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We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without back-mutation, added mutations reduce fitness, and recombination occurs on a faster time scale than mutation and selection. Some features of the model, such as existence and uniqueness of solutions and convergence to the dynamical system of an approximating sequence of discrete time models, were presented in earlier work by Evans, Steinsaltz, and Wachter for quite general selective costs. Here we study a special case where the selective cost of a genotype with a given accumulation of ancestral mutations from a wild type ancestor is a sum of costs attributable to each individual mutation plus successive interaction contributions from each $k$-tuple of mutations for $k$ up to some finite ``degree. Using ideas from complex chemical reaction networks and a novel Lyapunov function, we establish that the phenomenon of mutation-selection balance occurs for such selection costs under mild conditions. That is, we show that the dynamical system has a unique equilibrium and that it converges to this equilibrium from all initial conditions.
We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak assumptions on
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore sto
Recently, the selection-recombination equation with a single selected site and an arbitrary number of neutral sites was solved by means of the ancestral selection-recombination graph. Here, we introduce a more accessible approach, namely the ancestra
It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of the state s
The common understanding of protein evolution has been that neutral or slightly deleterious mutations are fixed by random drift, and evolutionary rate is determined primarily by the proportion of neutral mutations. However, recent studies have reveal