Georgia Institute of Technology College of Sciences

Discrete delay population models are often considered as a compromise between single-species models and more advanced age-structured population models, C.W. Clark, J. Math. Bio. 1976. This talk is based on a recent work (S. Streipert and G.S.K. Wolkowicz, 2023), where 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 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 two well-known population models, the Beverton–Holt and the Ricker population model. We analyze their dynamics and compare it to existing delay models.