The ESS under spatial variation with applications to sex allocation

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:

• 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.