Attenuant cycles of population models with periodic carrying capacity

Abstract

Republic (in press)]. We extend their result and obtain a sufficient condition for attenuation of cycles in population models. This sufficient condition is applicable to a wide class of periodic difference equations with arbitrary period. For an illustration, the result is applied to the Beverton-Holt equation and other specific population models.

Population models with periodic recruitment functions and survival rates

“…This showst hat the Beverton -Holt Model with survivorsp er generation supports ag lobally attracting cycle. Cushinga nd Henson [7], Kon [28,29], Kocic [26], Elaydia nd Sacker [11 -14] have obtained this result for the classic Beverton -Holt Model without survivors(g t ¼ 0).…”

“…Kon [ 28,29], Kocic [26], Elaydiand Sacker [13,14]havesince extended this result to include p -periodic BevertonHolt models without survivors( g ¼ 0). With survivors( g -0), periodice nvironments are not always deleterious for populations governed by the Beverton -Holt Model.However, when the carrying capacity is fluctuating and the survival rate is not fluctuating we show via the presence of ag lobally attracting attenuant cyclet hat periodic environmentsa re always disadvantageous for our population.…”

“…That is, the average of the resulting population oscillations in the periodice nvironment is less than the averageofthe carrying capacity in the corresponding constant environment (attenuance) [4,5,7,36]. In recent papers, Cushingand Henson [7], Kon [28,29], Kocic [26,27], Elaydiand Sacker [11 -14] obtainedasimilar result for populations governedbythe classic BevertonHolt model. In this paper,w eu se simplep opulation models with either constant or Beverton -Holt recruitment functions to showt hat periodic environments are not always deleterious [34].…”

The Stochastic Beverton-Holt Equation and the M. Neubert Conjecture

“…Independently, Ryusuke Kon in [19] and [20] established (C2) for an even wider class of maps including Ricker type maps with restrictions. Also Kocic [18] has given a solution to (C2).…”

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].…”