The Crow-Kimura evolution model in case of asymmetric mutation and recombination

The mutation and recombination often have different rates for forward and backward processes and this study explores the less common case of asymmetric mutation and recombination rates. The primary focus is on analyzing the error threshold transition in the context of asymmetric mutations. We investigate how the error threshold changes in the case of a single peak fitness landscape. We analyze how surplus (the availability of beneficial mutations) changes with the degree of asymmetry in mutation and recombination rates. The model is extended to include asymmetric recombination (horizontal gene transfer). We focus on the complex interplay between mutation and recombination rates in asymmetric scenarios and their effects on error thresholds, surplus, mean fitness, and other key aspects of evolutionary dynamics. The findings contribute to a more nuanced understanding of evolution in situations where biological processes do not follow the simplifying assumption of symmetric rates.