diagonal

Supporting material and manuscript "Self-regulation and the stability of large ecological networks". This repository contains:

• diagonal_final.pdf Manuscript plus supplementary information in one pdf.

• The folder Code which contains the following four files:

  • prob_stability.R This program can be used to replicate the numerical findings of Figure 1 in the manuscript. See detailed description in the source code itself.
  • Damuth.R This program calculates the community matrix using an explicit dynamical model with nonlinear functional responses, where parameters are chosen to lead to an equilibrium biomass distribution satisfying Damuth's law. It then evaluates the stability of the resulting matrix.

• The folder Distributions which contains three R-compatible files: distr-g-55.RData, distr-g-75.RData, and distr-g-95.RData. They can be loaded in R using load("distr-g-55.RData") etc. They contain the empirical bivariate distributions from which the matrix entries are drawn. The numbers in the file names refer to the value of the parameter g (See Methods in the manuscript, and Section 8 of the Supplementary Information): -0.55, -0.75, or -0.95.

• The folder EmpiricalWebs containing the adjacency matrices of the empirical networks. There are also two subfolders. Data_with_bodymasses contains the body mass information alongside the food web adjacency matrices, for the webs this data was available for. Ecopath_sorted contains the adjacency matrices of the Ecopath webs. They can be loaded in R using load(Ecopath_XX_sorted.RData); the adjacency matrix is loaded into the variable M1.

• The folder GeneticAlgorithm, with source code and makefiles for hill climbing (HC) and genetic algorithms (GA), plus an R wrapper to run them (launcher.R). To compile, simply run make in the GA and HC folders.

• The folder Videos containing animations of the analytical approximation to network stability, applied to all parameterizations of the empirical networks used in the manuscript. The naming convention follows

  [name of food web]_[number of species]_Distribution-Gamma-[value of g]_[value of f]_type-[type number]

  The parameters g and f are defined in the Methods section of the manuscript, and Section 8 of the Supplementary Information. "Type" refers to whether and what kinds of indirect effects are included; type=1: no indirect effects; type=2: indirect negative effects; type=3: indirect positive effects; type=4: indirect positive and negative effects (see Supplementary Information, Section 8 for details). The videos are essentially animated versions of Figures 15, 18, and 32 in the Supplementary Information.