Global geometry of the genotype-phenotype map illuminates a trade-off between penetrance and mutational adaptability
Evolution in changing environments requires both reliable expression of the currently favored phenotype, as quantified by penetrance, and the capacity to reach alternative phenotypes through mutation. Previous studies suggest that high penetrance may restrict such mutational access. However, because these studies focus on evolved genotypes and local mutational neighborhoods, they cannot determine whether this local constraint limits mutational adaptability under environmental change. Such adaptability depends on a genotype's position relative to high-fitness regions for other environments. Addressing this question requires reconstructing the full probability distribution over phenotypes for every genotype and the resulting environment-specific fitness landscapes across genotype space. Such reconstruction is generally infeasible because genotype and phenotype spaces grow combinatorially. Here, an abstract model of stochastic genotype-phenotype mapping, inspired by interacting spins in statistical physics, permits exhaustive reconstruction of the map. We find that high-penetrance genotypes tend to occupy the interior of environment-specific high-fitness regions and are mutationally robust, whereas lower-penetrance genotypes tend to lie near their boundaries and have greater mutational access to high-fitness regions for alternative environments. This global geometry generates a trade-off between penetrance and mutational adaptability. In evolutionary simulations, stronger phenotypic noise in a fixed environment increases the selective advantage of reliable expression, thereby favoring high penetrance and mutational robustness. Frequent environmental change instead favors mutational accessibility at the expense of penetrance. Thus, penetrance and adaptability are opposing consequences of the same global geometry, with environmental conditions determining their evolutionary balance.