Abstract
BackgroundAlu elements occupy about eleven percent of the human genome and are still growing in copy numbers. Since Alu elements substantially impact the shape of our genome, there is a need for modeling the amplification, mutation and selection forces of these elements.MethodsOur proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes. From this model, we derive a limit frequency spectrum of the Alu element distribution, which serves as the theoretical, neutral frequency to which real Alu insertion data can be compared through statistical goodness of fit tests. Departures from the neutral frequency spectrum may indicate selection.ResultsA comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.ConclusionsThis observation suggests that Alu sequences do not evolve neutrally and might be under selection.
Highlights
Introduction and backgroundHuman genome is a result of 109 years of evolution
We present a mathematical random process, the Griffiths-Pakes discrete-time branching process with infinite-allele mutations, which is almost ideally suited for modeling of Alu elements proliferation
The outcome is interesting in the sense that a generally plausible fit is obtained to the Alu element frequency distribution
Summary
Discrete branching process of Griffiths and Pakes with infinite allele mutations Branching processes have been widely used in modeling cell population dynamics. If an individual produces j offspring the number of progeny having the parental allele is distributed binomially with parameters j and 1 - μ, its pgf is equal to (μ + (1 - μ)s)j This implies that any new allele is followed by a branching process of its like-type descendants with offspring pgf H(s) = f(μ + (1 - μ)s). Let us denote Ψj the long-term expected proportion of alleles with frequency j ≥ 1, which is the formula that we will use to compute the theoretical distribution of Alu allele classes for given offspring pgfs.
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