the shape of the food web. To do this snapshot, all
morphs are considered, and the trophic links be-
tween them are retained if the interaction strength
is larger than a threshold value (here, 0.15). The
result is a binary food web that describes species
and trophic links but ignores quantitative informa-
tion on biomasses and nutrient fluxes. These
simulated food webs can then be compared with
empirical data from natural communities (e.g. War-
ren 1989; Winemiller 1990; Hall and Raffaelli 1991;
Martinez 1991; Polis 1991; Havens 1992; Memmott
et al. 2000). This comparison was done in the fol-
lowing way:
·Food webs were generated for 36 pairs of para-
meters a^0 ¼f^0 ;^0 :^1 ;^0 :^2 ;^0 :^3 ;^0 :^4 ;^0 :^5 g
nw¼f 0 : 5 ; 1 ; 2 ; 3 ; 4 ; 5 g
and theirproperties were examined.
·For each property, a surface was drawn in param-
eter space by interpolating the results of the 36
simulations.
·A least squares fit determined which pair of para-
meters yielded the community closest to empirical
data.
For each empirical data set, it is possible to find
parameters that generate a food web whose proper-
ties are very similar. For all simulated communities,
the properties used for the least squares fit are
compared with those of the empirical data in
Table 12.1. While the match between the commu-
nities produced by the model and the empirical
data sets is far from being perfect, it is as good as
the match obtained using the best binary food web
models, at least for the descriptors listed in Table
12.1 (Loeuille and Loreau 2005). The model intro-
duced here also produces the connectance and total
diversity of the community, while these quantities
were used as parameters (and therefore left unex-
plained) in the Niche model as well as in other
binary food web models.
12.2.3 Advantages of simple community evolution models
In discussing the advantages of the above model or
other simple community evolution models, our aim
is not to show that simple models based on one or a
few traits are better than more complex ones, but
rather to identify their specific contribution to un-
derstanding food webs.12.2.3.1 Comparison with other community evolution models
The main advantages of community evolution
models based on a restricted and clearly identified
set of traits are a better understanding of the role of
evolutionary constraints (trade-offs) and a greater
ability to test their predictions.
Models that use a large number of traits do not
identify these traits explicitly. The influence of
these traits on species interactions and demography
is usually determined using a matrix whose ele-
ments are drawn at random (see section 12.1).
Therefore, traits are not linked mechanistically to
the biology of the species. No benefits or costs of the
phenotypic traits are explicit. In community evolu-
tion models, community properties emerge sponta-
neously from the evolutionary dynamics, so that a
complete understanding of these evolutionary dy-
namics is required to discuss thoroughly the possi-
ble mechanisms producing these properties. In the
examples detailed in section 12.2.1.2, an explicit
link is made between body size and the biology of
species. Of course, such knowledge involves addi-
tional hypotheses on trade-offs producing the selec-
tive pressures acting on the phenotypic trait. But in
the case of body size, these trade-offs are well
known because body size has been the focus of a
lot of work in ecology and physiology (Kleiber
1961; Peters 1983; Brown 2004). It is then possible
to use our model as a tool to understand which
allometric components of the model are responsible
for the observed community structure. For instance,
it is possible to turn off the effects of body size on
the life-history parametersfandmand examine the
consequences of the allometric components of com-
petitive and trophic interactions, independently of
the effects of body size on life-history parameters.12.2.3.2 Comparison with binary qualitative models
A large part of food web theory concerns food web
topology in tight connection with empirical data.
These models use binary data, i.e. species and links
are either present or absent but are not quantified.170 FUTURE DIRECTIONS