Figure 2. Feasibility domain in random and empirical webs.

The top two panels show Ξ, the size of the domain of growth rates leading to coexistence, in the case of random networks. (a) The dependence of Ξ on E₁=Cμ (where C is the connectance and μ is the mean interaction strength), and the number of species S. (b) The match between our analytical prediction (equation (2) and Supplementary Note 6) and the numerical value of Ξ. The bottom panels show a comparison between Ξ computed for empirical webs (89 mutualistic networks in d, and 15 food webs in c, parameterized with different distributions of interaction strengths) and our analytical approximation. Mutualistic networks have values of Ξ comparable to random networks with similar interactions (R²=0.98), indicating that their structure has little effect on the size of the feasibility domain. Food webs have lower values of Ξ than their random counterparts (R²=0.80). Empirical networks were parameterized extracting interaction strengths from a bivariate normal distribution with different means, variances and correlations (see and Supplementary Note 8).