Adaptive mutation of biochemical reaction constants: Fisher's geometrical model without pleiotropy

The distribution of fitness effects of adaptive mutations remains poorly understood, both empirically and theoretically. We study this distribution using a version of Fisher’s geometrical model without pleiotropy, such that each mutation affects only a single trait. We are motivated by the notion of an organism’s 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.