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. 1993 Mar;133(3):711–727. doi: 10.1093/genetics/133.3.711

Spatial and Space-Time Correlations in Systems of Subpopulations with Genetic Drift and Migration

B K Epperson 1
PMCID: PMC1205354  PMID: 8454211

Abstract

The geographic distribution of genetic variation is an important theoretical and experimental component of population genetics. Previous characterizations of genetic structure of populations have used measures of spatial variance and spatial correlations. Yet a full understanding of the causes and consequences of spatial structure requires complete characterization of the underlying space-time system. This paper examines important interactions between processes and spatial structure in systems of subpopulations with migration and drift, by analyzing correlations of gene frequencies over space and time. We develop methods for studying important features of the complete set of space-time correlations of gene frequencies for the first time in population genetics. These methods also provide a new alternative for studying the purely spatial correlations and the variance, for models with general spatial dimensionalities and migration patterns. These results are obtained by employing theorems, previously unused in population genetics, for space-time autoregressive (STAR) stochastic spatial time series. We include results on systems with subpopulation interactions that have time delay lags (temporal orders) greater than one. We use the space-time correlation structure to develop novel estimators for migration rates that are based on space-time data (samples collected over space and time) rather than on purely spatial data, for real systems. We examine the space-time and spatial correlations for some specific stepping stone migration models. One focus is on the effects of anisotropic migration rates. Partial space-time correlation coefficients can be used for identifying migration patterns. Using STAR models, the spatial, space-time, and partial space-time correlations together provide a framework with an unprecedented level of detail for characterizing, predicting and contrasting space-time theoretical distributions of gene frequencies, and for identifying features such as the pattern of migration and estimating migration rates in experimental studies of genetic variation over space and time.

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Selected References

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  1. Barbujani G. Autocorrelation of gene frequencies under isolation by distance. Genetics. 1987 Dec;117(4):777–782. doi: 10.1093/genetics/117.4.777. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Fix A. G. The role of kin-structured migration in genetic microdifferentiation. Ann Hum Genet. 1978 Jan;41(3):329–339. doi: 10.1111/j.1469-1809.1978.tb01900.x. [DOI] [PubMed] [Google Scholar]
  3. Fleming W. H., Su C. H. Some one-dimensional migration models in population genetics theory. Theor Popul Biol. 1974 Jun;5(3):431–449. doi: 10.1016/0040-5809(74)90062-8. [DOI] [PubMed] [Google Scholar]
  4. Kimura M, Weiss G H. The Stepping Stone Model of Population Structure and the Decrease of Genetic Correlation with Distance. Genetics. 1964 Apr;49(4):561–576. doi: 10.1093/genetics/49.4.561. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Maruyama T. A Markov process of gene frequency change in a geographically structured population. Genetics. 1974 Feb;76(2):367–377. doi: 10.1093/genetics/76.2.367. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Morton N. E. Estimation of demographic parameters from isolation by distance. Hum Hered. 1982;32(1):37–41. doi: 10.1159/000153255. [DOI] [PubMed] [Google Scholar]
  7. Nagylaki T. The decay of genetic variability in geographically structured populations. Proc Natl Acad Sci U S A. 1974 Aug;71(8):2932–2936. doi: 10.1073/pnas.71.8.2932. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Nagylaki T. The strong-migration limit in geographically structured populations. J Math Biol. 1980 Apr;9(2):101–114. doi: 10.1007/BF00275916. [DOI] [PubMed] [Google Scholar]
  9. Rogers A. R. Three components of genetic drift in subdivided populations. Am J Phys Anthropol. 1988 Dec;77(4):435–449. doi: 10.1002/ajpa.1330770405. [DOI] [PubMed] [Google Scholar]
  10. Sawyer S., Felsenstein J. A continuous migration model with stable demography. J Math Biol. 1981 Feb;11(2):193–205. doi: 10.1007/BF00275442. [DOI] [PubMed] [Google Scholar]
  11. Smith C. A. Local fluctuations in gene frequencies. Ann Hum Genet. 1969 Jan;32(3):251–260. doi: 10.1111/j.1469-1809.1969.tb00074.x. [DOI] [PubMed] [Google Scholar]
  12. Sokal R. R., Smouse P. E., Neel J. V. The genetic structure of a tribal population, the Yanomama Indians. XV. Patterns inferred by autocorrelation analysis. Genetics. 1986 Sep;114(1):259–287. doi: 10.1093/genetics/114.1.259. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. 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]

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