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Evolutionary principles for polynomial models of frequency-dependent selection.

J W Curtsinger1

  • 1Department of Genetics and Cell Biology, University of Minnesota, 1445 Gortner Avenue, St. Paul, MN 55108.

Proceedings of the National Academy of Sciences of the United States of America
|May 1, 1984
PubMed
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This study analyzes frequency-dependent selection models, revealing that allelic frequencies stabilize at equilibria. A new function, T(q), approximates genetic variance and defines evolutionary landscapes.

Area of Science:

  • Population Genetics
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Frequency-dependent selection significantly impacts allele frequency dynamics.
  • Understanding evolutionary landscapes is crucial for predicting population trajectories.

Purpose of the Study:

  • To analyze a deterministic model of frequency-dependent selection.
  • To explore the behavior of allelic frequencies under polynomial fitness functions.
  • To define evolutionary landscapes for complex selection models.

Main Methods:

  • Analysis of a one-locus, two-allele deterministic model.
  • Modeling genotypic fitnesses as nth-degree polynomial functions of allelic frequency (q).
  • Investigation of conditions for monotonic convergence to stable equilibria.

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Main Results:

  • Allelic frequencies converge monotonically to stable equilibria under specific conditions.
  • A function T(q) was identified, nondecreasing and maximized at stable equilibria.
  • The rate of change of T(q) approximates additive genetic variance in fitness.

Conclusions:

  • The study defines evolutionary landscapes for complex selection processes.
  • Results extend Wright's mean fitness principle and Fisher's fundamental theorem.
  • The function T(q) provides insights into evolutionary dynamics and selection modes.