The Population Genetics of Adaptation: The Distribution of Factors Fixed during Adaptive Evolution

We know very little about the genetic basis of adaptation. Indeed, we can make no theoretical predictions, however heuristic, about the distribution of phenotypic effects among factors fixed during adaptation nor about the expected 'size' of the largest factor fixed. Study of this problem requires taking into account that populations gradually approach a phenotypic optimum during adaptation via the stepwise substitution of favorable mutations. Using Fisher's geometric model of adaptation, I analyze this approach to the optimum, and derive an approximate solution to the size distribution of factors fixed during adaptation. I further generalize these results to allow the input of any distribution of mutational effects. The distribution of factors fixed during adaptation assumes a pleasingly simple, exponential form. This result is remarkably insensitive to changes in the fitness function and in the distribution of mutational effects. An exponential trend among factors fixed appears to be a general property of adaptation toward a fixed optimum.