Eco-evolutionary Dynamics of Individual-Based Food Webs - Advances in Ecological Research - page 234

3. A Neutral Eco-evolutionary Dynamics Model for
Individual-Based Food Webs

Let us now merge the previous population genetics and community ecology
models in the context of two metacommunities, one composed by predators
(P) and the second by resources (R). Death is one of the basic elements in the
stochastic models already described. In the simplest interpretation of death,
at any given time, one individual resource of species k, R k , with abundance
N k dies as a consequence of an individual predator of species l, P l , with
abundance N l

and this event happens at rate d N k ; N l . This death-interaction

coupled event is described as

ð 18 Þ

R is an empty site in the resource metacommunity after the death of
the individual resource, R k . Similarly, we describe the predator-predator
individual interaction as

where

∅

ð 19 Þ

P is an empty site in the predator metacommunity after the death of
the individual predator, P l . If, as in the previous models, we scale time so that
a single time step is the mean time required for one death to occur, then equal
per-individual predation rate for the resource and predator individuals is
written, respectively, as

where

∅

N l
J P

N k
J R

R k
N k

P l
N l

D k ¼ ð 20 Þ

N l
J P

;

N k
J P

P k
N k

P l
N l

D k ¼

ð 21 Þ

and after simplification, we have:

R k P l
J R J P

D k ¼

ð Þ

22