On some models of fertility selection

Area of Science:

• Population genetics
• Mathematical modeling
• Evolutionary biology

Background:

• Fertility is a key factor in population dynamics and evolutionary processes.
• Understanding genetic control of fertility is crucial for predicting population behavior.
• Previous models often assumed symmetric fertility systems.

Purpose of the Study:

• To investigate additive, multiplicative, and symmetric models of fertility controlled by a diallelic gene.
• To analyze the equilibrium and stability of these fertility systems.
• To determine conditions under which different fertility models are equivalent.

Main Methods:

• Development and analysis of mathematical models for fertility.
• Equilibrium and local stability analysis of genetic models.
• Comparison of additive, multiplicative, and symmetric fertility systems.

Main Results:

• Complete equilibrium and local stability analysis is feasible for symmetric fertility systems.
• Demonstrated that asymmetric equilibria can be stable, challenging previous conjectures.
• Derived conditions for the equivalence of multiplicative and symmetric fertility models.

Conclusions:

• The study provides new insights into the stability of equilibria in genetic fertility models.
• The findings have implications for understanding population dynamics and evolution under different genetic scenarios.
• The equivalence conditions offer a simplified approach to analyzing certain multiplicative fertility models.