A glass transition in population genetics: Emergence of clones in populations

TYPEBio-Physics Seminar
Speaker:Marija Vucelja
Affiliation:Courant Institute of Mathematical Sciences, NYU
Time:14:30 - 15:30
Location:Lidow 724
Abstract:Recombination reshuffles genetic material, while selection amplifies the fittest genotypes. If recombination is more rapid than selection, a population consists of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime selection can amplify individual genotypes into large clones. The occurrence of this "clonal condensation" depends, in addition to the ratio of recombination and selection rates, on the heritability of fitness (expected number of offspring). Clonal condensation is an important phenomenon, present in many populations, that has not been captured by traditional population genetics measures (linkage disequilibrium). I hope to convince you that our work provides a qualitative explanation of clonal condensation. In my talk I will point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. Guided by this analogy I will derive one of the key quantities of interest: the probability that two individuals are genetically identical. This quantity is the analog of the spin-glass order parameter and 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. Next I will analyze the phase space spanned by time, heritability and the ratio of recombination and selection rates. I will conclude with a summary of our present understanding of the clonal condensation phenomena and describe future directions.