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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

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food webs explanations
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 explanations3
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
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Food Webs: explanations
  • Dynamic models used to predict these patterns are based on relatively simple Lotka-Volterra models that have been extended to include more than two species
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Food Webs: explanations
  • For a system of n species, the differential equation for the dynamics of species I looks like

where biis the per capita population growth rate of species i, ai,jis the per capita effect of species j on species i, including intraspecific effects when i=j, and Xiis the abundance of species i, in a system of n species

dXi / dt = Xi (bi + ∑ ai,jXj) = Fi

food webs explanations6
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
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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)
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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
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Food Webs: explanations
  • Pimm and Lawton suggested these longer return times as being less stable and less resilient (e.g. 2 sp system)
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Food Webs: explanations
  • Others have suggested the relatively short chains are stable because of the assumptions built into a density-dependent model…why?
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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
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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
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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
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Food Webs: explanations
  • The main result of this exercise was S becomes relatively large, the system becomes relatively stable onlyif 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
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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)
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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
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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 self-regulated, 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)
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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?
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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
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Food Webs: explanations
  • Examples of single and multiple trophic pathways in specialized and generalized predators (note multiple pathways)
food web theory
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
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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 theory23
Food Web Theory
  • Yet another problem: accurately determining feeding dynamics (even in the absence of population dynamics)
food web theory24
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
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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
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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
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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)
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Food Web Theory
  • Simple microcosm experiments also suggest dynamics become increasingly unstable with increases in productivity (top vs. bottom) or chain length
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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
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Food Web Theory
  • Increased temporal variation in Colpidium (predatory protist) in longer chains
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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
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Food Web Theory
  • At low productivity, length is determined by energy availability. More energy allows for longer chains, but may also decrease stability distribution
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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
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Food Web Theory
  • Pimm and Redfearn (1988) conducted a meta-analysis of MacArthur’s hypothesis using published accounts of population dynamics of herbivorous insects (which tended to support the theory)
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Food Web Theory
  • Lawler (1993) also tried to examine the relationship between chain length and stability using protists and microcosms
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Food Web Theory
  • Her simple systems ranged from many 2-member systems and 4 different 3-level chains (with different members); all were stable
  • She also formed a random 8 member community
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Food Web Theory
  • Probability of extinction at each level varied; 2 sp (2.5%), 4 sp (21.7%) and 8 sp (27.5%)
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Food Web Theory
  • Her result suggests that webs containing increased numbers of species exhibited increased likelihood of extinction
food web patterns39
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 patterns40
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)
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Food Web Patterns
  • Webs with high resolution tend to have more omnivores, longer chains, and roughly constant connectance (compared to aggregated chains)
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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)
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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
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