1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
|
<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Logistic kinetics — logistic.solution • mkin</title>
<!-- jquery -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script>
<!-- Bootstrap -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script>
<!-- bootstrap-toc -->
<link rel="stylesheet" href="../bootstrap-toc.css">
<script src="../bootstrap-toc.js"></script>
<!-- Font Awesome icons -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous" />
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous" />
<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script>
<!-- headroom.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script>
<!-- pkgdown -->
<link href="../pkgdown.css" rel="stylesheet">
<script src="../pkgdown.js"></script>
<meta property="og:title" content="Logistic kinetics — logistic.solution" />
<meta property="og:description" content="Function describing exponential decline from a defined starting value, with
an increasing rate constant, supposedly caused by microbial growth" />
<!-- mathjax -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script>
<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->
</head>
<body data-spy="scroll" data-target="#toc">
<div class="container template-reference-topic">
<header>
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<span class="navbar-brand">
<a class="navbar-link" href="../index.html">mkin</a>
<span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.0.3</span>
</span>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="../reference/index.html">Functions and data</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Articles
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<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>
<li>
<a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
</li>
<li>
<a href="../articles/web_only/benchmarks.html">Some benchmark timings</a>
</li>
</ul>
</li>
<li>
<a href="../news/index.html">News</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li>
<a href="https://github.com/jranke/mkin/">
<span class="fab fa-github fa-lg"></span>
</a>
</li>
</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>
<small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/parent_solutions.R'><code>R/parent_solutions.R</code></a></small>
<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='op'>(</span><span class='va'>t</span>, <span class='va'>parent_0</span>, <span class='va'>kmax</span>, <span class='va'>k0</span>, <span class='va'>r</span><span class='op'>)</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>Minimum 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="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="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="references"><a class="anchor" href="#references"></a>References</h2>
<p>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,
<a href='http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics'>http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>
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="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p>Other parent solutions:
<code><a href='DFOP.solution.html'>DFOP.solution</a>()</code>,
<code><a href='FOMC.solution.html'>FOMC.solution</a>()</code>,
<code><a href='HS.solution.html'>HS.solution</a>()</code>,
<code><a href='IORE.solution.html'>IORE.solution</a>()</code>,
<code><a href='SFO.solution.html'>SFO.solution</a>()</code>,
<code><a href='SFORB.solution.html'>SFORB.solution</a>()</code></p></div>
<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://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>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='op'>)</span>,
from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, ylim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>100</span><span class='op'>)</span>,
xlab <span class='op'>=</span> <span class='st'>"Time"</span>, ylab <span class='op'>=</span> <span class='st'>"Residue"</span><span class='op'>)</span>
</div><div class='input'> <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>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='op'>)</span>,
from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, add <span class='op'>=</span> <span class='cn'>TRUE</span>, lty <span class='op'>=</span> <span class='fl'>2</span>, col <span class='op'>=</span> <span class='fl'>2</span><span class='op'>)</span>
</div><div class='input'> <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>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='op'>)</span>,
from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, add <span class='op'>=</span> <span class='cn'>TRUE</span>, lty <span class='op'>=</span> <span class='fl'>3</span>, col <span class='op'>=</span> <span class='fl'>3</span><span class='op'>)</span>
</div><div class='input'> <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>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='op'>)</span>,
