Supplementary Material: Probabilistic patterns of interaction: The effects of link-strength variance on food-web structure

This journal is c © 2011 The Royal Society Probabilistic patterns of interaction 2 1. Appendix S1: Assessing structure from the NLID Several structural properties were quantified for each of the three empirical food-webs (see Appendix S2). Primary among these were nestedness (N; figure 1a) and modularity (M; figure 1b), because these properties are thought to have important ramifications for the dynamics of ecological systems [1, 2, 3]. To quantify nestedness, we use the NODF (Nestedness based on Overlap and Decreased Fill) metric [4], where a value of 0 denotes an un-nested network and a value of 1 denotes a fully nested network. Modularity has traditionally been quantified as the local density of links in a network [5], although other metrics exist [6]. Because our predator-prey networks have two trophic levels, we use the density of squares to estimate the average local link density [7]. A ‘square ’ occurs when four nodes are connected by at least four links, and the average density of squares (ρ̄s) equals the number of squares in a network divided by the number of potential squares in a completely connected network, i.e. the local link density. This metric has the advantage of being analytically tractable for any network size, whereas other metrics use optimization methods [6]. As the connectance, C, of a network increases (C = l/mn, where l is the number of links in a network, andm and n are the number of prey and predator species, respectively), the local link density increases. We calculate modularity as M= ρ̄s −