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Gene frequency changes and a per-generation time-scale for continuous-time populations with arbitrary size

Ola Hössjer1, Warren Ewens2

  • 1Department of Mathematics, Stockholm University, Stockholm, Sweden.

Evolution; International Journal of Organic Evolution
|March 9, 2026
PubMed
Summary

This study refines the continuous-time theory of allele frequency change under natural selection. It introduces a new model addressing limitations in population size variation and generation concepts for Mendelian populations.

Keywords:
Malthusian parametersallele frequency changebirth ratescontinuous-time modelsdeath ratesper-generation time-scale

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Area of Science:

  • Population Genetics
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Calculating allele frequency change over time is crucial for understanding natural selection's effects in Mendelian populations.
  • Current continuous-time theories for allele frequency change under natural selection have limitations regarding population size dynamics and generational concepts.

Purpose of the Study:

  • To analyze the limitations of the existing continuous-time theory of allele frequency change.
  • To propose a new, more comprehensive self-contained theory for allele frequency change in Mendelian populations.

Main Methods:

  • Analysis of the accepted continuous-time theory of allele frequency change.
  • Development of a new theoretical framework for allele frequency dynamics.

Main Results:

  • The current theory is incomplete, particularly concerning population size variations and the concept of generations.
  • A novel self-contained theory is proposed to overcome these limitations.

Conclusions:

  • The proposed theory offers a more robust framework for studying allele frequency dynamics under natural selection.
  • This advancement is vital for accurate modeling of evolutionary processes in large, monoecious diploid populations.