Richard A. Neher, Marija Vucelja, Mark Mezard and Boris I. Shraiman
Journal of Statistical Mechanics: Theory and Experiment, vol. 2013, P01008, 2013
In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection, populations consist of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, which is realized for example in the facultatively sexual populations that outcross in only a fraction of reproductive cycles, selection can amplify individual genotypes into large clones. Such clones emerge when the fitness advantage of some of the genotypes is large enough that they grow to a significant fraction of the population despite being broken down by recombination. The occurrence of this ‘clonal condensation’ depends, in addition to the outcrossing rate, on the heritability of fitness. Clonal condensation leads to a strong genetic heterogeneity of the population which is not adequately described by traditional population genetics measures, such as linkage disequilibrium. Here we point out the similarity between clonal condensation and the freezing transition in the random energy model of spin glasses. Guided by this analogy we explicitly calculate the probability, Y , that two individuals are genetically identical as a function of the key parameters of the model. While Y is the analog of the spin-glass order parameter, it is also closely related to rate of coalescence in population genetics: two individuals that are part of the same clone have a recent common ancestor.