Skip to main content
Log in

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

  • Published:
Journal of Agricultural, Biological, and Environmental Statistics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Curnow, R. N. (1998), “Estimating Genetic Similarities Within and Between Populations,” Journal of Agricultural, Biological, and Environmental Statistics, 3, 347–358.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Fieller, E. C. (1954), “Some Problems in Interval Estimation,” Journal of the Royal Statistical Society, Series B, 16, 175–185.

    MATH  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • — (1997), Randomisation, Bootstrap and Monte Carlo Methods in Biology (2nd ed.), London: Chapman and Hall.

    Google Scholar 

  • Mantel, N. (1967), “The Detection of Disease Clustering and a Generalised Regression Approach,” Cancer Research, 27, 209–220.

    Google Scholar 

  • Mills, L. S., and Allendorf, F. W. (1996), “The One-Migrant-Per-Generation Rule in Conservation and Management,” Conservation Biology, 10, 1509–1518.

    Article  Google Scholar 

  • Patterson, H. D., and Thompson, R. (1971), “Recovery of Inter-Block Information When Block Sizes Are Unequal,” Biometrika, 58, 545–554.

    Article  MATH  MathSciNet  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • Satterthwaite, F. E. (1946), “An Approximate Distribution of Estimates of Variance Components,” Biometrics, 2, 110–114.

    Article  Google Scholar 

  • Slatkin, M. (1985), “Gene Flow in Natural Populations,” Annual Review of Ecology and Systematics, 16, 393–430.

    Article  Google Scholar 

  • — (1993), “Isolation by Distance in Equilibrium and Non-Equilibrium Populations,” Evolution, 47, 264–279.

    Article  Google Scholar 

  • Tukey, J. W. (1958), “Bias and Confidence in Not Quite Large Enough Samples” (abstract), Annals of Mathematical Statistics, 29, 614.

    Article  Google Scholar 

  • Weir, B. S., and Cockerham, C. C. (1984), “Estimating F-Statistics for the Analysis of Population Structure,” Evolution, 38, 1358–1370.

    Article  Google Scholar 

  • Wright, S. (1931), “Evolution in Mendelian Populations,” Genetics, 16, 97–159.

    Google Scholar 

  • — (1943), “Isolation by Distance,” Genetics, 28, 114–138.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ralph T. Clarke.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Clarke, R.T., Rothery, P. & Raybould, A.F. Confidence limits for regression relationships between distance matrices: Estimating gene flow with distance. JABES 7, 361–372 (2002). https://doi.org/10.1198/108571102320

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1198/108571102320

Key Words

Navigation