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Related Concept Videos

Hardy-Weinberg Principle01:49

Hardy-Weinberg Principle

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.In the early 20th century,...
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Maximization principles for frequency-dependent selection I: the one-locus two-allele case.

Kristan A Schneider1

  • 1Department of Mathematics, University of Vienna, Nordbergstrasse 15, UZA 4, A-1090 Vienna, Austria. kristan.schneider@univie.ac.at

Theoretical Population Biology
|August 30, 2008
PubMed
Summary

This study explores frequency-dependent selection models, revealing that positive symmetric interactions ensure population fitness increases monotonically. Negative or asymmetric interactions introduce complex dynamics, preventing guaranteed convergence to equilibrium.

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Area of Science:

  • Population Genetics
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Frequency-dependent selection is a key evolutionary mechanism.
  • Understanding its dynamics is crucial for predicting population trajectories.
  • Maximization principles offer a framework for analyzing evolutionary models.

Purpose of the Study:

  • To establish conditions for maximization principles in frequency-dependent selection models.
  • To systematically analyze the dynamical behavior of the pairwise-interaction model.
  • To investigate the impact of interaction coefficients on population dynamics.

Main Methods:

  • Analysis of the one-locus, two-allele pairwise-interaction model.
  • Examination in both discrete and continuous time frameworks.
  • Derivation of necessary and sufficient conditions for maximization principles.

Main Results:

  • Mean population fitness is nondecreasing under symmetric, positive interaction coefficients.
  • Monotonic convergence to equilibria is guaranteed with symmetric, positive interactions.
  • Asymmetric interactions and negative coefficients can lead to complex dynamics, including limit cycles in discrete time.

Conclusions:

  • Maximization principles are valid under specific conditions related to interaction coefficients.
  • The nature of interactions (symmetric, asymmetric, positive, negative) critically determines model dynamics.
  • The study provides a comprehensive framework for understanding frequency-dependent selection models.