Food Web Patterns
Food Webs: explanations
• Explanations for food webs draw heavily on
two kinds of models: dynamic models base on
extensions of the Lotka-Volterra predator-prey
models, and static models that make no
specific reference between population
dynamics and food web patterns
Food Webs: explanations
• Dynamic models attempt to explain food web
patterns on the basis of food web
configurations that promote stable
equilibrium population dynamics, which
presumably allow populations to persist for
ong periods of time, as opposed to
configurations that are unstable and that
presumably fail to persist for a very long time
Food Webs: explanations
• Dynamic models used to predict these
patterns are based on relatively simple LotkaVolterra models that have been extended to
include more than two species
Food Webs: explanations
• For a system of n species, the differential
equation for the dynamics of species I looks
like
dX / dt = X (b + ∑ a X ) = F
i
i
i
i,j
j
i
where bi is the per capita population growth
rate of species i, ai,j is the per capita effect of
species j on species i, including intraspecific
effects when i=j, and Xi is the abundance of
species i, in a system of n species
Food Webs: explanations
• Different food chain
configurations can
be modeled by
setting entries to
zero, positive, or
negative values
• This is done with a
Jacobian matrix
Food Webs: explanations
• Pimm and Lawton (1977) used this approach
to assess the dynamics of systems of 4
‘species’ arranged in food chains of different
length
• For each food chain configuration, numerical
entries were in the appropriate Jacobian
matrix were selected at random (2000x;
producing a frequency distribution)
Food Webs: explanations
• One result, all 4 sp.
food chains missing
omnivores were
locally stable, but
return times were
substanially longer
than in longer chains
Food Webs: explanations
• Pimm and
Lawton suggested
these longer
return times as
being less stable
and less resilient
(e.g. 2 sp system)
Food Webs: explanations
• Others have
suggested the
relatively short
chains are stable
because of the
assumptions built
into a densitydependent
model…why?
Food Webs: explanations
• Another aspect of food chain architecture was
the effect of same-chain omnivory on
population dynamics within these relatively
simple 4-species food chains
• The result: omnivory had a more dramatic
effect on dynamics than chain length
Food Webs: explanations
• A striking 78% of the longer chains with an
omnivorous link were unstable
• Of the remaining 22% that were stable, return
times were on average shorter than in
comparable food chains without omnivores
• Thus omnivorous systems should be rare
(given the instability), but those few stable
ones with onmivores are more resilient
Food Webs: explanations
• May (1973) used a similar approach to
compare the stability of webs differing in
species richness, connectance, and the
intensity of interactions among species
• Rather than using a preconceived idea of
structure, May used randomly structured
webs consisting of S model species
Food Webs: explanations
• The main result of this exercise was S becomes
relatively large, the system becomes relatively
stable only if i(sc)1/2 < 1
• Thus, increases in i, S or c will tend to be
destabilizing in randomly connected food webs
• This finding is largely contrary to many field
biologists that typically link diversity and
stability
Food Webs: explanations
• One explanation is
that in increasingly
complex systems,
there are more ways
for things to go very
wrong (i.e. unstable
interactions to arise)
Food Webs: explanations
• Other theoretical ecologists have suggest that
May’s conclusions depend critically on the
way in which he constructed his models and
that different models lead to rather different
conclusions
Food Webs: explanations
• DeAngelis found that stability increased with
increasing values of connectance (c) under
conditions where 1) predators had a relatively
small impact on prey biomass, 2) predators in
higher trophic levels were strongly selfregulated, and 3) there was a bias toward
‘donor’ dependence in interactions (predator
dynamics are more strongly affected by
changes in prey than the reverse relationship)
Food Webs: explanations
• Others questioned the realistic nature of some
of May’s webs such as the randomly
assembled 3-species food loops (seem to
appear relatively rarely in nature yet
somewhat common in May’s models)..why?
