A generalized two-sex logistic model

Area of Science:

• Mathematical biology
• Population dynamics
• Demography

Background:

• The logistic model is a fundamental tool for population dynamics.
• Existing two-sex models often rely on specific functional forms for demographic rates.
• Understanding population dynamics with varying mating structures is crucial.

Purpose of the Study:

• To generalize the logistic two-sex model to include populations with ephemeral pair-bonds and stable couples.
• To establish a condition for logistic behavior independent of specific fertility, mortality, and mating functions.
• To compare and contrast the generalized model with existing frameworks.

Main Methods:

• Development of a generalized mathematical framework for two-sex population models.
• Analysis of density-dependent fertility and mortality ratios.
• Comparative analysis of model behaviors under different mating assumptions.

Main Results:

• A necessary and sufficient condition for logistic population growth was established.
• The generalized model accommodates both ephemeral and stable pair-bond structures.
• Key differences and similarities between the generalized and traditional models were identified.

Conclusions:

• The generalized logistic two-sex model offers a more flexible approach to population dynamics.
• The identified condition provides a robust criterion for logistic behavior.
• This work advances theoretical population modeling by relaxing restrictive assumptions.