from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, add <span class='op'>=</span> <span class='cn'>TRUE</span>, lty <span class='op'>=</span> <span class='fl'>4</span>, col <span class='op'>=</span> <span class='fl'>4</span><span class='op'>)</span>
</div><div class='input'> <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'>logistic.solution</span><span class='op'>(</span><span class='va'>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='op'>)</span>,
from <span class='op'>=</span> <span class='fl'>0</span>, to <span class='op'>=</span> <span class='fl'>100</span>, add <span class='op'>=</span> <span class='cn'>TRUE</span>, lty <span class='op'>=</span> <span class='fl'>5</span>, col <span class='op'>=</span> <span class='fl'>5</span><span class='op'>)</span>
</div><div class='input'> <span class='fu'><a href='https://rdrr.io/r/graphics/legend.html'>legend</a></span><span class='op'>(</span><span class='st'>"topright"</span>, inset <span class='op'>=</span> <span class='fl'>0.05</span>,
legend <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste0</a></span><span class='op'>(</span><span class='st'>"k0 = "</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</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='op'>)</span>,
<span class='st'>", r = "</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</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='op'>)</span><span class='op'>)</span>,
lty <span class='op'>=</span> <span class='fl'>1</span><span class='op'>:</span><span class='fl'>5</span>, col <span class='op'>=</span> <span class='fl'>1</span><span class='op'>:</span><span class='fl'>5</span><span class='op'>)</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='va'>logistic</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"logistic"</span><span class='op'>)</span><span class='op'>)</span>
<span class='va'>sampling_times</span> <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</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='op'>)</span>
<span class='va'>parms_logistic</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>kmax <span class='op'>=</span> <span class='fl'>0.08</span>, k0 <span class='op'>=</span> <span class='fl'>0.0001</span>, r <span class='op'>=</span> <span class='fl'>0.2</span><span class='op'>)</span>
<span class='va'>d_logistic</span> <span class='op'><-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>logistic</span>,
<span class='va'>parms_logistic</span>, <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>,
<span class='va'>sampling_times</span><span class='op'>)</span>
<span class='va'>d_2_1</span> <span class='op'><-</span> <span class='fu'><a href='add_err.html'>add_err</a></span><span class='op'>(</span><span class='va'>d_logistic</span>,
sdfunc <span class='op'>=</span> <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='sigma_twocomp.html'>sigma_twocomp</a></span><span class='op'>(</span><span class='va'>x</span>, <span class='fl'>0.5</span>, <span class='fl'>0.07</span><span class='op'>)</span>,
n <span class='op'>=</span> <span class='fl'>1</span>, reps <span class='op'>=</span> <span class='fl'>2</span>, digits <span class='op'>=</span> <span class='fl'>5</span>, LOD <span class='op'>=</span> <span class='fl'>0.1</span>, seed <span class='op'>=</span> <span class='fl'>123456</span><span class='op'>)</span><span class='op'>[[</span><span class='fl'>1</span><span class='op'>]</span><span class='op'>]</span>
<span class='va'>m</span> <span class='op'><-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"logistic"</span>, <span class='va'>d_2_1</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='fu'><a href='plot.mkinfit.html'>plot_sep</a></span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</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://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</span><span class='op'>$</span><span class='va'>bpar</span>
</div><div class='output co'>#> Estimate se_notrans t value Pr(>t) Lower
#> parent_0 1.057896e+02 1.9023449590 55.610120 3.768360e-16 1.016451e+02
#> kmax 6.398190e-02 0.0143201029 4.467978 3.841828e-04 3.929235e-02
#> k0 1.612775e-04 0.0005866813 0.274898 3.940351e-01 5.846688e-08
#> r 2.263946e-01 0.1718110662 1.317695 1.061043e-01 4.335843e-02
#> sigma 5.332935e+00 0.9145907310 5.830952 4.036926e-05 3.340213e+00
#> Upper
#> parent_0 109.9341588
#> kmax 0.1041853
#> k0 0.4448749
#> r 1.1821120
#> sigma 7.3256566</div><div class='input'> <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</span><span class='op'>$</span><span class='va'>distimes</span>
</div><div class='output co'>#> DT50 DT90 DT50_k0 DT50_kmax
#> parent 36.86533 62.41511 4297.853 10.83349</div><div class='input'>
</div></pre>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
<nav id="toc" data-toggle="toc" class="sticky-top">
<h2 data-toc-skip>Contents</h2>
</nav>
</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> 1.6.1.</p>
</div>
</footer>
</div>
</body>
</html>
|
