The Similarity Distribution of Paralogous Gene Pairs Created by Recurrent Alternation of Polyploidization and Fractionation

We study modeling and inference problems around the process of fractionation, or the genome-wide process of losing one gene per duplicate pair following whole genome doubling (WGD), motivated by the evolution of plants over many tens of millions of years, with their repeated cycles of genome doubling and fractionation. We focus on the frequency distribution of similarities between the two genes, over all the duplicate pairs in the genome. Our model is fully general, accounting for repeated duplication, triplication or other k-tupling events (all subsumed under the term WGD), as well as a general fractionation rate in any time period among multiple progeny of a single gene. It also has a biologically and combinatorially well-motivated way of handling the tendency for at least one sibling to survive fractionation. We show how the method reduces to previously proposed models for special cases, and settles unresolved questions about the expected number of gene pairs tracing their ancestry back to each WGD event.