Summary statistics for the degree distributions of each randomized network used for Fig \ref{948197} in the main text. Networks were constructed to have the same size and approximate connectance, but with the network structure (which populations are connected to which other popuations) otherwise generated according to one of five algorithms: Erdős-Rényi, Barabasi-Albert, and Watts-Strogatz, stochastic block, and tree (see Section \ref{930618} of the main text). Some algorithms allowed perfect matching of connectance (Erdős-Rényi, Barabasi-Albert, and Watts-Strogatz), while others necessitated some minor variation (stochastic block and tree).