Exploring the interplay of biodiversity and mutation in cyclic competition systems

In this study, we investigate the consequences of significant mutations using a Rock–Paper–Scissors (RPS) model as a framework. By introducing mutant species into normal species, we elucidate the factors that influence species survival and coexistence. We examine the role of mobility, mutation rates in normal species, and the interspecific competition strength differential between mutants and normals. Our results demonstrate that these factors have a profound impact on the survival dynamics of each species. Specifically, we reveal the existence of a critical mutation rate that triggers rapid changes in the survival probabilities of normal species when mobility is low. The critical mutation rate is increasing monotonically for the intermediate mobility region. We show the asymptotic characteristics of the critical mutation rate according to the interspecific competition strength differential between mutant and normal species. In addition, we identify specific ranges of mobility and mutation rates that enable the coexistence of normal and mutant species. Furthermore, we derive the relevant partial differential equation that incorporates the emergence of mutant species. When these results are compared with those obtained from the Rock–Paper–Scissors (RPS) model, we establish notable consistency between the two approaches.