Abstract
Population genetics theory has dealt only with the spatial or geographic pattern of degrees of relatedness or genetic similarity separately for each point in time. However, a frequent goal of experimental studies is to infer migration patterns that occurred in the past or over extended periods of time. To fully understand how a present geographic pattern of genetic variation reflects one in the past, it is necessary to build genealogy models that directly relate the two. For the first time, space-time probabilities of identity by descent and coalescence probabilities are formulated and characterized in this article. Formulations for general migration processes are developed and applied to specific types of systems. The results can be used to determine the level of certainty that genes found in present populations are descended from ancient genes in the same population or nearby populations vs. geographically distant populations. Some parameter combinations result in past populations that are quite distant geographically being essentially as likely to contain ancestors of genes at a given population as the past population located at the same place. This has implications for the geographic point of origin of ancestral, "Eve," genes. The results also form the first model for emerging "space-time" molecular genetic data.
Full Text
The Full Text of this article is available as a PDF (148.7 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Batzer M. A., Arcot S. S., Phinney J. W., Alegria-Hartman M., Kass D. H., Milligan S. M., Kimpton C., Gill P., Hochmeister M., Ioannou P. A. Genetic variation of recent Alu insertions in human populations. J Mol Evol. 1996 Jan;42(1):22–29. doi: 10.1007/BF00163207. [DOI] [PubMed] [Google Scholar]
- Bodmer W. F., Cavalli-Sforza L. L. A migration matrix model for the study of random genetic drift. Genetics. 1968 Aug;59(4):565–592. doi: 10.1093/genetics/59.4.565. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Epperson B. K. Spatial and space-time correlations in systems of subpopulations with genetic drift and migration. Genetics. 1993 Mar;133(3):711–727. doi: 10.1093/genetics/133.3.711. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Malécot G. Heterozygosity and relationship in regularly subdivided populations. Theor Popul Biol. 1975 Oct;8(2):212–241. doi: 10.1016/0040-5809(75)90033-7. [DOI] [PubMed] [Google Scholar]
- Rannala B. The Sampling Theory of Neutral Alleles in an Island Population of Fluctuating Size. Theor Popul Biol. 1996 Aug;50(1):91–104. doi: 10.1006/tpbi.1996.0024. [DOI] [PubMed] [Google Scholar]
- Wright S. Isolation by Distance. Genetics. 1943 Mar;28(2):114–138. doi: 10.1093/genetics/28.2.114. [DOI] [PMC free article] [PubMed] [Google Scholar]