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Nuclear androdioecy and gynodioecy.

J A Vargas¹, R F del Castillo

¹Independent scholar, Constitución 204, (centro), Oaxaca, Oaxaca, México, 68000. javargas1@excite.com

Journal of Mathematical Biology

|September 5, 2003

Summary

This study models the evolution of androdioecy and gynodioecy, revealing conditions for stable sexual polymorphism. Findings show that stable androdioecy is more demanding than gynodioecy under specific pollen conditions.

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Area of Science:

Population genetics
Evolutionary biology
Mathematical modeling

Background:

Understanding the evolution of sexual systems is crucial in population genetics.
Androdioecy and gynodioecy represent complex reproductive strategies with varying stability.
Previous models often assumed constant self-pollination rates, limiting their applicability.

Purpose of the Study:

To develop and analyze novel Mendelian models for androdioecy and gynodioecy.
To investigate the dynamics of sexual polymorphism evolution under different fitness parameters.
To compare new findings with existing models and introduce a generalized fitness concept.

Main Methods:

Formulation of two single-locus Mendelian models with parameters for fertility, selfing, and inbreeder fitness.
Representation of models as rational maps of a 3D zygotic algebra.
Analysis of evolutionary dynamics and convergence to equilibrium points.
Introduction of a general fitness concept and its properties.

Main Results:

Models provide a framework for studying the evolution of androdioecy and gynodioecy.
Identified threshold conditions for the stability of sexual polymorphism.
Demonstrated that genotype fitnesses depend linearly on their frequencies.
Simulations show convergence to higher fitness equilibria, with occasional intermediate fitness decreases.

Conclusions:

The stability conditions for androdioecy are more stringent than for gynodioecy when selfing pollen is negligible.
The developed models offer a more nuanced understanding by assuming constant selfing progeny fraction.
The study introduces a relative measure of population growth computable as an eigenvalue.

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