Structural Cycles in Food Webs

Halnes, G. (2005). Structural Cycles in Food Webs. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-05-052

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Abstract

Traditionally, food webs have been constructed as structural directed graphs that describe "who eats whom," but it is common to interpret them directly as energy flow diagrams, where predations represent energy transfers from the prey to the predator. It is the aim of this work to point out that food webs are incomplete as energy flow diagrams if they ignore passive flows to detritus (dead organic material), a misconception that is common both in empirical data sets and in assembly models, where detritus often is either ignored or treated as an unlimited energy source. When individuals die, they contribute to the detritus pool, and might be an energy source for other species in the system. This feedback loop is of high importance, since it increases the number of pathways available for energy flow, revealing the significance of indirect effects, and making the functional role of the top predators less clear. These additional energy pathways increase the structural cyclicity of the system (measured in terms of of the dominant eigenvalue (lambda) of the adjacency matrix A). In this work we show the importance of the structural cyclicity by comparing empirical data sets to 5 different assembly models. Of these models: cascade (Cohen & Newman 1985), constant connectance (Martinez 1992), niche (Williams & Martinez 2000), modified niche (original in this work), and cyber-ecosystem (Fath 2004), the two last include detritus feedback. We show that when passive flows to detritus are included, the structural cyclicity is increased both in models and empirical data sets. We also show that there is in an approximately linear relationship with the link density (L/N), defined as the number of links per specie.

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