Iteroparous reproduction strategies and population dynamics

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Continuous partial differential equations and discrete matrix models are used to study population dynamics.
• Iteroparous populations, characterized by reproduction at specific equidistant ages, present unique modeling challenges.
• Understanding density-dependent mortality and environmental factors is crucial for accurate population predictions.

Purpose of the Study:

• To derive asymptotic relationships between continuous population models and discrete matrix equations for iteroparous populations.
• To investigate the convergence of discrete population models to steady-state age distributions.
• To explore the influence of the iteroparous vital ratio on population dynamics and model convergence.

Main Methods:

• Development of a discrete population matrix model incorporating reproductive information and density-dependent mortality.
• Analysis of continuous-time population dynamics and their relation to the steady-state solution.
• Mathematical derivation of asymptotic behaviors for discrete models based on the vital ratio.

Main Results:

• A discrete matrix model was constructed for iteroparous populations with juvenile and adult stages.
• Convergence to steady-state age distribution in discrete models depends on the iteroparous vital ratio.
• Rational vital ratios lead to periodic dynamics and finite cohorts, while irrational ratios approximate steady-state convergence with infinite cohorts.

Conclusions:

• The iteroparous vital ratio is a fundamental parameter governing the convergence of discrete population models.
• Discrete event reproduction models may not always converge to a steady-state age distribution.
• The developed matrix model aids in clarifying numerical results for continuous density and delta measure age distribution models, with applications in ecotoxicology.