Technique to derive discrete population models with delayed growth.

Area of Science:

• Population dynamics
• Mathematical biology
• Ecological modeling

Background:

• Traditional population models often simplify the maturation process.
• Accounting for the time lag and survival of immature individuals is crucial for realistic population dynamics.

Purpose of the Study:

• To develop a procedure for deriving discrete population models with maturation delays.
• To investigate the impact of delay duration on population stability and extinction.
• To apply the procedure to create and analyze Beverton-Holt and Ricker adult models.

Main Methods:

• Derivation of discrete population models incorporating a delay period for immature individuals.
• Inclusion of survival probability for immature individuals during the delay.
• Analysis of model properties, including critical delay thresholds.
• Application to Beverton-Holt and Ricker models for global dynamics analysis.

Main Results:

• A procedure for deriving discrete delay-differential population models was established.
• A critical delay threshold was identified, beyond which population extinction occurs.
• The derived Beverton-Holt and Ricker adult models exhibit distinct dynamic behaviors.

Conclusions:

• Discrete population models with maturation delays provide a more realistic representation of population dynamics.
• The duration of the juvenile immaturity period significantly influences population persistence.
• The developed framework allows for the analysis of complex population behaviors in established ecological models.