Utrecht
22 May 2001
Email: a.neutel@geog.uu.nl
Stability of Complex food webs
Chapter 1 shows that patterns of interaction strengths in Jacobian "community" matrices derived from observations on real food webs are much more stable than those with "randomised" interaction strengths. The "randomised" systems are systems that have the same complexity (in the sense of diversity, connectance and average interaction strength (May 1972)) as the observed systems, that even have the same structure of positive and negative interaction strengths and the same set of paired positive and negative values, but where the pairs of interaction strengths are randomly exchanged (Yodzis 1981). We obtained the patterns of interaction strengths by assuming that our (average) observations on population sizes represent equilibrium states, assuming Lotka-Volterra dynamics to translate these equilibria in Jacobian community matrices.
Chapter 2 explains the stabilising effect of the patterns of interaction strengths. It shows that the incorporation of a "biomass pyramid" in food-web models gives that the longer loops in the food webs have relatively many weak links. This results in systems with a low maximum loop "weight". It is this low maximum loop weight that enhances stability through enhancing "diagonal dominance" in the community matrix.
Chapter 3 analyses the relation between a biomass pyramid and food-web stability in more detail, and shows that the stronger the biomass decrease over trophic levels, the more stable the resulting system. It shows why a high degree of complexity or omnivory does not lead to instability in food webs with "strong" biomass pyramids.
Chapter 4 argues that the considerable decrease in biomass over trophic levels commonly observed in ecosystems is brought about by trophic-level dependent body sizes and conversion efficiencies. Conversion efficiencies imply that energy is lost in converting food into new biomass at each step along the food chain, so that less and less energy is available along the food chain. It is argued however that it is not enough to assume the existence of conversion efficiencies, but that the commonly observed trend of increasing body sizes and conversion efficiencies along the food chain contributes importantly to a decrease in biomass over trophic levels.
Chapter 5 returns to field observations and shows that in primary vegetation successions, below-ground complexity and food-chain length increases with developmental age. The average strengths of the interactions does not decrease with increasing complexity. Stability is strongly enhanced by the particular distribution of the interaction strengths among the trophic loops. The maximum weight of loops of length three and longer is found to correspond with food-web stability. The slope of the biomass pyramid in the bacterial "chain" in the food webs turns out to be a good indicator of food-web stability. The results identify properties of the "energetic" organisation of trophic communities that explain differences in stability of the communities.
Chapter 6 describes earlier work on the global stability of detritus-decomposer food chains. By finding a Lyapunov function, we show that detritus-decomposer food chains can be asymptotically stable without assuming intraspecific interaction of the decomposer. The chapter deals with an aspect of food-web complexity that has been given relatively little attention in studies on food-web stability, and the results are of new interest in the light of the results of the other chapters of the thesis.
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