $SFO
##                   Estimate       Pr(>t)       Lower        Upper
## parent_0      101.73153064 4.954950e-11 90.96832870 112.49473259
## k_parent_sink   0.04952864 3.398569e-07  0.03930194   0.06241642
## 
## $IORE
##                      Estimate       Pr(>t)      Lower       Upper
## parent_0            96.855416 2.706118e-12 89.8843855 103.8264461
## k__iore_parent_sink  2.960977 1.308097e-01  0.4609504  19.0202303
## N_parent             0.000000 5.000000e-01 -0.4728922   0.4728922
## 
## $DFOP
##              Estimate Pr(>t) Lower Upper
## parent_0 101.73153022     NA    NA    NA
## k1         0.04952864     NA    NA    NA
## k2         0.04952864     NA    NA    NA
## g          0.66344649     NA    NA    NA
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO  14.0 46.5    14.00
## IORE 16.4 29.4     8.86
## DFOP 14.0 46.5    14.00
## 
## Representative half-life:
## [1] 8.862193

Here, a value below N is given for the IORE model, because the data suggests a faster decline towards the end of the experiment, which appears physically rather unlikely in the case of a photolysis study. It seems PestDF does not constrain N to values above zero, thus the slight difference in IORE model parameters between PestDF and mkin.

The DT50 was not observed during the study

Example on page 11

p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p11)

print(p11)

## Sums of squares:
##      SFO     IORE     DFOP 
## 579.6805 204.7932 144.7783 
## 
## Critical sum of squares for checking the SFO model:
## [1] 251.6944
## 
## Parameters:
## $SFO
##                   Estimate       Pr(>t)        Lower        Upper
## parent_0      96.158200840 1.560217e-13 89.913728706 1.024027e+02
## k_parent_sink  0.003208498 5.266271e-05  0.002183575 4.714497e-03
## 
## $IORE
##                         Estimate Pr(>t)        Lower        Upper
## parent_0            1.045981e+02     NA 9.798102e+01 1.112151e+02
## k__iore_parent_sink 3.110367e-17     NA 6.875825e-25 1.407014e-09
## N_parent            8.360812e+00     NA 4.397006e+00 1.232462e+01
## 
## $DFOP
##              Estimate       Pr(>t) Lower Upper
## parent_0 1.045607e+02 7.502642e-13    NA    NA
## k1       4.414526e-02 3.343950e-02    NA    NA
## k2       7.246905e-13 5.000000e-01    NA    NA
## g        3.217737e-01 7.868540e-03    NA    NA
## 
## 
## DTx values:
##          DT50     DT90 DT50_rep
## SFO  2.16e+02 7.18e+02 2.16e+02
## IORE 9.73e+02 1.37e+08 4.11e+07
## DFOP 4.21e+11 2.64e+12 9.56e+11
## 
## Representative half-life:
## [1] 41148169

In this case, the DFOP fit reported for PestDF resulted in a negative value for the slower rate constant, which is not possible in mkin. The other results are in agreement.

N is less than 1 and the DFOP rate constants are like the SFO rate constant

In the following three examples, the same results are obtained with mkin as reported for PestDF. As in the case on page 10, the N values below 1 are deemed unrealistic and appear to be the result of an overparameterisation.

Example on page 12, upper panel

p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p12a)

print(p12a)

## Sums of squares:
##      SFO     IORE     DFOP 
## 695.4440 220.0685 695.4440 
## 
## Critical sum of squares for checking the SFO model:
## [1] 270.4679
## 
## Parameters:
## $SFO
##                  Estimate       Pr(>t)      Lower       Upper
## parent_0      100.5206988 5.606929e-12 91.6867692 109.3546284
## k_parent_sink   0.1243142 7.235485e-08  0.1017305   0.1519113
## 
## $IORE
##                       Estimate       Pr(>t)       Lower       Upper
## parent_0            96.8234045 1.242894e-13 91.56908085 102.0777281
## k__iore_parent_sink  2.4360714 3.893118e-02  0.78536982   7.5562415
## N_parent             0.2627157 3.639503e-02 -0.02875633   0.5541876
## 
## $DFOP
##             Estimate Pr(>t) Lower Upper
## parent_0 100.5206988     NA    NA    NA
## k1         0.1243142     NA    NA    NA
## k2         0.1243142     NA    NA    NA
## g          0.8772377     NA    NA    NA
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO  5.58 18.5     5.58
## IORE 6.49 13.2     3.99
## DFOP 5.58 18.5     5.58
## 
## Representative half-life:
## [1] 3.987308

Example on page 12, lower panel

p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p12b)

print(p12b)

