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Background  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.    Results  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 .    Conclusions  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.

A model for biased fractionation after whole genome duplication