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<h1>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
<h4 class="author">Johannes Ranke</h4>
<h4 class="date">2019-07-05</h4>
<div class="hidden name"><code>NAFTA_examples.Rmd</code></div>
</div>
<div id="introduction" class="section level1">
<h1 class="hasAnchor">
<a href="#introduction" class="anchor"></a>Introduction</h1>
<p>In this document, the example evaluations provided in Attachment 1 to the SOP of US EPA for using the NAFTA guidance <span class="citation">(US EPA 2015)</span> 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).</p>
<p>The datasets are now distributed with the mkin package.</p>
</div>
<div id="examples-where-dfop-did-not-converge-with-pestdf-0-8-4" class="section level1">
<h1 class="hasAnchor">
<a href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4" class="anchor"></a>Examples where DFOP did not converge with PestDF 0.8.4</h1>
<p>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.</p>
<div id="example-on-page-5-upper-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-5-upper-panel" class="anchor"></a>Example on page 5, upper panel</h2>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" title="1">p5a <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p5a"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5a)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5a)</a></code></pre></div>
<pre><code>## 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 95.8401 1.10e-21 92.121 99.5597
## k_parent_sink 0.0102 1.71e-12 0.009 0.0117
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 1.01e+02 2.37e-26 9.89e+01 1.03e+02
## k__iore_parent_sink 1.54e-05 8.73e-02 3.48e-06 6.85e-05
## N_parent 2.57e+00 1.14e-11 2.22e+00 2.92e+00
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.99e+01 4.33e-27 NA NA
## k1 2.67e-02 3.17e-05 NA NA
## k2 2.86e-12 5.00e-01 NA NA
## g 6.47e-01 2.13e-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 4.42e+11 2.42e+11
##
## Representative half-life:
## [1] 321.5119</code></pre>
</div>
<div id="example-on-page-5-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-5-lower-panel" class="anchor"></a>Example on page 5, lower panel</h2>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" title="1">p5b <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p5b"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p5b)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p5b)</a></code></pre></div>
<pre><code>## 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 96.497 2.62e-25 94.77653 98.21774
## k_parent_sink 0.008 1.35e-14 0.00736 0.00871
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 9.85e+01 1.02e-29 9.78e+01 9.93e+01
## k__iore_parent_sink 1.53e-04 1.15e-02 6.60e-05 3.56e-04
## N_parent 1.94e+00 8.18e-13 1.74e+00 2.14e+00
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.84e+01 1.90e-28 NA NA
## k1 1.55e-02 2.83e-03 NA NA
## k2 1.16e-11 5.00e-01 NA NA
## g 6.89e-01 1.31e-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 9.80e+10 5.98e+10
##
## Representative half-life:
## [1] 215.8655</code></pre>
</div>
<div id="example-on-page-6" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-6" class="anchor"></a>Example on page 6</h2>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" title="1">p6 <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p6"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb19-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p6)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p6)</a></code></pre></div>
<pre><code>## 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 94.7759 1.25e-24 92.2558 97.2960
## k_parent_sink 0.0179 2.35e-16 0.0166 0.0194
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 97.12446 5.62e-27 95.49343 98.75549
## k__iore_parent_sink 0.00252 3.54e-03 0.00126 0.00502
## N_parent 1.49587 6.13e-13 1.32380 1.66794
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.66e+01 4.17e-26 NA NA
## k1 2.55e-02 2.12e-05 NA NA
## k2 4.90e-11 5.00e-01 NA NA
## g 8.61e-01 2.10e-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 6.66e+09 1.41e+10
##
## Representative half-life:
## [1] 53.16582</code></pre>
</div>
<div id="example-on-page-7" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-7" class="anchor"></a>Example on page 7</h2>
<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1">p7 <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p7"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p7)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p7)</a></code></pre></div>
<pre><code>## 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 96.41796 1.52e-53 93.29554 99.54038
## k_parent_sink 0.00735 3.59e-21 0.00641 0.00842
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 9.92e+01 7.33e-49 9.53e+01 1.03e+02
## k__iore_parent_sink 1.60e-05 3.47e-01 9.98e-08 2.57e-03
## N_parent 2.45e+00 6.14e-05 1.26e+00 3.63e+00
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.89e+01 8.13e-48 NA NA
## k1 1.81e-02 2.20e-01 NA NA
## k2 1.97e-10 5.00e-01 NA NA
## g 6.06e-01 2.60e-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 6.97e+09 3.52e+09
##
## Representative half-life:
## [1] 454.5528</code></pre>
</div>