Food Webs: explanations
• MacArthur (1955) argued that predators
feeding on multiple prey species are more
likely to weather crashes in the abundance of
a single prey species for their food than are
specialized predators that depend entirely on
a single prey species for their food
Food Webs: explanations
• Examples of
single and
multiple trophic
pathways in
specialized and
generalized
predators (note
multiple
pathways)
Food Web Theory
• Causes of Food Chain Length
• Most of the information on food webs comes
from theory as actual webs are rather difficult
to observe in nature (e.g. consider long-lived
organisms; field studies may indicate stability
in almost all cases due to longevity)
• This could be accounted for by scaling to
generation time
Food Web Theory
• It is also difficult to
collect accurate
information on webs
where species within the
web have different life
spans
• Consequently, most
experimental systems
are relatively simple
Food Web Theory
• Yet another problem: accurately determining
feeding dynamics (even in the absence of
population dynamics)
Food Web Theory
• In an attempt to test if chain length is
influenced by the inefficiency of energy
transfer, Pimm and Kitching (1987) tested the
effects of productivity on the relatively simple
food webs that develop in water-filled tree
holes
Food Web Theory
• Tree holes communties include a 1) detritous
2) mosquitoe larvae and midges 3) larvae of a
predatory midge and 4) predatory tadpoles
(tree frogs)
• In artificial containers,
the productivity can be
manipulated
Food Web Theory
• Results: increases in productivity resulted in
increases in abundances (albeit NS)
• When ranges of productivity were
exaggerated, decreasing natural levels of
productivity decreased the number of
coexisting species
Food Web Theory
• Number of sp., no.
of links, and chain
length in tree hole
communities with
varying levels of
productivity (more
species, but not
more trophic links
were supported)
Food Web Theory
• Simple microcosm
experiments also
suggest dynamics
become increasingly
unstable with
increases in
productivity (top vs.
bottom) or chain
length
Food Web Theory
• Prediction: If population dynamics are less
stable in long food chains than in short ones,
experimental manipulations of food chain
length should produce observable differences
in population dynamics (i.e. more variable in
longer chains)
• Experimental evidence (microcosms of
protists) supports modest increases in food
chain length result in decreased stability
Food Web Theory
• Increased
temporal
variation in
Colpidium
(predatory
protist) in
longer chains
Food Web Theory
• It appears there may be a curvilinear
relationship in which below natural levels or
productivity there is insufficient energy to
sustain higher trophic levels and higher levels
may lose species by direct toxic effects of
eutrophication or through increasingly
unstable dynamics
Food Web Theory
• At low productivity, length is determined by energy
availability. More energy allows for longer chains,
but may also decrease stability distribution
Food Web Theory
• Omnivory, Trophic Complexity and Stability
• Morin and Lawler (1996) could not prove
omnivores destabilize simple lab-chains
(although they maintained larger populations
than nonomnivorous species)
• MacArthur predicted omnivores would be
temporally less variable than specialized
predators/feeders
Food Web Theory
• Pimm and Redfearn (1988) conducted a metaanalysis of MacArthur’s hypothesis using
published accounts of population dynamics of
herbivorous insects (which tended to support
the theory)
Food Web Theory
• Lawler (1993) also tried to examine the
relationship between chain length and
stability using protists and microcosms
Food Web Theory
• Her simple systems ranged from many 2member systems and 4 different 3-level chains
(with different members); all were stable
• She also formed a random 8 member
community
Food Web Theory
• Probability of
extinction at each
level varied; 2 sp
(2.5%), 4 sp
(21.7%) and 8 sp
(27.5%)
Food Web Theory
• Her result suggests that webs containing
increased numbers of species exhibited
increased likelihood of extinction
Food Web Patterns
• Food web research is still a very active field
• Novel techniques are being utilized to gain a
better understanding of energy in flow in
systems where it was not previously possible
Food Web Patterns
• One key issue is the importance of ‘scale
dependence’; specifically whether basic
patterns involving connectance, linkage
density, chain length, or ratios of the number
of species in different trophic categories,
depend critically on the level of taxonomic
resolution (e.g. is aggregating species
appropriate)
Food Web Patterns
• Webs with high resolution tend to have more
omnivores, longer chains, and roughly
constant connectance (compared to
aggregated chains)
Food Web Patterns
• A second major question concerns the degree
of temporal variation in web patterns
• Most published studies depict interactions
that are possible, but may include interactions
that are infrequent or with species that are
highly seasonsal (or even segregated in time)
• Example of how
including temporal
variation in web
structure can
greatly influence
web structure (top:
aggregated
community;
bottom: all
interactions)
Food Web Patterns
• Even in the simple tree-hole communities,
high temporal variation (turnover) was
observed
• One problem is that temporal aggregation of
food web patterns probably overestimates the
actual number of taxa that are interacting at
any particular time
Food Web Summary
• Even if early generalizations prove inaccurate,
they provide a good tool to examine
community structure
• Food webs can identify important pathways,
including indirect effects
• Experimental tests of web theory remains a
fruitful and productive area that could be
exploited
Food Web Patterns