Auxiliary files for invasion resistance in multispecies systems based on the replicator equation

In this study we propose a replicator equation framework to model multi-species dynamics. In this replicator equation, the coefficients describe pairwise invasion fitnesses between constituent members, and an explicit quadratic term represents the systemic invasion resistance. This invasion resistance (system trait) is dependent on species frequencies and can be linked with specific structures of their pairwise invasion fitness matrix. Within this replicator framework, mean invasion fitness arises, evolves dynamically, and may undergo critical shifts with global environmental changes (e.g. mean growth rate, mean propensity for co-colonization). In the paper, extending an analogy with an SIS epidemiological model, we derive the conceptual mechanistic link between such replicator equation and N microbial species' growth and interaction traits, stemming from micro-scale environmental modification. We also study several specific invasion matrix structures in detail, their role for the quality of species dynamics and also for systemic invasion resistance. In this Dryad repository, we provide some auxiliary files and links to simulation codes, used and presented in our paper, to aid a mathematical understanding of invasion resistance using the replicator equation. We propose the framework can be applied to study colonization resistance in a wide range of microbial ecosystems.