Biology, methodology or chance? The degree distributions of bipartite ecological networks.

Jörg Langowski,Richard J Williams

doi:10.1371/journal.pone.0017645

Abstract

The distribution of the number of links per species, or degree distribution, is widely used as a summary of the topology of complex networks. Degree distributions have been studied in a range of ecological networks, including both mutualistic bipartite networks of plants and pollinators or seed dispersers and antagonistic bipartite networks of plants and their consumers. The shape of a degree distribution, for example whether it follows an exponential or power-law form, is typically taken to be indicative of the processes structuring the network. The skewed degree distributions of bipartite mutualistic and antagonistic networks are usually assumed to show that ecological or co-evolutionary processes constrain the relative numbers of specialists and generalists in the network. I show that a simple null model based on the principle of maximum entropy cannot be rejected as a model for the degree distributions in most of the 115 bipartite ecological networks tested here. The model requires knowledge of the number of nodes and links in the network, but needs no other ecological information. The model cannot be rejected for 159 (69%) of the 230 degree distributions of the 115 networks tested. It performed equally well on the plant and animal degree distributions, and cannot be rejected for 81 (70%) of the 115 plant distributions and 78 (68%) of the animal distributions. There are consistent differences between the degree distributions of mutualistic and antagonistic networks, suggesting that different processes are constraining these two classes of networks. Fit to the MaxEnt null model is consistently poor among the largest mutualistic networks. Potential ecological and methodological explanations for deviations from the model suggest that spatial and temporal heterogeneity are important drivers of the structure of these large networks.

Highlights

Describing complex ecosystems as networks of interacting components and explaining the structure of those interaction networks is an essential part of understanding the role of biodiversity in the function and robustness of ecological communities [1,2]
The degree distributions analyzed are from 68 mutualistic networks compiled for two earlier studies [30,31] and 47 bipartite networks formed by retaining only the basal taxa, their consumers and the links between these two groups of taxa from food webs used in an earlier study of food web degree distributions [29]
None of the antagonistic networks have S.134, so the relative performance of the maximum entropy (MaxEnt) model on mutualistic and antagonistic networks is studied in more detail on the 98 networks with S,135; the 17 mutualistic networks with S.140 are studied separately

Summary

Introduction

Describing complex ecosystems as networks of interacting components and explaining the structure of those interaction networks is an essential part of understanding the role of biodiversity in the function and robustness of ecological communities [1,2]. Networks of antagonistic consumerresource interactions, have a long history of study and are the most familiar example of ecological networks [3,4,5], significant attention has recently been focused on networks of mutualistic interactions such as plants and their pollinators or plants and seed dispersers [6,7]. These networks provide a valuable overview of one type of mutualism occurring within a community and several apparently general patterns in the structure of mutualistic networks have been found [8,9]. The obvious difference between the observed skewed distributions and the binomial distributions of random networks [20] has driven the assumption that these skewed distributions are a result of ecological or evolutionary processes shaping species interactions [7,9]

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