Derivation and dynamics of discrete population models with distributed delay in reproduction

We introduce a class of discrete single species models with distributed delay in the reproductive process and a cohort dependent survival function that accounts for survival pressure during that delay period. These delay recurrences track the mature population for species in which individuals reach maturity after at least τ and at most τ+τ_M breeding cycles. Under realistic model assumptions, we prove the existence of a critical delay threshold, …