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We introduce a multi-allele Wright-Fisher model with non-recurrent,reversible mutation and directional selection. In this setting, the allelefrequencies at a single locus track the path of a hybrid jump-diffusion processwith state space given by the vertex and edge set of a graph. Verticesrepresent monomorphic population states and edge-positions mark the biallelicproportions of ancestral and derived alleles during polymorphic segments. Wederive the stationary distribution in mutation-selection-drift equilibrium andobtain the expected allele frequency spectrum under large population sizescaling. For the extended model with multiple independent loci we deriverigorous upper bounds for a wide class of associated measures of geneticvariation. Within this framework we present mathematically precise arguments toconclude that the presence of directional selection reduces the magnitude ofgenetic variation, as constrained by the bounds for neutral evolution.

A Wright-Fisher graph model and the impact of directional selection on genetic variation