Population models with periodic recruitment functions and survival rates

Abstract

We study the combined effects of periodically varying carrying capacity and survivalrate on populations. We showthat our populations with constant recruitment functions do not experience either resonance or attenuance when either only the carrying capacity or the survivalrate is fluctuating. However,when both carrying capacity and survivalr ate are fluctuatingt he populations experience either attenuance or resonance, depending on parameter regimes. In addition, we showthat our populations with BevertonHolt recruitment functions experience attenuance when only the carrying capacity is fluctuating.

On the stochastic Beverton–Holt equation with survival rates

“…If one assumes that γ n = γ is constant in (1.2), then it may be shown that the same result holds, that is, (1.2) is attenuant in the mean. However, if both parameters γ n and K n are random sequences, we are still unable to determine either attenuance in the mean or resonance in the mean, that is for almost every ω ∈ Ω and every x ∈ R + , The problem of attenuance or resonance has not been yet resolved even when γ n and K n are periodic sequences on Z + , (see for example Elaydi-Sacker [3], and FrankeYakubu [4]). It would be of great interest to develop criteria for attenuance and resonance for the case of two varying parameters Beverton-Holt equation with a survival rate.…”

“…In a recent paper, Franke and Yakubu [4] studied (3.2) with the periodic constant recruitment function…”

Population models in almost periodic environments

“…Jillson performed such an experiment with laboratory cultures of Tribolium [34]. Others have used mathematical models to study the effects of periodic forcing on population dynamics [8,9,10], [12,13,14,15,16,17], [20,21,22,23,24], [29,30], and [35,36,37,38].…”

“…The ecological literature is filled with future life-history studies of periodically forced (nonautonomous) classical parametric population models with time t in Z + . Examples of such periodically forced parametric models with time t in Z + include the Beverton-Holt, Ricker, Smith-Slatkin and LPA models [9,10], [13,14,15,16], and [21,22,23,24].…”

“…Despite the fact that all natural populations suffer temporal environmental fluctuations on some scale, experimental and theoretical studies of population responses to external fluctuations remain relatively rare [8,9,10], [12,13,14,15,16,17], [20,21,22,23,24], [28,29,30], [32], and [35,36,36,38,39,40,41]. To study the effects of fluctuating environments on population dynamics, one can deliberately fluctuate environmental parameters in controlled laboratory experiments.…”