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<li> + <a href="../articles/mkin.html">Introduction to mkin</a> + </li> + <li> + <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> + </li> + <li> + <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> + </li> + <li> + <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> + </li> + <li> + <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> + </li> + <li> + <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> + </li> + </ul> +</li> +<li> + <a href="../news/index.html">News</a> +</li> + </ul> + + <ul class="nav navbar-nav navbar-right"> + + </ul> + + </div><!--/.nav-collapse --> + </div><!--/.container --> +</div><!--/.navbar --> + + + </header> + +<div class="row"> + <div class="col-md-9 contents"> + <div class="page-header"> + <h1>Logistic kinetics</h1> + + <div class="hidden name"><code>logistic.solution.Rd</code></div> + </div> + + <div class="ref-description"> + + <p>Function describing exponential decline from a defined starting value, with + an increasing rate constant, supposedly caused by microbial growth</p> + + </div> + + <pre class="usage"><span class='fu'>logistic.solution</span>(<span class='no'>t</span>, <span class='no'>parent.0</span>, <span class='no'>kmax</span>, <span class='no'>k0</span>, <span class='no'>r</span>)</pre> + + <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2> + <table class="ref-arguments"> + <colgroup><col class="name" /><col class="desc" /></colgroup> + <tr> + <th>t</th> + <td><p>Time.</p></td> + </tr> + <tr> + <th>parent.0</th> + <td><p>Starting value for the response variable at time zero.</p></td> + </tr> + <tr> + <th>kmax</th> + <td><p>Maximum rate constant.</p></td> + </tr> + <tr> + <th>k0</th> + <td><p>Minumum rate constant effective at time zero.</p></td> + </tr> + <tr> + <th>r</th> + <td><p>Growth rate of the increase in the rate constant.</p></td> + </tr> + </table> + + <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2> + + <p>The solution of the logistic model reduces to the + <code><a href='SFO.solution.html'>SFO.solution</a></code> if <code>k0</code> is equal to + <code>kmax</code>.</p> + + <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2> + + <p>The value of the response variable at time <code>t</code>.</p> + + <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2> + + <p>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 + <a href='http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics'>http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a></p> + + + <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2> + <pre class="examples"><div class='input'> <span class='co'># Reproduce the plot on page 57 of FOCUS (2014)</span> + <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.2</span>), + <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>ylim</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>100</span>), + <span class='kw'>xlab</span> <span class='kw'>=</span> <span class='st'>"Time"</span>, <span class='kw'>ylab</span> <span class='kw'>=</span> <span class='st'>"Residue"</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.4</span>), + <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>2</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>2</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.8</span>), + <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>3</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>3</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.001</span>, <span class='fl'>0.2</span>), + <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>4</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>4</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/plot'>plot</a></span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>logistic.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>0.08</span>, <span class='fl'>0.08</span>, <span class='fl'>0.2</span>), + <span class='kw'>from</span> <span class='kw'>=</span> <span class='fl'>0</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>add</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>5</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>5</span>)</div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/graphics/topics/legend'>legend</a></span>(<span class='st'>"topright"</span>, <span class='kw'>inset</span> <span class='kw'>=</span> <span class='fl'>0.05</span>, + <span class='kw'>legend</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/paste'>paste0</a></span>(<span class='st'>"k0 = "</span>, <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.0001</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.0001</span>, <span class='fl'>0.001</span>, <span class='fl'>0.08</span>), + <span class='st'>", r = "</span>, <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0.2</span>, <span class='fl'>0.4</span>, <span class='fl'>0.8</span>, <span class='fl'>0.2</span>, <span class='fl'>0.2</span>)), + <span class='kw'>lty</span> <span class='kw'>=</span> <span class='fl'>1</span>:<span class='fl'>5</span>, <span class='kw'>col</span> <span class='kw'>=</span> <span class='fl'>1</span>:<span class='fl'>5</span>)</div><div class='img'><img src='logistic.solution-1.png' alt='' width='700' height='433' /></div><div class='input'> + <span