The predation kernel as used by the encounter quadrature
Source:R/setPredKernel.R
encounter_kernel.Rd![[Experimental]](figures/lifecycle-experimental.svg)
Returns the kernel array \(\Phi_i(w_k, w_p)\) for which
$$E_i(w_k) = \gamma_i(w_k) \sum_p \Phi_i(w_k, w_p) N^{eff}_i(w_p)
w_p \Delta w_p$$
reproduces exactly the available energy computed by mizerEncounter(),
where \(N^{eff}\) is the interaction-weighted prey density. It is the
kernel that any summary function must use if its result is to be consistent
with getEncounter().
Details
On the default first-order path this is just the point-sampled kernel
returned by pred_kernel(). When second-order bin-averaging is switched on
(see second_order_w()) the two differ: setPredKernel() then builds the
Fourier-transformed kernel from the kernel integrated over the prey bin,
divided by \(\beta - 1\) so that the plain point weight \(w_p \Delta
w_p\) carried by the prey vector is cancelled. Those bin-integrated weights
are recovered here from params@ft_pred_kernel_e by an inverse Fourier
transform, which costs one FFT and keeps this helper automatically in step
with whatever quadrature setPredKernel() used.
Pair it with the plain point prey weight params@w_full * params@dw_full.
That weight is a normalisation which the kernel construction is built to
cancel, not a first-order quadrature weight, so it must not be passed through
bin_average_weight(): doing so applies the prey-bin integral twice. A
summary function that instead pairs the point-sampled pred_kernel() with a
bin-averaged prey weight double-counts that quadrature; that was the bug
behind issue #474.
See also
pred_kernel() for the point-sampled kernel used for plotting and
for supplying a custom kernel, second_order_w(), bin_average_weight()