# Consumption

In the bioenergetic model, species gain and/or lose biomass through consumption. Gains and losses depends on the focus species biomass, a functional response and an interaction-specific assimilation efficiency. In the original bio-energetic model (as developped by Yodzis and Innes, 1992), the functional response is function of consumer-specific maximum consumption rates and half-saturation densities. However, it is sometimes more convenient to be able to work with a more classical functional response with interaction-specific attack rates and handling times. You can switch between the two implementation by setting the argument functional_response (model_parameters function) to either :bioenergetic (default) or :classical. The function will take care of calculating the various rates using allometric scaling. You can still modify the arguments or modify the rates values afterwards if needed.

Here is a list of the parameters that are common to the two implementations:

• e_carnivore is the carnivores assimilation efficiency (default = 0.85)
• e_herbivore is the herbivores assimilation efficiency (default = 0.45)
• c is the value of the predator interference. Either one value, common for all consumers or a vector of consumer-specific values can be passed (default = 0.0.)
• h is the Hill exponent. It controls the shape of the functional response (default = 1.)
• y_invertebrateand y_vertebrate are the maximum consumption rates for the invertebrates and ectotherm vertebrates respectively.
• Γ is the half saturation density ($B_0$)

If you chose a :bioenergetic functional response, the following equations are used:

$gainsi = \sum{j \in resources} Bi xi yi FR{ij}$

$lossesi = \sum{j \in consumers} \frac{Bj xj yj FR{ji}{e_{ji}}}$

where

$FR{ij} = \frac {\omega{ij}B{j}^{h}}{B{0}^{h}+ciBiB{0}^{h}+\sum{k=resources}\omega{ik}B{k}^{h}}$

$\omega_{ij}$

(w) is the consumer $i$ preference for resource $j$, by default it is calculated as $1/n$ where $n$ is the number of resource for $i$ (homogenous consumption effort).

A = [0 1 0 0 ; 0 0 1 1 ; 0 0 0 0 ; 0 0 0 0]
p = model_parameters(A, functional_response = :bioenergetic, e_carnivore = 0.9)
#you can change consumer preference in the parameter object
p[:w] = [.0 1.0 .0 .0 ; .0 .0 .9 .1 ; .0 .0 .0 .0 ; .0 .0 .0 .0]

If a :classical functional response is more suited for your project, then the consumer-specific maximum consumption rate and half saturation density will be transformed into interaction-specific attack rates and handling times using the following substitutions:

• $ht_{ij} = 1/y_{i}$
• $ar_{ij} = 1/(B_0 ht_{ij})$

And the following equations are used for gains and losses linked to consumption:

$gainsi = \sum{j \in resources} e{ij} Bi FR_{ij}$

$lossesi = \sum{j \in consumers} Bj FR{ji}$

with

$FR{ij} = \frac {ar{ij} B{j}^{h}} {1 + ciBi + \sum{k=resources} ht{ik} ar{ik}B_{k}^{h}}$

you can also change the values for attack rates and handling time directly from the parameter object:

A = [0 1 0 0 ; 0 0 1 1 ; 0 0 0 0 ; 0 0 0 0]
p = model_parameters(A, functional_response = :classical)
#you can change consumer preference in the parameter object
p[:ar] = [.0 1e-6 .0 .0 ; .0 .0 2.5e-5 8.2e-5 ; .0 .0 .0 .0 ; .0 .0 .0 .0]`