Community Ecology Processes, Models, and Applications

mortality and excretion. The equation that de-
scribes nutrient dynamics is then:

dN 0

dt

¼IeN 0 S

n

i¼ 1

gðxiÞNiN 0 þvNi



S

n

i¼ 1

mðxiÞ

þS

n

i¼ 1

S

n

j¼ 1

aðjxixjjÞNj

þS

n

i¼ 1

S

i 1

j¼ 0



1 fðxiÞ



gðxixjÞNj



ð 12 : 5 Þ

Each simulation starts with a single speciesN 1 ,
which consumes the inorganic nutrientN 0. At each
time step, mutation may occur with a probability
Nifor each species (but the inorganic nutrient
does not mutate), whereis the mutation rate
per unit biomass. If a mutation occurs, a mutant
is introduced, whose trait is drawn at random in a
uniform interval centred on the trait of the parent.
When a mutant is introduced, its biomass is set
equal to the threshold biomass below which a

species goes extinct and is removed from the

system.

There are other models based on few species

traits. For instance, Ito and Ikegami (2006) used a

continuous version of the Webworld model to

include two traits for each species, one that de-

scribes the species as a prey, and the other that

describes it as a predator. We focus below on

our own model because it provides an intuitive

illustration of how evolutionary dynamics may

influence food web structure via one clearly de-

fined trait.

12.2.2 Evolutionary emergence of body-size structured food webs

While the model presented in section 12.2.1.2 starts

with a single species, the mutation-selection pro-

cess adds new morphs to the system, so that total

Body size

2

4

0

(^0) Time 4 10^6
ABC DE
A, Initial condition B, Replacement C, Coexistence D, Diversification E, Divergence
Body size
0
High
Figure 12.2First steps of the emergence of a size-structured food web. The main panel shows the trait composition of
the community through time, while the lower panel details the different steps of the emergence. The simulation starts
with one species that is consuming inorganic nutrient (A). Once in a while, mutants appear (here larger than the resident)
and replace their parent (B, in which the grey morph goes to extinction). After several replacements, an evolutionary
branching happens, as the mutant and the resident are able to coexist (C). A rapid diversification then occurs in which
several morphs are able to coexist (D) but then are selected in differentiated trophic levels (E).
168 FUTURE DIRECTIONS