## Sums of squares:
##      SFO     IORE     DFOP 
## 58.90242 19.06353 58.90242 
## 
## Critical sum of squares for checking the SFO model:
## [1] 51.51756
## 
## Parameters:
## $SFO
##                 Estimate       Pr(>t)       Lower        Upper
## parent_0      97.6840211 0.0000535970 86.32050115 109.04754103
## k_parent_sink  0.0589177 0.0009869932  0.04320553   0.08034377
## 
## $IORE
##                       Estimate       Pr(>t)       Lower      Upper
## parent_0            95.5232270 0.0003860431 84.09629121 106.950163
## k__iore_parent_sink  0.3329365 0.1708863327  0.01026046  10.803285
## N_parent             0.5677771 0.0548808046 -0.31606833   1.451622
## 
## $DFOP
##            Estimate Pr(>t) Lower Upper
## parent_0 97.6840212     NA    NA    NA
## k1        0.0589177     NA    NA    NA
## k2        0.0589177     NA    NA    NA
## g         0.6901929     NA    NA    NA
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO  11.8 39.1    11.80
## IORE 12.9 31.4     9.46
## DFOP 11.8 39.1    11.80
## 
## Representative half-life:
## [1] 9.461912

Example on page 13

p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p13)

print(p13)

## Sums of squares:
##      SFO     IORE     DFOP 
## 174.5971 142.3951 174.5971 
## 
## Critical sum of squares for checking the SFO model:
## [1] 172.131
## 
## Parameters:
## $SFO
##                   Estimate       Pr(>t)        Lower        Upper
## parent_0      92.735003006 1.453426e-17 89.389064698 96.080941315
## k_parent_sink  0.002581189 2.630396e-09  0.002198171  0.003030945
## 
## $IORE
##                        Estimate       Pr(>t)       Lower     Upper
## parent_0            91.60158658 2.932498e-16 88.08710837 95.116065
## k__iore_parent_sink  0.03960674 2.810573e-01  0.00102485  1.530656
## N_parent             0.35408757 1.972378e-01 -0.51942545  1.227601
## 
## $DFOP
##              Estimate Pr(>t) Lower Upper
## parent_0 92.735003208     NA    NA    NA
## k1        0.002581186     NA    NA    NA
## k2        0.002581188     NA    NA    NA
## g         0.004422859     NA    NA    NA
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO   269  892      269
## IORE  261  560      169
## DFOP  269  892      269
## 
## Representative half-life:
## [1] 168.5123

DT50 not observed in the study and DFOP problems in PestDF

p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p14)

print(p14)

## Sums of squares:
##      SFO     IORE     DFOP 
## 48.43249 28.67746 27.26248 
## 
## Critical sum of squares for checking the SFO model:
## [1] 32.83337
## 
## Parameters:
## $SFO
##                   Estimate       Pr(>t)        Lower        Upper
## parent_0      99.471243637 1.708290e-31 98.373131052 1.005694e+02
## k_parent_sink  0.002789581 2.222078e-15  0.002554583 3.046197e-03
## 
## $IORE
##                         Estimate Pr(>t)        Lower        Upper
## parent_0            1.003522e+02     NA 9.926773e+01 1.014366e+02
## k__iore_parent_sink 9.443770e-08     NA 6.810412e-11 1.309536e-04
## N_parent            3.308552e+00     NA 1.690051e+00 4.927053e+00
## 
## $DFOP
##              Estimate       Pr(>t) Lower Upper
## parent_0 1.003398e+02 2.698790e-28    NA    NA
## k1       9.532677e-03 3.394353e-01    NA    NA
## k2       9.189935e-12 5.000000e-01    NA    NA
## g        3.982564e-01 3.920847e-01    NA    NA
## 
## 
## DTx values:
##          DT50     DT90 DT50_rep
## SFO  2.48e+02 8.25e+02 2.48e+02
## IORE 4.34e+02 2.22e+04 6.70e+03
## DFOP 2.02e+10 1.95e+11 7.54e+10
## 
## Representative half-life:
## [1] 6697.437

The slower rate constant reported by PestDF is negative, which is not physically realistic, and not possible in mkin. The other fits give the same results in mkin and PestDF.

