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Related Experiment Videos

Eigenvalue effective population numbers for populations that vary cyclically in size.

Edward Pollak1

  • 1Department of Statistics, Iowa State University, Ames, IA 50011-1210, USA. pllk@iastate.edu

Mathematical Biosciences
|April 20, 2002
PubMed
Summary

In population genetics, the eigenvalue effective number (N(eE)) is generally similar to the variance effective number (N(eV)) in large, randomly mating populations. This finding holds for both sexes and includes autosomal and sex-linked genes.

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Area of Science:

  • Population Genetics
  • Quantitative Genetics
  • Evolutionary Biology

Background:

  • Several effective population numbers are used in population genetics to model population dynamics.
  • Previous work by Wang and Pollak established equality of variance, inbreeding, and mutation effective numbers in specific cyclic populations.
  • A special case showed equality between variance effective number (N(eV)) and eigenvalue effective number (N(eE)).

Purpose of the Study:

  • To investigate the general relationship between the eigenvalue effective number (N(eE)) and the variance effective number (N(eV)).
  • To determine if N(eE) is approximately equal to N(eV) under broader conditions than previously shown.
  • To consider both autosomal and sex-linked loci and allow for partial inbreeding.

Main Methods:

Related Experiment Videos

  • Theoretical analysis of population genetics models.
  • Calculation of the largest non-unit eigenvalue of the transition probability matrix for allele frequency changes.
  • Comparison of N(eE) derived from eigenvalues with N(eV) related to the rate of increase in variance between lines.

    • Main Results:

    • The eigenvalue effective number (N(eE)) is shown to be approximately the same as the variance effective number (N(eV)) under general conditions.
    • This approximation holds when the numbers of males and females in the population are consistently large.
    • The results apply to both autosomal and sex-linked genetic loci.

    Conclusions:

    • The eigenvalue effective number provides a generally good approximation for the variance effective number in large populations.
    • This finding simplifies the estimation and interpretation of effective population size in models with large numbers of males and females.
    • The theoretical framework accommodates complex reproductive systems, including partial inbreeding.