Background: Fractionation is the genome-wide process of losing one gene per duplicate pair following whole genome multiplication (doubling, tripling, …). This is important in the evolution of plants over tens of millions of years, because of their repeated cycles of genome multiplication and fractionation. One type of evidence in the study of these processes is the frequency distribution of similarities between the two genes, over all the duplicate pairs in the genome.
Results: We study modeling and inference problems around the processes of fractionation and whole genome multiplication focusing first on the frequency distribution of similarities of duplicate pairs in the genome. Our birth-and-death model accounts for repeated duplication, triplication or other multiplication events, as well as fractionation rates among multiple progeny of a single gene specific to each event. It also has a biologically and combinatorially well-motivated way of handling the tendency for at least one sibling to survive fractionation. The method settles previously unexplored questions about the expected number of gene pairs tracing their ancestry back to each multiplication event. We exemplify the algebraic concepts inherent in our models and on Brassica rapa, whose evolutionary history is well-known. We demonstrate the quantitative analysis of high-similarity gene pairs and triples to confirm the known ploidies of events in the lineage of B. rapa.
Conclusions: Our birth-and-death model accounts for the similarity distribution of paralogs in terms of multiple rounds of whole genome multiplication and fractionation. An analysis of high-similarity gene triples confirms the recent Brassica triplication.
Keywords: Birth and death process; Brassica rapa; Gene loss; Multinomial model; Paralog gene tree; Sequence divergence; Whole genome duplication.