Which locus has the oldest allele? (English) Zbl 0732.92013
Summary: This paper studies aspects of the distribution of nonmutant ancestors of a sample of gametes in a two-locus infinitely-many-alleles model. The ancestral process of two gametes is considered in detail. Included are algorithms for calculating the probability that the oldest allele is from the first locus, and the expected age of the oldest allele. Extensions to an r-locus model in the cases of complete linkage and independence are also studied.
MSC:
| 92D10 | Genetics and epigenetics |
Keywords:
ages of alleles; genealogical process; distribution of nonmutant ancestors; two-locus infinitely-many-alleles model; algorithms; expected age of the oldest allele; r-locus model; complete linkage; independenceReferences:
| [1] | Donnelly, P.: The transient behaviour of the Moran model in population genetics. Math. Proc. Camb. Philos. Soc. 95, 349-358 (1984) · Zbl 0533.92012 · doi:10.1017/S0305004100061624 |
| [2] | Ethier, S. N., Griffiths, R. C.: The neutral two-locus diffusion model as a measure-valued diffusion. Adv. Appl. Prob. 22, 733-786 (1990) · Zbl 0718.92009 |
| [3] | Ethier S. N., Griffiths, R. C.: On the two-locus sampling distribution. J. Math. Biol. 29, 131-159 (1990) · Zbl 0729.92012 · doi:10.1007/BF00168175 |
| [4] | Griffiths, R. C.: Lines of descent in the diffusion approximation of neutral Wright-Fisher models. Theor. Popul. Biol. 17, 37-50 (1980) · Zbl 0434.92011 · doi:10.1016/0040-5809(80)90013-1 |
| [5] | Griffiths, R. C.: The two-locus ancestral graph. In: Basawa, I. V., Taylor, R. L. (eds.) Selected Proceedings of the Symposium on Applied Probability, Sheffield, 1989 · Zbl 0781.92022 |
| [6] | Hudson, R. R.: Properties of a neutral allele model with intragenic recombination. Theor. Popul. Biol. 23, 183-201 (1983) · Zbl 0505.62090 · doi:10.1016/0040-5809(83)90013-8 |
| [7] | Hudson, R. R.: The sampling distribution of linkage disequilibrium under an infinite allele model without selection. Genetics 109, 611-631 (1985) |
| [8] | Hudson, R. R., Kaplan, N. L.: Statistical properties of the number of recombination events in the history of a sample of DNA sequences. Genetics 111, 147-164 (1985) |
| [9] | Kaplan, N. L., Hudson, R. R.: The use of sample genealogies for studying a selectively neutral m-loci model with recombination. Theor. Popul. Biol. 28, 382-396 (1985) · Zbl 0571.92013 · doi:10.1016/0040-5809(85)90036-X |
| [10] | Kingman, J. F. C.: The coalescent. Stochastic Processes Appl. 13, 235-240 (1982) · Zbl 0491.60076 · doi:10.1016/0304-4149(82)90011-4 |
| [11] | Tavaré, S.: Line-of-descent and genealogical processes, and their applications in population genetics models. Theor. Popul. Biol. 26, 119-164 (1984) · Zbl 0555.92011 · doi:10.1016/0040-5809(84)90027-3 |
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