lognormal_pred_kernel: Lognormal predation kernel

Description

This is the most commonly-used predation kernel. The log of the predator/prey mass ratio is normally distributed.

Usage

lognormal_pred_kernel(ppmr, beta, sigma)

Value

A vector giving the value of the predation kernel at each of the predator/prey mass ratios in the ppmr argument.

Arguments

ppmr: A vector of predator/prey size ratios
beta: The preferred predator/prey size ratio
sigma: The width parameter of the log-normal kernel

Details

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 beta and sigma.

This function is called from setPredKernel() to set up the predation kernel slots in a MizerParams object.

Examples

Run this code

params <- NS_params
plot(w_full(params), getPredKernel(params)["Cod", 10, ], type="l", log="x")
# The restriction that the kernel is zero for w/w_p < 1 is more
# noticeable for larger sigma
species_params(params)$sigma <- 4
plot(w_full(params), getPredKernel(params)["Cod", 10, ], type="l", log="x")