</div>
<div id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50" class="section level1">
<h1 class="hasAnchor">
<a href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50" class="anchor"></a>Examples where the representative half-life deviates from the observed DT50</h1>
<div id="example-on-page-8" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-8" class="anchor"></a>Example on page 8</h2>
<p>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.</p>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1">p8 <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p8"</span>]], <span class="dt">parms.ini =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dt">k__iore_parent_sink =</span> <span class="fl">1e-3</span>))</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb33-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p8)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p>
<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb34-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p8)</a></code></pre></div>
<pre><code>## 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 88.16549 NA NA NA
## k__iore_parent_sink 0.00100 NA NA NA
## k_parent_sink 0.00803 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 9.77e+01 1.05e-35 9.44e+01 1.01e+02
## k__iore_parent_sink 6.14e-05 2.76e-02 2.21e-05 1.71e-04
## N_parent 2.27e+00 6.00e-19 2.02e+00 2.53e+00
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 95.70619 NA NA NA
## k__iore_parent_sink 0.00100 NA NA NA
## k1 0.02500 NA NA NA
## k2 0.00273 NA NA NA
## g 0.58835 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</code></pre>
</div>
</div>
<div id="examples-where-sfo-was-not-selected-for-an-abiotic-study" class="section level1">
<h1 class="hasAnchor">
<a href="#examples-where-sfo-was-not-selected-for-an-abiotic-study" class="anchor"></a>Examples where SFO was not selected for an abiotic study</h1>
<div id="example-on-page-9-upper-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-9-upper-panel" class="anchor"></a>Example on page 9, upper panel</h2>
<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb36-1" title="1">p9a <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9a"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb40"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb40-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9a)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p>
<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb41-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9a)</a></code></pre></div>
<pre><code>## 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 88.1933 1.12e-12 79.7671 96.6195
## k_parent_sink 0.0409 9.50e-08 0.0326 0.0513
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 9.89e+01 5.16e-17 9.50e+01 1.03e+02
## k__iore_parent_sink 1.93e-05 1.48e-01 2.65e-06 1.40e-04
## N_parent 2.91e+00 3.74e-09 2.43e+00 3.39e+00
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.85e+01 1.31e-21 NA NA
## k1 1.38e-01 3.63e-09 NA NA
## k2 6.02e-13 5.00e-01 NA NA
## g 6.52e-01 1.50e-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</code></pre>
<p>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.</p>
</div>
<div id="example-on-page-9-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-9-lower-panel" class="anchor"></a>Example on page 9, lower panel</h2>
<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb43-1" title="1">p9b <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p9b"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb47-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p9b)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
<div class="sourceCode" id="cb48"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb48-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p9b)</a></code></pre></div>
<pre><code>## 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 94.7123 2.21e-20 93.0673 96.357
## k_parent_sink 0.0389 1.48e-14 0.0369 0.041
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 93.863 2.91e-19 92.2996 95.426
## k__iore_parent_sink 0.127 2.73e-02 0.0457 0.354
## N_parent 0.711 3.13e-05 0.4605 0.961
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 94.7123 NA NA NA
## k1 0.0389 NA NA NA
## k2 0.0389 NA NA NA
## g 0.7742 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] 14.80012</code></pre>
<p>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.</p>
</div>
<div id="example-on-page-10" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-10" class="anchor"></a>Example on page 10</h2>
<div class="sourceCode" id="cb50"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb50-1" title="1">p10 <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p10"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb54"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb54-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p10)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
<div class="sourceCode" id="cb55"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb55-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p10)</a></code></pre></div>
