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lognormal_pred_kernel.html
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lognormal_pred_kernel.html
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<title>Lognormal predation kernel — lognormal_pred_kernel • mizer</title>
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<h1>Lognormal predation kernel</h1>
<small class="dont-index">Source: <a href='https://github.com/sizespectrum/mizer/blob/master/R/pred_kernel_funcs.R'><code>R/pred_kernel_funcs.R</code></a></small>
<div class="hidden name"><code>lognormal_pred_kernel.Rd</code></div>
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<div class="ref-description">
<p>This is the most commonly-used predation kernel. The log of the predator/prey
mass ratio is normally distributed.</p>
</div>
<pre class="usage"><span class='fu'>lognormal_pred_kernel</span>(<span class='no'>ppmr</span>, <span class='no'>beta</span>, <span class='no'>sigma</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>ppmr</th>
<td><p>A vector of predator/prey size ratios</p></td>
</tr>
<tr>
<th>beta</th>
<td><p>The preferred predator/prey size ratio</p></td>
</tr>
<tr>
<th>sigma</th>
<td><p>The width parameter of the log-normal kernel</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>A vector giving the value of the predation kernel at each of the
predator/prey mass ratios in the <code>ppmr</code> argument.</p>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>Writing the predator mass as \(w\) and the prey mass as \(w_p\),
the feeding kernel is given as
$$\phi_i(w, w_p) =
\exp \left[ \frac{-(\ln(w / w_p / \beta_i))^2}{2\sigma_i^2} \right]
$$
if \(w/w_p\) is larger than 1 and zero otherwise.
Here \(\beta_i\) is the preferred predator-prey mass ratio and \(\sigma_i\)
determines the width of the kernel.
These two parameters need to be given in the species parameter dataframe in
the columns <code>beta</code> and <code>sigma</code>.</p>
<p>This function is called from <code><a href='setPredKernel.html'>setPredKernel()</a></code> to set up the
predation kernel slots in a MizerParams object.</p>
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