Frequency distributions in population genetics parallel those in statistical physics

A class of problems from statistical physics is discussed that is shown to be identical to a class of problems in population genetics. The mathematical treatment of these problems has arisen independently in the two subjects. The important results of both literatures are presented here, together with cross references. In each case there is a stochastic process generating a set of variables xi that satisfy tsumixi=1. For example, the xi may represent the weights of valleys in a spin glass, the sizes of attractors in dynamical systems, the frequency of different alleles in a population, or the sizes of different families in a genealogical tree. The frequency distributions f(x) of the valleys or alleles are calculated, together with the distribution Π(Y) of the quantity Y=tsumixi2. The distribution Π(Y) can be written as a sum of universal functions Πk(Y) that are independent of the parameters of the problem. It is shown that the rather abstract concepts in the physical models are directly related to observables that are experimentally measurable in biology.