<pre><code>## 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_0 101.7315 4.95e-11 90.9683 112.4947
## k_parent_sink 0.0495 3.40e-07 0.0393 0.0624
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 96.86 2.71e-12 89.884 103.826
## k__iore_parent_sink 2.96 1.31e-01 0.461 19.020
## N_parent 0.00 5.00e-01 -0.473 0.473
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 101.7315 NA NA NA
## k1 0.0495 NA NA NA
## k2 0.0495 NA NA NA
## g 0.6634 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</code></pre>
<p>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.</p>
</div>
</div>
<div id="the-dt50-was-not-observed-during-the-study" class="section level1">
<h1 class="hasAnchor">
<a href="#the-dt50-was-not-observed-during-the-study" class="anchor"></a>The DT50 was not observed during the study</h1>
<div id="example-on-page-11" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-11" class="anchor"></a>Example on page 11</h2>
<div class="sourceCode" id="cb57"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb57-1" title="1">p11 <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p11"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb61"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb61-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p11)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
<div class="sourceCode" id="cb62"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb62-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p11)</a></code></pre></div>
<pre><code>## 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 96.15820 1.56e-13 89.91373 1.02e+02
## k_parent_sink 0.00321 5.27e-05 0.00218 4.71e-03
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 1.05e+02 NA 9.80e+01 1.11e+02
## k__iore_parent_sink 3.11e-17 NA 6.88e-25 1.41e-09
## N_parent 8.36e+00 NA 4.40e+00 1.23e+01
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 1.05e+02 7.50e-13 NA NA
## k1 4.41e-02 3.34e-02 NA NA
## k2 7.25e-13 5.00e-01 NA NA
## g 3.22e-01 7.87e-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</code></pre>
<p>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.</p>
</div>
</div>
<div id="n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant" class="section level1">
<h1 class="hasAnchor">
<a href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant" class="anchor"></a>N is less than 1 and the DFOP rate constants are like the SFO rate constant</h1>
<p>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.</p>
<div id="example-on-page-12-upper-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-12-upper-panel" class="anchor"></a>Example on page 12, upper panel</h2>
<div class="sourceCode" id="cb64"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb64-1" title="1">p12a <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12a"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb68"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb68-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12a)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
<div class="sourceCode" id="cb69"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb69-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12a)</a></code></pre></div>
<pre><code>## 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_0 100.521 5.61e-12 91.687 109.355
## k_parent_sink 0.124 7.24e-08 0.102 0.152
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 96.823 1.24e-13 91.5691 102.078
## k__iore_parent_sink 2.436 3.89e-02 0.7854 7.556
## N_parent 0.263 3.64e-02 -0.0288 0.554
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 100.521 NA NA NA
## k1 0.124 NA NA NA
## k2 0.124 NA NA NA
## g 0.877 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</code></pre>
</div>
<div id="example-on-page-12-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
<div class="sourceCode" id="cb71"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb71-1" title="1">p12b <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p12b"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb75"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb75-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p12b)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
<div class="sourceCode" id="cb76"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb76-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p12b)</a></code></pre></div>
<pre><code>## 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 97.6840 5.36e-05 86.3205 109.0475
## k_parent_sink 0.0589 9.87e-04 0.0432 0.0803
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 95.523 0.000386 84.0963 106.95
## k__iore_parent_sink 0.333 0.170886 0.0103 10.80
## N_parent 0.568 0.054881 -0.3161 1.45
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 97.6840 NA NA NA
## k1 0.0589 NA NA NA
## k2 0.0589 NA NA NA
## g 0.6902 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</code></pre>
</div>
<div id="example-on-page-13" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-13" class="anchor"></a>Example on page 13</h2>
