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This article is part of the supplement: Selected articles from the Tenth Asia Pacific Bioinformatics Conference (APBC 2012)

Open Access Proceedings

A model for biased fractionation after whole genome duplication

David Sankoff*, Chunfang Zheng and Baoyong Wang

Author Affiliations

Department of Mathematics and Statistics, University of Ottawa, Ottawa K1N 6N5, Canada

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BMC Genomics 2012, 13(Suppl 1):S8  doi:10.1186/1471-2164-13-S1-S8

Published: 17 January 2012



Paralog reduction, the loss of duplicate genes after whole genome duplication (WGD) is a pervasive process. Whether this loss proceeds gene by gene or through deletion of multi-gene DNA segments is controversial, as is the question of fractionation bias, namely whether one homeologous chromosome is more vulnerable to gene deletion than the other.


As a null hypothesis, we first assume deletion events, on either homeolog, excise a geometrically distributed number of genes with unknown mean μ, and a number r of these events overlap to produce deleted runs of length l. There is a fractionation bias 0 ≤ ϕ ≤ 1 for deletions to fall on one homeolog rather than the other. The parameter r is a random variable with distribution π(·). We simulate the distribution of run lengths l, as well as the underlying π(·), as a function of μ, ϕ and θ, the proportion of remaining genes in duplicate form. We show how sampling l allows us to estimate μ and ϕ. The main part of this work is the derivation of a deterministic recurrence to calculate each π(r) as a function of μ, ϕ and θ.


The recurrence for π provides a deeper mathematical understanding of fractionation process than simulations. The parameters μ and ϕ can be estimated based on run lengths of single-copy regions.