Griffiths–Pakes branching process as a model for evolution of Alu elements

Abstract

Alu 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. Our proposed theoretical neutral model follows a discrete-time branching process described by Griffith 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. A 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. This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

Mathematics Subject Classification (2000): 92D10, 92D15, 92D20, 60J80, 60J85.