parasitoid and host would lead to specialization.
Whereas parasitoids can often suspend their devel-
opment in the absence of appropriate prey, the
fungal pathogens studied do not, and so might be
expected to have a broader host range. Finally, the
predators have a less intimate and prolonged inter-
action with their resources and so may be even
more generalized. Observations supported these
explanations of connectance. The parasitoid web
showed the lowest connectance, the pathogen web
was intermediate, and the predator web had high-
est connectance (when based on quantitative mea-
sures of connectance). Examination of parasite–host
feeding interactions suggests that food webs con-
structed of these also are quite different from those
focused on predation (Leaper and Huxham 2002).
Quantitative foraging-based explanations of food
web structure require a prediction of the number of
resource species each consumer species will feed
upon. One classic paradigm for predicting species’
diets is optimal foraging theory (MacArthur and
Pianka 1966; Schoener 1971). Here, species are as-
sumed to forage on the suite of resources species
(items) that maximize their rate of energy intake.
While optimal foraging theory has its critics (Pierce
and Ollason 1987), for example that it poorly deals
with species interactions, it does seem to make rea-
sonable predictions about the connectance of a suite
of real food webs (Beckermanet al.2006), and it
seems likely that models of diet choice or constraint
have value in explaining and predicting food web
connectance and structure.
The determinants of diet breadth are central to
understanding how connectance scales with spe-
cies richness. If consumers feed on a constant pro-
portion of all available species, then average diet
breadth is equal tokS, wherekis the average pro-
portion of resources fed upon by consumers. Here,
the total number of linksLwill bekS^2 , and connec-
tance,L/S^2 , will be constant atk. In contrast, if
consumers can feed only on a particular number
of resources, sayn(the average across consumers),
regardless of how many different ones are avail-
able, thenL¼nSand connectance will ben/S.So
whether consumers eat a constant proportion of all
available species or a fixed number of species de-
fines how connectance scales with species richness.
Presumably, this will depend on the mechanism of
foraging and resource selection, on the outcome of
evolution and on physical constraints of consump-
tion, and these could differ between broad classes
of species and consumption (e.g. Warren 1990; Van
Veenet al.2008). Analyses of food web data suggest
that a range of relationships may exist, but that the
number of links scales withSx, wherexis not 1 or
2 but somewhere in between (Murtaugh and Kol-
lath 1997; Schmid-Arayaet al.2002; Montoya and
Sole 2003). Most likely there is not a single relation
between connectance and species richness, but
rather a range of possible relations, depending on
the taxonomic identity and range of organisms con-
sidered.
Stability-based explanations of connectance orig-
inate from observations that model systems with
large numbers of species and large numbers of
connections tend to be less stable than systems
with fewer species or connections (Gardner and
Ashby 1970; May 1972). However, many good ex-
amples of species-rich and well-connected systems
have been discovered (e.g. DeAngelis 1975; Neutel
et al.2002; Broseet al.2006; Rooneyet al.2006).
Furthermore, studies suggest that there are many
ways for highly connected speciose communities to
be stable (McCannet al.1998; Neutelet al.2002;
Rooneyet al.2006; Ottoet al.2007).
Another enduring problem in food web ecology
concerns the factors that limit the length of food
chains embedded in larger trophic webs. Although
simple linear food chains are a convenient abstrac-
tion and are absent from most natural systems, one
can still trace chains of energy flow within complex
food webs. The fundamental question is what limits
the length of food chains.
A well-accepted and intuitive explanation for the
short length of food chains based on the inefficiency
of energy transfer between trophic levels began to
be questioned in the late 20th century. Simple mod-
els of food chains suggested that the slow recovery
from perturbations seemed to characterize longer
model chains (Pimm and Lawton 1977, 1978), and
that this aspect of reduced stability might account
for the rarity of longer chains. Subsequent work
suggested that this result was an artefact caused
by confounding the frequency of stabilizing densi-
ty-dependent population regulation with the length
of model food chains (Sterneret al.1997). AnotherTHE TOPOLOGY OF ECOLOGICAL INTERACTION NETWORKS 19