Fisher's geometric model of adaptation in two dimensions. (*A*) Two orthogonal axes represent independent character traits. Fitness is determined by a symmetrical Gaussian function centered at the origin. Consider a population initially monomorphic for the wild-type allele *r*_{aa} = (2,0). A mutation *m* gives rise to a mutant phenotype vector *r*_{bb} = *r*_{aa} + *m*. The phenotype of the mutant heterozygote assuming phenotypic codominance (*h* = 1/2) is *r*_{ab} = *r*_{aa} + *m*/2. The different circles specify the areas in which mutations are adaptive in haploids (*α*_{hap}), adaptive in diploids (*α*_{dip}), and replacing in diploids (*γ*). (*B*) Frequency trajectories of all alleles present during a representative adaptive walk in a diploid population with *N* = 5⋅10^{4}, *r*_{aa} = (2,0), and <*m*> = *σ*_{w} = 1. Different colors represent different alleles. The black bars over the graph indicate the periods during which a balanced polymorphism was present. (*C*) Representative adaptive walks in a haploid population and a diploid population. Vectors depict the successive mutations that led to the prevalent allele at the end of the walk. The haploid walk consists of a single lineage of successive mutations, each conferring a selective advantage over the previous one. In the diploid walk, the first mutation overshoots the fitness optimum, generating a sequence of intermediate balanced states. Note that the areas *α*_{hap}, *α*_{dip}, and *γ* (dotted circles) from *A* apply only to the first mutation in the walk when the population is still monomorphic for *r*_{a}. (*D*) Probability of observing balanced polymorphism during adaptive walks toward a fixed fitness optimum as a function of mutation sizes scaled by effective drift radius *r*_{0} (*SI Text*) for the various settings of *N*, *σ*_{w}, and <*m*> specified in Table S1. Circles show the probability of at least one balanced state arising over the course of a walk, and squares show the fraction of time during which balanced states were present. Coloration indicates the average “adaptedness” achieved during a walk, defined by the improvement in mean population fitness over the walk (<*w*_{end}> − <*w*_{start}>) relative to the maximally possible improvement (1 − <*w*_{start}>).

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