<div class="sourceCode" id="cb78"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb78-1" title="1">p13 <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p13"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb82"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb82-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p13)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
<div class="sourceCode" id="cb83"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb83-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p13)</a></code></pre></div>
<pre><code>## 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 92.73500 1.45e-17 89.3891 96.08094
## k_parent_sink 0.00258 2.63e-09 0.0022 0.00303
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 91.6016 2.93e-16 88.08711 95.12
## k__iore_parent_sink 0.0396 2.81e-01 0.00102 1.53
## N_parent 0.3541 1.97e-01 -0.51943 1.23
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 92.73500 NA NA NA
## k1 0.00258 NA NA NA
## k2 0.00258 NA NA NA
## g 0.00442 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</code></pre>
</div>
</div>
<div id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="section level1">
<h1 class="hasAnchor">
<a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="anchor"></a>DT50 not observed in the study and DFOP problems in PestDF</h1>
<div class="sourceCode" id="cb85"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb85-1" title="1">p14 <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p14"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb89"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb89-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p14)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
<div class="sourceCode" id="cb90"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb90-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p14)</a></code></pre></div>
<pre><code>## 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 99.47124 1.71e-31 98.37313 1.01e+02
## k_parent_sink 0.00279 2.22e-15 0.00255 3.05e-03
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 1.00e+02 NA 9.93e+01 1.01e+02
## k__iore_parent_sink 9.44e-08 NA 6.81e-11 1.31e-04
## N_parent 3.31e+00 NA 1.69e+00 4.93e+00
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 1.00e+02 2.70e-28 NA NA
## k1 9.53e-03 3.39e-01 NA NA
## k2 7.29e-12 5.00e-01 NA NA
## g 3.98e-01 3.92e-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 2.54e+10 2.46e+11 9.51e+10
##
## Representative half-life:
## [1] 6697.437</code></pre>
<p>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.</p>
</div>
<div id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="section level1">
<h1 class="hasAnchor">
<a href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="anchor"></a>N is less than 1 and DFOP fraction parameter is below zero</h1>
<div class="sourceCode" id="cb92"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb92-1" title="1">p15a <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15a"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb96"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb96-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15a)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
<div class="sourceCode" id="cb97"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb97-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15a)</a></code></pre></div>
<pre><code>## 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 97.96751 4.98e-16 94.03829 101.8967
## k_parent_sink 0.00952 5.24e-09 0.00813 0.0112
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 95.874 8.30e-16 92.5802 99.167
## k__iore_parent_sink 0.629 2.39e-01 0.0316 12.519
## N_parent 0.000 5.00e-01 -0.7219 0.722
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 97.96752 NA NA NA
## k1 0.00952 NA NA NA
## k2 0.00952 NA NA NA
## g 0.17247 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</code></pre>
<div class="sourceCode" id="cb99"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb99-1" title="1">p15b <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p15b"</span>]])</a></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
## singular system.</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb103"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb103-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p15b)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
<div class="sourceCode" id="cb104"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb104-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p15b)</a></code></pre></div>
<pre><code>## 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 1.01e+02 4.99e-18 98.12761 1.04e+02
## k_parent_sink 4.86e-03 1.76e-10 0.00432 5.46e-03
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 99.83 4.49e-17 97.19753 102.5
## k__iore_parent_sink 0.38 3.41e-01 0.00206 70.0
## N_parent 0.00 5.00e-01 -1.20105 1.2
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 1.01e+02 NA NA NA
## k1 4.86e-03 NA NA NA
## k2 4.86e-03 NA NA NA
## g 1.50e-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</code></pre>
<p>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.</p>
</div>
