Advertisement

Confidence limits for regression relationships between distance matrices: Estimating gene flow with distance

  • Ralph T. ClarkeEmail author
  • Peter Rothery
  • Alan F. Raybould
Article

Abstract

There is growing interest in assessing relation ships between two or more distance matrices, where distances are based on genetic, geographical, and/or environmental measures of dissimilarity for all pairwise combinations of n populations. Methods are developed and assessed for estimating confidence limits for the regression relationship between dependent matrix Y and matrix X and for estimating the value of x given critical y. Methods include a regression mixed model that incorporates an additional population effects variance and a jackknife-by-population regression method that omits the (n −1) distance observations for each population in turn. The approaches are illustrated using data to quantify rates of gene flow with distance between wild plant populations of sea beet and are assessed using simulations.

Key Words

Isolation by distance Jackknife by population Mantel randomization tests Residual maximum likelihood 

References

  1. Curnow, R. N. (1998), “Estimating Genetic Similarities Within and Between Populations,” Journal of Agricultural, Biological, and Environmental Statistics, 3, 347–358.CrossRefMathSciNetGoogle Scholar
  2. Dutilleul, P., Stockwell, J. D., Frigon, D., and Legendre, P. (2000), “The Mantel Test Versus Pearson’s Correlation Analysis: Assessment of the Differences for Biological and Environmental Studies,” Journal of Agricultural, Biological, and Environmental Statistics, 5, 131–150.CrossRefMathSciNetGoogle Scholar
  3. Fieller, E. C. (1954), “Some Problems in Interval Estimation,” Journal of the Royal Statistical Society, Series B, 16, 175–185.zbMATHMathSciNetGoogle Scholar
  4. Gilmour, A. R., Thompson, R., and Cullis, B. R. (1995), “Average Information REML: An Efficient Algorithm for Variance Component Estimation in Linear Mixed Models,” Biometrics, 51, 1440–1450.zbMATHCrossRefGoogle Scholar
  5. Littell, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, Cary, NC: SAS Institute, Inc.Google Scholar
  6. Manly, B. F. J. (1986), “Randomisation and Regression Methods for Testing for Association with Geographical, Environmental and Biological Distances Between Populations,” Researches in Population Ecology, 28, 201–218.CrossRefGoogle Scholar
  7. — (1997), Randomisation, Bootstrap and Monte Carlo Methods in Biology (2nd ed.), London: Chapman and Hall.Google Scholar
  8. Mantel, N. (1967), “The Detection of Disease Clustering and a Generalised Regression Approach,” Cancer Research, 27, 209–220.Google Scholar
  9. Mills, L. S., and Allendorf, F. W. (1996), “The One-Migrant-Per-Generation Rule in Conservation and Management,” Conservation Biology, 10, 1509–1518.CrossRefGoogle Scholar
  10. Patterson, H. D., and Thompson, R. (1971), “Recovery of Inter-Block Information When Block Sizes Are Unequal,” Biometrika, 58, 545–554.zbMATHCrossRefMathSciNetGoogle Scholar
  11. Raybould, A. F., Clarke, R. T., Bond, J. M., Welters, R. E., and Gliddon, C. J. (in press), “Inferring Patterns of Dispersal From Allele Frequency Data,” in Dispersal Ecology, eds. J. M. Bullock, R. E. Kenward, and R. S. Hails, Oxford: Blackwell.Google Scholar
  12. Raybould, A. F., Mogg, R. J., and Gliddon, C. J. (1997), “The Genetic Structure of Sea Beet (Beta vulgaris ssp. maritima) Populations. II. Differences in Gene Flow Estimated From RFLP and Isozyme Loci Are Habitat-Specific,” Heredity, 78, 532–538.CrossRefGoogle Scholar
  13. Satterthwaite, F. E. (1946), “An Approximate Distribution of Estimates of Variance Components,” Biometrics, 2, 110–114.CrossRefGoogle Scholar
  14. Slatkin, M. (1985), “Gene Flow in Natural Populations,” Annual Review of Ecology and Systematics, 16, 393–430.CrossRefGoogle Scholar
  15. — (1993), “Isolation by Distance in Equilibrium and Non-Equilibrium Populations,” Evolution, 47, 264–279.CrossRefGoogle Scholar
  16. Tukey, J. W. (1958), “Bias and Confidence in Not Quite Large Enough Samples” (abstract), Annals of Mathematical Statistics, 29, 614.CrossRefGoogle Scholar
  17. Weir, B. S., and Cockerham, C. C. (1984), “Estimating F-Statistics for the Analysis of Population Structure,” Evolution, 38, 1358–1370.CrossRefGoogle Scholar
  18. Wright, S. (1931), “Evolution in Mendelian Populations,” Genetics, 16, 97–159.Google Scholar
  19. — (1943), “Isolation by Distance,” Genetics, 28, 114–138.Google Scholar

Copyright information

© International Biometric Society 2002

Authors and Affiliations

  • Ralph T. Clarke
    • 1
    Email author
  • Peter Rothery
    • 2
  • Alan F. Raybould
    • 1
  1. 1.Centre for Ecology and Hydrology DorsetWinfrith Technology CentreDorchesterU.K.
  2. 2.Centre for Ecology and Hydrology Monks WoodHuntingdonU.K.

Personalised recommendations