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The distribution of fitness effects of adaptive mutations remains poorly understood, both empirically and theoretically. We study this distribution using a version of Fishers geometrical model without pleiotropy, such that each mutation affects only a single trait. We are motivated by the notion of an organisms chemotype, the set of biochemical reaction constants that govern its molecular constituents. From physical considerations, we expect the chemotype to be of high dimension and to exhibit very little pleiotropy. Our model generically predicts striking cusps in the distribution of the fitness effects of arising and fixed mutations. It further predicts that a single element of the chemotype should comprise all mutations at the high-fitness ends of these distributions. Using extreme value theory, we show that the two cusps with the highest fitnesses are typically well-separated, even when the chemotype possesses thousands of elements; this suggests a means to observe these cusps experimentally. More broadly, our work demonstrates that new insights into evolution can arise from the chemotype perspective, a perspective between the genotype and the phenotype.
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
Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees - Model R (recombin
Eigens quasi-species model describes viruses as ensembles of different mutants of a high fitness master genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When the mutation ra
New models for evolutionary processes of mutation accumulation allow hypotheses about the age-specificity of mutational effects to be translated into predictions of heterogeneous population hazard functions. We apply these models to questions in the
A question in evolutionary biology is why the number of males is approximately equal to that of females in many species, and Fishers theory of equal investment answers that it is the evolutionarily stable state. The Fisherian mechanism can be given a