Bioenergetic module Simplified equations

Simplified bioenergetics

In the original implementation, $E_{net}$ is computed as the difference of mobilised energy and maintenance, as a function of $I$ (ingestion), $T$ (temperature) and $O_2$ (saturation of disolved oxygen), given by

$E_{net}= E_M - E_m = \xi I \phi_M(T) \lambda(O_2) - c_m w^\beta \phi_m(T)$,

where $\xi$ is the assimilation efficiency (species.bioen.assimilation.sp0).

Now, we will consider

$E_{net}= q \xi I \phi(T) \lambda(O_2)$,

where

$\phi(T)= \frac{(T-T_{min})(T-T_{max})}{(T-T_{min})(T-T_{max})-(T-T_{opt})^2}$

for $T \in [T_{min}, T_{max}]$ and 0 otherwise.

The parameters $q$, $T_{min}$, $T_{max}$ and $T_{opt}$ will be provided in the configuration by

species.netenergy.scaling.sp0 = 0.9
species.temperature.tmin.sp0 = 3
species.temperature.tmax.sp0 = 20
species.temperature.topt.sp0 = 16

where $q\in[0,1]$ and $T_{min}<T_{opt}<T_{max}$.

$\phi(T)$ implementation in R:

phi = function(T, Tmin, Tmax, Topt) {
  numerator = (T - Tmin) * (T - Tmax)
  denominator = numerator - (T - Topt)^2
  phi = numerator / denominator
  phi = ifelse(T>Tmax | T<Tmin, 0, phi)
  return(phi)
}

The model used for the computation of $E_{net}$ can be chosen at the species level. The original implementation is used when species.bioenergetics.model.sp0 = full (default if missing) and the new simplified one when species.bioenergetics.model.sp0 = lite. In the future, more simplified models for $E_{net}$ could be added.