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.
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References
Athreya, K.B., Ney, P.E.: Branching Processes. Dover Publications, Inc., Mineola: New York (2004)
Batzer, M.A., Deininger, P.L.: Alu repeats and human genomic diversity. Nat. Rev. Genet. 3, 370–380 (2004)
Griffiths, R.C., Pakes, A.G.: An infinite-alleles version of the simple branching process. Adv. Appl. Probab. 20 (3), 489–524 (1988)
Kimmel, M., Matthaes, M.: Modeling neutral evolution of Alu elements using a branching process. BMC Genomics 11 (suppl 1): s11 (2010)
Lander, E.S., Linton, L.M., Birren, B., Nusbaum, C., Zody, M.C., Baldwin, J., Devon, K., Dewar, K., Doyle, M., FitzHugh, W. et al.: Initial sequencing and analysis of the human genome. Nature 40 (6822), 860–921 (2001)
Mills, R.E., Bennett, E.A., Iskow, R.C., Devine, S.E.: Which transposable elements are active in the human genome? Trends Genet. 23 (4), 183–191 (2007)
Acknowledgements
The authors acknowledge the generous contribution of Dr. Jerzy Jurka of the Genetic Information Research Institute (GIRI) who kindly supplied all Alu sequences employed in this study, together with invaluable advice. Anthony Pakes of the School of Mathematics and Statistics of the University of Western Australia provided helpful comments concerning the Griffiths-Pakes process.
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Kimmel, M., Mathaes, M. (2010). Griffiths–Pakes branching process as a model for evolution of Alu elements. In: González Velasco, M., Puerto, I., Martínez, R., Molina, M., Mota, M., Ramos, A. (eds) Workshop on Branching Processes and Their Applications. Lecture Notes in Statistics(), vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11156-3_13
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DOI: https://doi.org/10.1007/978-3-642-11156-3_13
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