Common Patterns of Energy Flow and Biomass Distribution on Weighted Food Webs

Jiang Zhang; Yuanjing Feng

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arXiv · 1208.1560

Common Patterns of Energy Flow and Biomass Distribution on Weighted Food Webs

Jiang Zhang·Yuanjing Feng

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Abstract

Weights of edges and nodes on food webs which are available from the empirical data hide much information about energy flows and biomass distributions in ecosystem. We define a set of variables related to weights for each species $i$, including the throughflow $T_i$, the total biomass $X_i$, and the dissipated flow $D_i$ (output to the environment) to uncover the following common patterns in 19 empirical weighted food webs: (1) DGBD distributions (Discrete version of a Generalized Beta Distribution), a kind of deformed Zipf's law, of energy flow and storage biomass; (2) The allometric scaling law $T_i\propto X_i^α$, which can be viewed as the counterpart of the Kleiber's 3/4 law at the population level; (3) The dissipation law $D_i\propto T_i^β$; and (4) The gravity law, including univariate version $f_{ij}\propto (T_iT_j)^γ$ and bivariate approvement $f_{ij}\propto T_i^{γ_1}T_j^{γ_2}$. These patterns are very common and significant in all collected webs, as a result, some remarkable regularities are hidden in weights.

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Jiang Zhang, Yuanjing Feng. 2012-08-08. Common Patterns of Energy Flow and Biomass Distribution on Weighted Food Webs. https://arxiv.org/abs/1208.1560

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