The long-term effects of time-dependent maternity behavior.

Area of Science:

• Mathematical Biology
• Population Dynamics
• Demography

Background:

• Integral population models are crucial for understanding population dynamics.
• The Sharpe and Lotka model provides a framework for analyzing population growth.
• Variations in maternity functions can complicate long-term population predictions.

Purpose of the Study:

• To investigate the impact of time-varying maternity functions on population model predictions.
• To determine conditions under which standard analytical methods remain valid.
• To explore extensions for piecewise time-dependent maternity functions and population management.

Main Methods:

• Utilizing the integral population model of Sharpe and Lotka.
• Analyzing the effects of time variation solely on the parent population.
• Applying recent extensions for exponential time dependence (Cerone and Keane).

Main Results:

• Standard methods for determining long-term population behavior are applicable when time variation affects only the parent population.
• These methods remain valid even with explicit time dependence in the net maternity function before the minimum childbearing age.
• Piecewise time-dependent net maternity functions can be defined, and their long-term behavior determined.

Conclusions:

• The study validates the use of standard techniques for population models with specific time-dependent maternity functions.
• It provides a method for analyzing populations with complex, piecewise time-varying reproductive rates.
• The findings offer insights into population management strategies for achieving desired population sizes.