Population Diversity and Fitness Uncertainty Allow for Faster Evolutionary Rates

I show uncertainty relations that bound the rate of evolutionary processes driven by natural selection, mutations, or by stochastic forces. These rate limits imply that diversity in a population allows for faster evolutionary rates. In particular, the uncertainty of the fitness function is singled out as necessary for fast evolution driven by natural selection. These results generalize Fisher's fundamental theorem of natural selection to dynamics that allow for mutations in terms of uncertainty relations that constrain evolutionary rates.