ask to what extent the nestedness in mutualism
networks is a consequence of the structure of phy-
logenies, or of more ecological constraints?
So far, the mutualisms depicted in these net-
works are restricted to interactions involving trans-
port of pollen or fruits/seeds by animals and the
reciprocal energetic or nutritional reward obtained
by the animals that consume nectar, pollen or fruits.
These are only a fraction of the kinds of positive
interactions that characterize mutualisms. Other
kinds of positive interactions, such as defensive/
domicile mutualisms involving the defence of host
plants by insects (Janzen 1966), or trading in energy
and nutrients between plants and mycorrhizal
fungi (Schwartz and Hoeksema 1998), have not yet
received this kind of analysis.
Another problem is that effects of mutualisms on
the dynamics of the larger ecological networks in
which they embedded are essentially unknown.
Most models of mutualisms focus on the dynamics
of a pair of species involved in a mutualistic inter-
action (Dean 1983; Wolin 1985). Consequences of
mutualisms for the stability of the larger communi-
ty network in which they occur remain largely un-
explored (but see Ringelet al.1996).
1.4 Food webs
1.4.1 Structural regularities
Food webs are perhaps the oldest and most fre-
quently studied type of ecological network. The
links in food webs are determined by observing
evidence of a resource–consumer interaction be-
tween two species. This can be done in a qualitative
way (presence/absence of a trophic interaction) or
quantitative way (e.g. through feeding rates, preda-
tion rates, conversion efficiencies). Much effort has
been expended collecting this type of information,
especially the qualitative type, for constructing
food webs, and examining whether they exhibit
particular structure. One of the earliest ideas was
that food chain lengths (the number of links from a
species at the bottom of the food web to one at the
top) were shorter than expected by chance (Pimm
and Lawton 1977; Pimm 1982). Another was a rela-
tive paucity of omnivores, species that feed on re-
sources at different trophic levels (Pimm and
Lawton 1978; Pimm 1980). These and other appar-
ent regularities have been challenged many times
(Yodzis 1984; Paine 1988; Polis 1991); some are sup-
ported by more recent and higher quality data,
others are not (Pimm 1991; Martinez 1994; Warren
1994). Rather than review the literature concerning
all of the patterns, we will focus on one of the most
important properties of food webs with ‘qualita-
tive’ (presence/absence) links: connectance. (Note
that there are quantitative versions of some proper-
ties, including connectance (e.g. Bersieret al.2002).)
In a food web ofSspecies, connectance is the
number of realized links (L) divided by the number
of possible links (S^2 orS(S1) if excluding cannibal-
istic links), i.e. when all species interact. It has strong
effects on many other structural features, such as the
frequency distribution of the number of links per
species (Dunneet al.2002; Stoufferet al.2005), and
has long been known to affect the stability of model
food webs (Gardner and Ashby 1970; May 1972;
DeAngelis 1975; Pimm 1984). One might say that
recording and explaining patterns of connectance is
a first step towards understanding many other as-
pects of food web structure. Earlier researchers out-
lined a number of ideas abouthow structure depends
on the number of species in a food web. In particular,
there was much debate about whether connectance
remains constant or increases or decreases as the
number of species in food webs increases.
There has been a great deal of research about the
magnitude of connectance in food webs and how it
changes with the overall species richness of the web
(Sugiharaet al.1989; Winemiller 1989; Havens 1992,
1993; Martinez 1992, 1993; Bengtsson 1994). Some of
this early discussion was hampered by problems
with the source and quality of the data used to
construct food webs. In contrast, over the last two
decades or so, a large amount of data was collected
with the explicit goal of constructing highly de-
tailed food webs, and we will focus on 15 excep-
tionally well-characterized food webs.
In these webs, connectance varies from about 0.01
to 0.35, that is, from 1% to 35% of all possible links
are realized (Fig. 1.6). Furthermore, connectance
appears to decrease with increasing species rich-
ness, and this pattern seems to be well supported
by recent analyses (Murtaugh and Kollath 1997;
Schmid-Arayaet al.2002; Montoya and Sole 2003).THE TOPOLOGY OF ECOLOGICAL INTERACTION NETWORKS 17