Technique to derive discrete population models with delayed growth

Abstract

We provide a procedure for deriving discrete population models for the size of the adult population at the beginning of each breeding cycle and assume only adult individuals reproduce. This derivation technique includes delay to account for the number of breeding cycles that a newborn individual remains immature and does not contribute to reproduction. These models include a survival probability (during the delay period) for the immature individuals, since these individuals have to survive to reach maturity and become members of, what we consider, the adult population. We discuss properties of this class of discrete delay population models and show that there is a critical delay threshold. The population goes extinct if the delay exceeds this threshold. We apply this derivation procedure to obtain two models, a Beverton–Holt adult model and a Ricker adult model and discuss the global dynamics of both models.

Keywords

• Delay difference equations
• global stability
• persistence
• critical delay threshold
• Beverton–Holt
• Ricker