Intraspecific interactions facilitate mutualism across multilayer networks under weak selection

Interspecific mutualism is a universal phenomenon that exists in biological and social populations. The generation and maintenance of such mutualism have always been a hotspot in evolutionary biology. This study enriches the research on the evolution of mutualism in structured populations from a theoretical perspective. In particular, we develop an evolutionary model of arbitrary interdependent populations using the coalescent random walk theory and employ it to derive the conditions for mutualism under weak selection. We find that evolution favors mutualism when the strength of intraspecific interactions exceeds a threshold value, which depends on the structure of multiple populations and game parameters. We thus reveal the positive role of intraspecific interactions on the evolution of mutualism, which extends prior research that considered the single effect of interspecific interactions.