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Ancestral processes for non-neutral models of complex diseases. (English) Zbl 1104.92043

Summary: We consider non-neutral models for unlinked loci, where the fitness of a chromosome or individual is not multiplicative across loci. Such models are suitable for many complex diseases, where there are gene-interactions. We derive a genealogical process for such models, called the complex selection graph (CSG). This coalescent-type process is related to the ancestral selection graph, and is derived from the ancestral influence graph by considering the limit as the recombination rate between loci gets large.
We analyse the CSG both theoretically and via simulation. The main results are that the gene-interactions do not produce linkage disequilibrium, but do produce dependencies in allele frequencies between loci. For small selection rates, the distributions of the genealogy and the allele frequencies at a single locus are well-approximated by their distributions under a single locus model, where the fitness of each allele is the average of the true fitnesses of that allele with respect to the distribution of alleles at other loci.

MSC:

92D10 Genetics and epigenetics
92C50 Medical applications (general)
60J99 Markov processes
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[1] Cordell, H. J.; Todd, J. A.; Hill, N. J.; Lyons, P. A.; Peterson, L. B.; Wicker, L. S.; Clayton, D. G., Statistical modeling of interlocus interactions in a complex diseaserejection of the multiplicative model of epistasis in type 1 diabetes, Genetics, 158, 357-367 (2001)
[2] Donnelly, P.; Kurtz, T., Genealogical processes for Fleming-Viot models with selection and recombination, Ann. Appl. Probab., 9, 1091-1148 (1999) · Zbl 0964.60075
[3] Fearnhead, P., Perfect simulation from population genetic models with selection, Theoret. Popul. Biol., 59, 263-279 (2001) · Zbl 1045.92034
[4] Fearnhead, P., 2002. Haplotypes: the joint distribution of alleles at linked loci. J. Appl. Probab., submitted (Available from http://www.maths.lancs.ac.uk/ fearnhea/; Fearnhead, P., 2002. Haplotypes: the joint distribution of alleles at linked loci. J. Appl. Probab., submitted (Available from http://www.maths.lancs.ac.uk/ fearnhea/ · Zbl 1028.92018
[5] Griffiths, R. C.; Marjoram, P., Ancestral inference from samples of DNA sequences with recombination, J. Comput. Biol., 3, 479-502 (1996)
[6] Griffiths, R. C.; Marjoram, P., An ancestral recombination graph, (Donnelly, P.; Tavaré, S., IMA Volume on Mathematical Population Genetics (1996), Springer: Springer Berlin), 257-270 · Zbl 0893.92020
[7] Griffiths, R. C.; Tavaré, S., Ancestral inference in population genetics, Statist. Sci., 9, 307-319 (1994) · Zbl 0955.62644
[8] Hartl, D. L.; Clark, A. G., Principles of Population Genetics (1997), Singauer Associates Inc: Singauer Associates Inc Sunderland, MA
[9] Hudson, R. R., Gene genealogies and the coalescent process, (Futuyma, D.; Antonovics, J., Oxford Surveys in Evolutionary Biology, Vol. 7 (1990), Oxford University Press: Oxford University Press New York), 1-44
[10] Kingman, J. F.C., The coalescent, Stochastic Processes Appl., 13, 235-248 (1982) · Zbl 0491.60076
[11] Krone, S. M.; Neuhauser, C., Ancestral processes with selection, Theoret. Popul. Biol., 51, 210-237 (1997) · Zbl 0910.92024
[12] Neuhauser, C.; Krone, S. M., The genealogy of samples in models with selection, Genetics, 145, 519-534 (1997)
[13] Niu, T. H.; Xu, X. P.; Cordell, H. J.; Rogus, J.; Zhou, Y. S.; Fang, Z.; Lindpaintner, K., Linkage analysis of candidate genes and gene-gene interactions in Chinese hypertensive sib pairs, Hypertension, 33, 1332-1337 (1999)
[14] Pritchard, J. K., Are rare variants responsible for susceptibility to complex diseases?, Am. J. Human Genet., 69, 124-137 (2001)
[15] Propp, J. G.; Wilson, D. B., Exact sampling with coupled Markov chains and applications to statistical mechanics, Random Struct. Algorithms, 9, 223-252 (1996) · Zbl 0859.60067
[16] Risch, N., Linkage strategies for genetically complex traits. I. Multilocus models, Am. J. Human Genet., 46, 222-228 (1990)
[17] Risch, N.; Merikangas, K., The future of genetics studies of complex human diseases, Science, 273, 1516-1517 (1996)
[18] Wiesch, D. G.; Meyers, D. A.; Bleecker, E. R., Genetics of asthma, J. Allergy Clin. Immunol., 104, 895-901 (1999)
[19] Wright, S., Adaption and selection, (Jepson, G. L.; Simpson, G. G.; Mayr, E., Genetics, Paleontology and Evolution (1949), Princeton University Press: Princeton University Press Princeton, NJ), 365-389
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