A Nonlinear Dynamics Framework for Mutation-Selection Balance Reveals Dominance-Dependent Bistability in Auto- and Allotetraploids

Abstract

Polyploidy and whole genome duplication (WGD) are widespread biological phenomena with substantial cellular, meiotic, and genetic effects. Despite their prevalence and significance across the tree of life, population genetics theory for polyploids is not well developed. The lack of theoretical models limits our understanding of polyploid evolution and restricts our ability to harness polyploidy for crop improvement amidst increasing environmental stress. To address this gap, we developed and analyzed deterministic models of mutation-selection balance for tetraploids under polysomic (autotetraploid) and disomic (allotetraploid) inheritance patterns and arbitrary dominance relationships. We also introduced a new mathematical framework based on ordinary differential equations and nonlinear dynamics for analyzing the models. We find that the autotetraploid and allotetraploid models generally exhibit negligible differences in mutation load and allele frequency at mutation-selection balance. Our model also reveals two bistable points of mutation-selection balance for dominant alleles with biased mutation rates over a wide range of selection coefficients in the tetraploid models compared to bistability in only a narrow range for diploids. In addition, for overdominant mutations, we find a distinct equilibrium structure with bistable equilibria in only the allotetraploid model. Finally, using discrete time simulations, we explore the temporal dynamics of allele frequency and fitness change and show that the presence of bistability and bifurcations fundamentally alters the temporal dynamics of allele frequency and load. Overall, this work develops foundational theoretical models that will facilitate the development of population genetic models and methodologies to study evolution in empirical tetraploid populations.