The global dynamics of a discrete juvenile–adult model with continuous and seasonal reproduction

Ackleh, Azmy S.; Chiquet, Ross A.

doi:10.1080/17513750802379010

Cited by 10 publications

(5 citation statements)

References 28 publications

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“…For example, small, but not large, long-term environmental variation can favour the evolution of bet-hedging over rising-tide when the mean environmental condition deviates from the optimal environment of the two strategies. We also show that whether population size changes continuously or discretely, such as in species that are continuous versus seasonal breeders [40,41], can also impact biological adaptation because the rising-tide strategy is selected for under a broader range of environmental conditions than the bet-hedging strategy under continuous dynamics, whereas bet-hedging dominates under discrete dynamics. Thus, our model results are consistent with previous analytic models, which find that natural selection maximizes a compromise between a high growth rate and a small environmental variance in population growth rate in the continuous-time setting, provided that fluctuations in population size around carrying capacity are relatively small [16,30,32].…”

Section: Discussionmentioning

confidence: 87%

A continuum of biological adaptations to environmental fluctuation

et al. 2019

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Bet-hedging—a strategy that reduces fitness variance at the expense of lower mean fitness among different generations—is thought to evolve as a biological adaptation to environmental unpredictability. Despite widespread use of the bet-hedging concept, most theoretical treatments have largely made unrealistic demographic assumptions, such as non-overlapping generations and fixed or infinite population sizes. Here, we extend the concept to consider overlapping generations by defining bet-hedging as a strategy with lower variance and mean per capita growth rate across different environments. We also define an opposing strategy—the rising-tide—that has higher mean but also higher variance in per capita growth. These alternative strategies lie along a continuum of biological adaptions to environmental fluctuation. Using stochastic Lotka–Volterra models to explore the evolution of the rising-tide versus bet-hedging strategies, we show that both the mean environmental conditions and the temporal scales of their fluctuations, as well as whether population dynamics are discrete or continuous, are crucial in shaping the type of strategy that evolves in fluctuating environments. Our model demonstrates that there are likely to be a wide range of ways that organisms with overlapping generations respond to environmental unpredictability beyond the classic bet-hedging concept.

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Section: Discussionmentioning

confidence: 87%

A continuum of biological adaptations to environmental fluctuation

et al. 2019

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“…Proof The proof is similar to that of [18][19][20] with some minor modifications. Since 0 (γ 1 , γ 2 , γ 3 ) < 1, system (1.2) only has a trivial steady state E 0 = (0, 0, 0, 0).…”

Section: )mentioning

confidence: 91%

A discrete-time mathematical model of stage-structured mosquito populations

2019

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This paper proposes a system of difference equations to model mosquito population. In this study, we develop and analyze the stage-structured models which consist of four distinct mosquito metamorphic stages: eggs, larvae, pupae, and adults. First, a model with constant birth rate is studied, and the inherent net reproduction number 0 of the model is derived. If 0 < 1, the extinction equilibrium is globally asymptotically stable. If 0 > 1, there exists a unique positive equilibrium which is uniformly persistent. When breeding is seasonal for a special case, it indicates that a unique globally asymptotically stable periodic solution is admitted when the net reproductive number is larger than one. When this value is less than one, the mosquito population goes to extinction. Finally, numerical simulations to demonstrate our findings and brief discussion are also provided.At last, we proceed to verifying the last inequality (v). For convenience, we denote m = -bs 3 J 21 J 32 , n = -J 44 . Then (v) is equal to 1b 2 s 2 3 J 2 21 J 2 32 2b 2 s 2 3 J 2 21 J 2 32 J 2 44 --bs 3 J 21 J 32 J 2 44

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“…This definition was utilized in several applications of matrix models to structured populations in a seasonally fluctuating environment [1,7,8,14,15] and our main goal in this paper was to develop the general theory and investigate the properties of this particular definition of R 0 .…”

Section: Some Concluding Remarksmentioning

confidence: 99%

“…Following Caswell [7] for the period p = 2 case, we show in Section 2 that the coefficient matrix of the composite map can be additively decomposed in a fashion analogous to Equation (1) in which reproductive and class transition processes during one period are separated. That is to say, the composite projection matrix for maps of period p has the form…”

Section: Introductionmentioning

confidence: 99%

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A net reproductive number for periodic matrix models

Cushing

Ackleh

2012

Journal of Biological Dynamics

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We give a definition of a net reproductive number R 0 for periodic matrix models of the type used to describe the dynamics of a structured population with periodic parameters. The definition is based on the familiar method of studying a periodic map by means of its (period-length) composite. This composite has an additive decomposition that permits a generalization of the Cushing-Zhou definition of R 0 in the autonomous case. The value of R 0 determines whether the population goes extinct (R 0 < 1) or persists (R 0 > 1). We discuss the biological interpretation of this definition and derive formulas for R 0 for two cases: scalar periodic maps of arbitrary period and periodic Leslie models of period 2. We illustrate the use of the definition by means of several examples and by applications to case studies found in the literature. We also make some comparisons of this definition of R 0 with another definition given recently by Bacaër.

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The global dynamics of a discrete juvenile–adult model with continuous and seasonal reproduction

Cited by 10 publications

References 28 publications

A continuum of biological adaptations to environmental fluctuation

A continuum of biological adaptations to environmental fluctuation

A discrete-time mathematical model of stage-structured mosquito populations

A net reproductive number for periodic matrix models

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