N is less than 1 and DFOP fraction parameter is below zero

p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p15a)

print(p15a)

## Sums of squares:
##      SFO     IORE     DFOP 
## 245.5248 135.0132 245.5248 
## 
## Critical sum of squares for checking the SFO model:
## [1] 165.9335
## 
## Parameters:
## $SFO
##                   Estimate       Pr(>t)        Lower       Upper
## parent_0      97.967511635 4.984358e-16 94.038286642 101.8967366
## k_parent_sink  0.009522227 5.239115e-09  0.008126698   0.0111574
## 
## $IORE
##                       Estimate       Pr(>t)       Lower      Upper
## parent_0            95.8736780 8.295860e-16 92.58018331 99.1671726
## k__iore_parent_sink  0.6285106 2.386496e-01  0.03155477 12.5187302
## N_parent             0.0000000 5.000000e-01 -0.72189225  0.7218923
## 
## $DFOP
##              Estimate Pr(>t) Lower Upper
## parent_0 97.967516468     NA    NA    NA
## k1        0.009522243     NA    NA    NA
## k2        0.009522223     NA    NA    NA
## g         0.172466840     NA    NA    NA
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO  72.8  242     72.8
## IORE 76.3  137     41.3
## DFOP 72.8  242     72.8
## 
## Representative half-life:
## [1] 41.32749

p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The half-life obtained from the IORE model may be used

plot(p15b)

print(p15b)

## Sums of squares:
##       SFO      IORE      DFOP 
## 106.91629  68.55574 106.91629 
## 
## Critical sum of squares for checking the SFO model:
## [1] 84.25618
## 
## Parameters:
## $SFO
##                   Estimate       Pr(>t)        Lower        Upper
## parent_0      1.008816e+02 4.987925e-18 98.127607367 1.036355e+02
## k_parent_sink 4.856586e-03 1.756208e-10  0.004316334 5.464459e-03
## 
## $IORE
##                       Estimate       Pr(>t)       Lower     Upper
## parent_0            99.8268283 4.490292e-17 97.19753163 102.45613
## k__iore_parent_sink  0.3799625 3.406003e-01  0.00206198  70.01593
## N_parent             0.0000000 5.000000e-01 -1.20105017   1.20105
## 
## $DFOP
##              Estimate Pr(>t) Lower Upper
## parent_0 1.008816e+02     NA    NA    NA
## k1       4.856586e-03     NA    NA    NA
## k2       4.856586e-03     NA    NA    NA
## g        1.496838e-01     NA    NA    NA
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO   143  474    143.0
## IORE  131  236     71.2
## DFOP  143  474    143.0
## 
## Representative half-life:
## [1] 71.18014

In mkin, only the IORE fit is affected (deemed unrealistic), as the fraction parameter of the DFOP model is restricted to the interval between 0 and 1 in mkin. The SFO fits give the same results for both mkin and PestDF.

The DFOP fraction parameter is greater than 1

p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])

## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

## The representative half-life of the IORE model is longer than the one corresponding

## to the terminal degradation rate found with the DFOP model.

## The representative half-life obtained from the DFOP model may be used

plot(p16)

print(p16)

## Sums of squares:
##      SFO     IORE     DFOP 
## 3831.804 2062.008 1550.980 
## 
## Critical sum of squares for checking the SFO model:
## [1] 2247.348
## 
## Parameters:
## $SFO
##                 Estimate       Pr(>t)      Lower      Upper
## parent_0      71.9528227 3.923531e-14 61.0870510 82.8185944
## k_parent_sink  0.1594518 2.271601e-06  0.1110583  0.2289327
## 
## $IORE
##                         Estimate       Pr(>t)        Lower        Upper
## parent_0            8.738846e+01 1.739390e-16 7.706991e+01 97.707005461
## k__iore_parent_sink 4.549683e-04 2.282721e-01 3.008533e-05  0.006880303
## N_parent            2.696278e+00 1.869479e-08 1.966442e+00  3.426114200
## 
## $DFOP
##             Estimate Pr(>t)       Lower      Upper
## parent_0 88.53333334     NA 79.36733990 97.6993268
## k1       18.55624337     NA  0.00000000        Inf
## k2        0.07759679     NA  0.04709945  0.1278414
## g         0.47333008     NA  0.31375096  0.6385506
## 
## 
## DTx values:
##      DT50 DT90 DT50_rep
## SFO  4.35 14.4     4.35
## IORE 1.48 32.1     9.67
## DFOP 0.67 21.4     8.93
## 
## Representative half-life:
## [1] 8.932679

In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower \(\chi^2\) error level. As the half-life from the slower rate constant of the DFOP model is larger than the IORE derived half-life, the NAFTA recommendation obtained with mkin is to use the DFOP representative half-life of 8.9 days.

Conclusions

The results obtained with mkin deviate from the results obtained with PestDF either in cases where one of the interpretive rules would apply, i.e. the IORE parameter N is less than one or the DFOP k values obtained with PestDF are equal to the SFO k values, or in cases where the DFOP model did not converge, which often lead to negative rate constants returned by PestDF.

Therefore, mkin appears to suitable for kinetic evaluations according to the NAFTA guidance.

References

US EPA. 2015. “Standard Operating Procedure for Using the NAFTA Guidance to Calculate Representative Half-Life Values and Characterizing Pesticide Degradation.”