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Related Experiment Videos

The ESS under spatial variation with applications to sex allocation.

S R Proulx1

  • 1Department of Biology, University of Utah, Salt Lake City, Utah 84112, USA. proulx@proulxresearch.org

Theoretical Population Biology
|August 17, 2000
PubMed
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A new evolutionary approximation models variable offspring numbers, revealing that increased offspring variance requires higher mean offspring numbers for evolutionary stability. This impacts evolutionary stable strategies (ESS) and sex allocation, favoring less variable functions.

Area of Science:

  • Evolutionary Biology
  • Population Genetics
  • Mathematical Modeling

Background:

  • Previous models often assume fixed offspring numbers, limiting their applicability to variable reproductive scenarios.
  • Understanding how variance in offspring number affects evolutionary dynamics is crucial for predicting adaptation.
  • Sex allocation strategies are influenced by the relative returns and variability of male and female reproductive functions.

Purpose of the Study:

  • To develop a novel approximation for evolutionary dynamics with variable offspring numbers using the backward Kolmogorov equation.
  • To identify conditions for evolutionary stable strategies (ESS) under variable reproductive success.
  • To apply the model to determine optimal sex allocation strategies when male and female functions have different variances.

Main Methods:

Related Experiment Videos

  • Derivation of a new approximation based on the backward Kolmogorov equation with a fixed population size assumption.
  • Analysis of conditions for accepting increased offspring number variance, requiring compensation by increased mean offspring number.
  • Graphical methods to identify four types of evolutionary stable strategies (ESS).
  • Adaptation of the theory to sex allocation problems with variable returns to male and female function.

Main Results:

  • Individuals must be compensated with increased mean offspring number to accept higher variance in offspring number.
  • Four distinct types of evolutionary stable strategies (ESS) are identified, dependent on population size.
  • Population size can be reinterpreted as deme size in structured populations.
  • The optimal sex allocation strategy involves reducing investment in the more variable sexual function.
  • This reduction in variable function allocation decreases with increasing population size and decreasing variability.

Conclusions:

  • The new approximation provides a robust framework for studying evolution with variable offspring numbers.
  • The findings offer insights into the evolution of reproductive strategies, including sex allocation.
  • Results demonstrate strong congruence with exact matrix models and computer simulations, validating the approximation.