class='co'># Fit with synthetic data</span> + <span class='no'>logistic</span> <span class='kw'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"logistic"</span>)) + + <span class='no'>sampling_times</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span>) + <span class='no'>parms_logistic</span> <span class='kw'><-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='kw'>kmax</span> <span class='kw'>=</span> <span class='fl'>0.08</span>, <span class='kw'>k0</span> <span class='kw'>=</span> <span class='fl'>0.0001</span>, <span class='kw'>r</span> <span class='kw'>=</span> <span class='fl'>0.2</span>) + <span class='no'>parms_logistic_optim</span> <span class='kw'><-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='kw'>parent_0</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='no'>parms_logistic</span>) + <span class='no'>d_logistic</span> <span class='kw'><-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>logistic</span>, + <span class='no'>parms_logistic</span>, <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>), + <span class='no'>sampling_times</span>) + <span class='no'>d_2_1</span> <span class='kw'><-</span> <span class='fu'><a href='add_err.html'>add_err</a></span>(<span class='no'>d_logistic</span>, + <span class='kw'>sdfunc</span> <span class='kw'>=</span> <span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'><a href='sigma_twocomp.html'>sigma_twocomp</a></span>(<span class='no'>x</span>, <span class='fl'>0.5</span>, <span class='fl'>0.07</span>), + <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>reps</span> <span class='kw'>=</span> <span class='fl'>2</span>, <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>5</span>, <span class='kw'>LOD</span> <span class='kw'>=</span> <span class='fl'>0.1</span>, <span class='kw'>seed</span> <span class='kw'>=</span> <span class='fl'>123456</span>)<span class='kw'>[[</span><span class='fl'>1</span>]] + + <span class='no'>m</span> <span class='kw'><-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"logistic"</span>, <span class='no'>d_2_1</span>)</div><div class='output co'>#> Model cost at call 1 : 789.6044 +#> Model cost at call 2 : 789.6043 +#> Model cost at call 7 : 716.9934 +#> Model cost at call 12 : 697.1186 +#> Model cost at call 15 : 697.1185 +#> Model cost at call 16 : 697.1184 +#> Model cost at call 17 : 661.1574 +#> Model cost at call 20 : 661.1573 +#> Model cost at call 22 : 620.0542 +#> Model cost at call 25 : 620.0541 +#> Model cost at call 29 : 616.6874 +#> Model cost at call 32 : 616.6874 +#> Model cost at call 33 : 616.6874 +#> Model cost at call 34 : 615.1671 +#> Model cost at call 37 : 615.1671 +#> Model cost at call 39 : 612.0795 +#> Model cost at call 42 : 612.0795 +#> Model cost at call 43 : 612.0795 +#> Model cost at call 44 : 605.9119 +#> Model cost at call 45 : 593.0433 +#> Model cost at call 46 : 548.0815 +#> Model cost at call 47 : 504.9062 +#> Model cost at call 50 : 504.9061 +#> Model cost at call 51 : 504.9061 +#> Model cost at call 53 : 485.929 +#> Model cost at call 55 : 485.929 +#> Model cost at call 56 : 485.929 +#> Model cost at call 58 : 485.241 +#> Model cost at call 60 : 485.241 +#> Model cost at call 61 : 485.2409 +#> Model cost at call 62 : 485.2409 +#> Model cost at call 63 : 484.0717 +#> Model cost at call 69 : 483.9062 +#> Model cost at call 74 : 483.5646 +#> Model cost at call 79 : 483.4908 +#> Model cost at call 84 : 483.4859 +#> Model cost at call 85 : 483.4859 +#> Model cost at call 89 : 483.4848 +#> Model cost at call 90 : 483.4836 +#> Model cost at call 92 : 483.4836 +#> Model cost at call 94 : 483.4836 +#> Model cost at call 97 : 483.4833 +#> Model cost at call 100 : 483.4833 +#> Model cost at call 105 : 483.4832 +#> Model cost at call 108 : 483.4832 +#> Model cost at call 114 : 483.4832 +#> Model cost at call 128 : 483.4832 +#> Optimisation by method Port successfully terminated.</div><div class='input'> <span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span>(<span class='no'>m</span>)</div><div class='img'><img src='logistic.solution-2.png' alt='' width='700' height='433' /></div><div class='input'> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>m</span>)$<span class='no'>bpar</span></div><div class='output co'>#> Estimate se_notrans t value Pr(>t) Lower +#> parent_0 1.057896e+02 2.3743105248 44.5559374 6.656664e-16 1.006602e+02 +#> kmax 6.398190e-02 0.0193490291 3.3067243 2.836921e-03 3.329058e-02 +#> k0 1.612775e-04 0.0009640761 0.1672871 4.348592e-01 3.972250e-10 +#> r 2.263946e-01 0.2822811886 0.8020181 2.184792e-01 1.531165e-02 +#> Upper +#> parent_0 110.9190170 +#> kmax 0.1229682 +#> k0 65.4803698 +#> r 3.3474197</div></pre> + </div> + <div class="col-md-3 hidden-xs hidden-sm" id="sidebar"> + <h2>Contents</h2> + <ul class="nav nav-pills nav-stacked"> + <li><a href="#arguments">Arguments</a></li> + + <li><a href="#note">Note</a></li> + + <li><a href="#value">Value</a></li> + + <li><a href="#references">References</a></li> + + <li><a href="#examples">Examples</a></li> + </ul> + + </div> +</div> + + <footer> + <div class="copyright"> + <p>Developed by Johannes Ranke.</p> +</div> + +<div class="pkgdown"> + <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.3.0.</p> +</div> + </footer> + </div> + + + + </body> +</html> + |