Evolutionary dynamics under phenotype uncertainty

The diffusion limit of population genetics has provided robust descriptions of evolution dynamics for more than 70 years. However, this description ignores the fact that real genotype-to-phenotype maps are often noisy: e.g. stochastic gene expression or structural noise in protein folds. Here, we analytically derive a new stochastic differential equation for evolutionary dynamics under phenotype uncertainty and uncover surprising genetic consequences. Remarkably, many central tenets of classical population genetics break down, such as invariance of evolutionary dynamics to global shifts in absolute fitness, even at fixed population size. Next, we show that high-fitness phenotypes with low genotype-to-phenotype mapping probability can cause low-fitness phenotypes to survive at high frequencies in the population. This phenomenon of "phenotype buoying" leads to complex phase diagrams of simultaneous coexistence between genotype-phenotype pairs. We also discover "phenotype bridges," which describe how phenotype noise can substantially accelerate fitness valley crossing. Our new diffusion limit of population genetics provides promise for describing and predicting the evolutionary dynamics of cancers, which exploit phenotype noise to evade treatment.