<div id="the-dfop-fraction-parameter-is-greater-than-1" class="section level1">
<h1 class="hasAnchor">
<a href="#the-dfop-fraction-parameter-is-greater-than-1" class="anchor"></a>The DFOP fraction parameter is greater than 1</h1>
<div class="sourceCode" id="cb106"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb106-1" title="1">p16 <-<span class="st"> </span><span class="kw"><a href="../../reference/nafta.html">nafta</a></span>(NAFTA_SOP_Attachment[[<span class="st">"p16"</span>]])</a></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The representative half-life of the IORE model is longer than the one corresponding</code></pre>
<pre><code>## to the terminal degradation rate found with the DFOP model.</code></pre>
<pre><code>## The representative half-life obtained from the DFOP model may be used</code></pre>
<div class="sourceCode" id="cb111"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb111-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(p16)</a></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
<div class="sourceCode" id="cb112"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb112-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/print">print</a></span>(p16)</a></code></pre></div>
<pre><code>## 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 71.953 3.92e-14 61.087 82.819
## k_parent_sink 0.159 2.27e-06 0.111 0.229
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 8.74e+01 1.74e-16 7.71e+01 97.70701
## k__iore_parent_sink 4.55e-04 2.28e-01 3.01e-05 0.00688
## N_parent 2.70e+00 1.87e-08 1.97e+00 3.42611
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 88.5333 NA 79.3673 97.699
## k1 18.5561 NA 0.0000 Inf
## k2 0.0776 NA 0.0471 0.128
## g 0.4733 NA 0.3138 0.639
##
##
## 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</code></pre>
<p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower <span class="math inline">\(\chi^2\)</span> 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.</p>
</div>
<div id="conclusions" class="section level1">
<h1 class="hasAnchor">
<a href="#conclusions" class="anchor"></a>Conclusions</h1>
<p>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.</p>
<p>Therefore, mkin appears to suitable for kinetic evaluations according to the NAFTA guidance.</p>
</div>
<div id="references" class="section level1 unnumbered">
<h1 class="hasAnchor">
<a href="#references" class="anchor"></a>References</h1>
<div id="refs" class="references">
<div id="ref-usepa2015">
<p>US EPA. 2015. “Standard Operating Procedure for Using the NAFTA Guidance to Calculate Representative Half-Life Values and Characterizing Pesticide Degradation.”</p>
</div>
</div>
</div>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
<div id="tocnav">
<h2 class="hasAnchor">
<a href="#tocnav" class="anchor"></a>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#introduction">Introduction</a></li>
<li>
<a href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4">Examples where DFOP did not converge with PestDF 0.8.4</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-5-upper-panel">Example on page 5, upper panel</a></li>
<li><a href="#example-on-page-5-lower-panel">Example on page 5, lower panel</a></li>
<li><a href="#example-on-page-6">Example on page 6</a></li>
<li><a href="#example-on-page-7">Example on page 7</a></li>
</ul>
</li>
<li>
<a href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50">Examples where the representative half-life deviates from the observed DT50</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-8">Example on page 8</a></li>
</ul>
</li>
<li>
<a href="#examples-where-sfo-was-not-selected-for-an-abiotic-study">Examples where SFO was not selected for an abiotic study</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-9-upper-panel">Example on page 9, upper panel</a></li>
<li><a href="#example-on-page-9-lower-panel">Example on page 9, lower panel</a></li>
<li><a href="#example-on-page-10">Example on page 10</a></li>
</ul>
</li>
<li>
<a href="#the-dt50-was-not-observed-during-the-study">The DT50 was not observed during the study</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-11">Example on page 11</a></li>
</ul>
</li>
<li>
<a href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant">N is less than 1 and the DFOP rate constants are like the SFO rate constant</a><ul class="nav nav-pills nav-stacked">
<li><a href="#example-on-page-12-upper-panel">Example on page 12, upper panel</a></li>
<li><a href="#example-on-page-12-lower-panel">Example on page 12, lower panel</a></li>
<li><a href="#example-on-page-13">Example on page 13</a></li>
</ul>
</li>
<li><a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf">DT50 not observed in the study and DFOP problems in PestDF</a></li>
<li><a href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero">N is less than 1 and DFOP fraction parameter is below zero</a></li>
<li><a href="#the-dfop-fraction-parameter-is-greater-than-1">The DFOP fraction parameter is greater than 1</a></li>
<li><a href="#conclusions">Conclusions</a></li>
<li><a href="#references">References</a></li>
</ul>
</div>
</div>
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