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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,...
Frequency-dependent Selection01:21

Frequency-dependent Selection

When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to as frequency-dependent selection. Frequency-dependent selection may occur between species or within a single species. This type of selection can either be positive—with more common phenotypes having higher fitness—or negative, with rarer phenotypes conferring increased fitness.Positive Frequency-Dependent SelectionIn positive...
Multiple Allele Traits01:49

Multiple Allele Traits

The Concept of Multiple Allelism
Multiple Allele Traits01:49

Multiple Allele Traits

The Concept of Multiple Allelism
Types of Selection01:46

Types of Selection

Natural selection influences the frequencies of particular alleles and phenotypes within populations in several different ways. Primarily, natural selection can be directional, stabilizing, or disruptive. Directional selection favors one extreme trait and shifts the population towards that phenotype while selecting against individuals displaying alternate traits. Stabilizing selection favors an intermediate trait with a narrow range of variation. Deviation from the optimal phenotype towards an...
Inclusive Fitness00:57

Inclusive Fitness

Most altruistic behavior—in which one animal helps another at a cost to themselves—occurs between relatives. Scientists think these altruistic behaviors evolved because they increase the inclusive fitness of the animal providing help.

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Related Experiment Video

Updated: Jun 20, 2026

Navigating MARRVEL, a Web-Based Tool that Integrates Human Genomics and Model Organism Genetics Information
09:37

Navigating MARRVEL, a Web-Based Tool that Integrates Human Genomics and Model Organism Genetics Information

Published on: August 15, 2019

Maximization principles for frequency-dependent selection II: the one-locus multiallele case.

Kristan Alexander Schneider1

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

Journal of Mathematical Biology
|August 27, 2009
PubMed
Summary
This summary is machine-generated.

This study explores population genetics models, focusing on pairwise-interaction models (PIM) and density-dependent models (D-PIM). It establishes conditions for evolutionary principles like Fisher

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Area of Science:

  • Population Genetics
  • Mathematical Biology
  • Evolutionary Dynamics

Background:

  • The study investigates frequency-dependent selection in population genetics.
  • It focuses on pairwise-interaction models (PIM) and density-dependent models (D-PIM).
  • The research extends existing models to single-locus multiallele scenarios in discrete and continuous time.

Purpose of the Study:

  • To establish necessary and sufficient conditions for maximization principles analogous to Fisher's Fundamental Theorem.
  • To analyze the behavior of mean fitness and related quantities in PIM and D-PIM.
  • To provide a systematic analysis with concrete examples.

Main Methods:

  • Analysis of single-locus multiallele PIM in discrete and continuous time.
  • Investigation of density-dependent PIM (D-PIM) in continuous time.
  • Derivation of conditions for nondecreasing mean and adjusted-mean fitness.

Main Results:

  • In discrete time, mean fitness is nondecreasing for non-negative, symmetric interactions in PIM.
  • For asymmetric interactions, adjusted-mean fitness is nondecreasing under pseudo-symmetric conditions.
  • In continuous time, stronger results are found, with adjusted-mean fitness nondecreasing in D-PIM for pseudo-symmetric interactions.

Conclusions:

  • Maximization principles analogous to Fisher's theorem can be extended to PIM and D-PIM under specific conditions.
  • The concept of adjusted-mean fitness is crucial for understanding evolutionary dynamics with asymmetric interactions.
  • The findings provide a theoretical framework for analyzing complex frequency-dependent selection scenarios.