Fractionation statistics

Abstract

BackgroundParalog 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.ResultsAs a null hypothesis, we first assume deletion events, on one homeolog only, excise a geometrically distributed number of genes with unknown mean µ, and these events combine to produce deleted runs of length l, distributed approximately as a negative binomial with unknown parameter r, itself a random variable with distribution π(·). A more realistic model requires deletion events on both homeologs distributed as a truncated geometric. We simulate the distribution of run lengths l in both models, as well as the underlying π(r), as a function of µ, and show how sampling l allows us to estimate µ. We apply this to data on a total of 15 genomes descended from 6 distinct WGD events and show how to correct the bias towards shorter runs caused by genome rearrangements. Because of the difficulty in deriving π(·) analytically, we develop a deterministic recurrence to calculate each π(r) as a function of µ and the proportion of unreduced paralog pairs.ConclusionsThe parameter µ can be estimated based on run lengths of single-copy regions. Estimates of µ in real data do not exclude the possibility that duplicate gene deletion is largely gene by gene, although it may sometimes involve longer segments.

A Model for Biased Fractionation after Whole Genome Duplication

“…Whether we work with G and H on an interval of ℤ of length 100,000 or, as previously [8], length 300,000, gives virtually the same results. Figure 2 shows the relationship, for three values of the fractionation bias j and for a range of values of μ, between the proportion of genes deleted, on one chromosome or the other, and the average run length.…”

“…In this paper, we present a detailed version of the excision model of fractionation with geometrically distributed deletion lengths, for which we previously analyzed a tractable, but biologically unrealistic, special case [8]. The key problem in this field is to determine μ, the mean of the hypothesized geometric distribution ρ( 1 μ , .…”

Structural vs. functional mechanisms of duplicate gene loss following whole genome doubling

“…The "skipping" procedure, introduced in [ 6 ], is a natural way to model the deletion process, since deletion of part of a chromosome and the subsequent rejoining of the chromosome directly before and directly after the deleted fragment means that this fragment is no longer "visible" to the deletion process. As observers, however, we have a record of the deleted genes, as one copy of each gene must be retained in the genome.…”

A model for biased fractionation after whole genome duplication

“…In this paper, we present a detailed version of the excision model of fractionation with geometrically distributed deletion lengths, for which we previously analyzed a tractable, but biologically unrealistic, special case [8]. The key problem in this field is to determine μ , the mean of the hypothesized geometric distribution $\rho \left(\frac{1}{\mu }MathClass-punc,MathClass-punc.\right)$, since this bears directly on the main biological question of the relative importance of random excision versus gene-by-gene inactivation.…”