Chaos

Cushing, J.M.; Costantino, R.F.; Dennis, B. R.; Desharnais, Robert A.; Henson, Shandelle M.

doi:10.1016/b978-012198876-0/50005-1

Cited by 47 publications

(89 citation statements)

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“…For these numbers, ρ 2 ranges from 0.17414 to −37.994 and, as a result, the bifurcating positive equilibria are stable for β 23 = 0 and unstable for β 23 = 1. This model prediction is confirmed by the experimental outcomes reported in [3,12,16]. It is also interesting to note that for β 23 = 1, the beetle cultures displayed synchronous oscillations in which the three life stages were non-overlapping.…”

Section: Examplesupporting

confidence: 75%

“…The well-known LPA model is the basic model used in extensive experimental studies of nonlinear dynamics involving the species Tribolium (flour beetles) [4,12]. The LPA model is not semelparous, but in many of the key experiments, the protocol manipulated the adult death rate to nearly 100% and therefore gave the insects, in effect, a semelparous life history [3,12,16].…”

Section: Examplementioning

confidence: 99%

“…In the experimental studies of nonlinear dynamics in Tribolium [3,12,16], numerical estimates of the parameters were made from data and the inter-class competition parameter β 23 was experimentally manipulated. Specifically, β 31 = 0.01731, β 33 = 0.01310, s 1 = 0.8 and β 23 ranged from 0 to 1.…”

Section: Examplementioning

confidence: 99%

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Stable bifurcations in semelparous Leslie models

Cushing

Henson

2012

Journal of Biological Dynamics

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In this paper, we consider nonlinear Leslie models for the dynamics of semelparous age-structured populations. We establish stability and instability criteria for positive equilibria that bifurcate from the extinction equilibrium at R 0 = 1. When the bifurcation is to the right (forward or super-critical), the criteria consist of inequalities involving the (low-density) between-class and within-class competition intensities. Roughly speaking, stability (respectively, instability) occurs if between-class competition is weaker (respectively, stronger) than within-class competition. When the bifurcation is to the left (backward or sub-critical), the bifurcating equilibria are unstable. We also give criteria that determine whether the boundary of the positive cone is an attractor or a repeller. These general criteria contribute to the study of dynamic dichotomies, known to occur in lower dimensional semelparous Leslie models, between equilibration and age-cohort-synchronized oscillations.

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Section: Examplesupporting

confidence: 75%

Section: Examplementioning

confidence: 99%

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Stable bifurcations in semelparous Leslie models

Cushing

Henson

2012

Journal of Biological Dynamics

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“…0 tend (monotonically) to the equilibrium x ¼ ðb 2 1Þ=c 11 : This difference equation is an appropriate analog of the logistic differential equation [12]. Just as the famous Lotka/Volterra two species (differential equation) competition model is a modification of the logistic differential equation, the Leslie/Gower (difference equation) competition model [26] …”

Section: The Leslie/gower Modelmentioning

confidence: 99%

Some Discrete Competition Models and the Competitive Exclusion Principle^†

Cushing

LeVarge

Chitnis

et al. 2004

Journal of Difference Equations and Applications

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157

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A difference equation model, called that Leslie/Gower model, played a key historical role in laboratory experiments that helped establish the "competitive exclusion principle" in ecology. We show that this model has the same dynamic scenarios as the famous Lotka/Volterra (differential equation) competition model. It is less well known that some anomalous results from the experiments seem to contradict the exclusion principle and Lotka/Volterra dynamics. We give an example of a competition model that has non-Lotka/Volterra dynamics that are consistent with the anomalous case.

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“…(Many examples are documented in, for example, Renshaw [1991], Roughgarden [1998], Caswell [2001] and Allen [2003]). Further, environmental or demographic stochasticity can be included into a known deterministic model by adding noise on logarithm or square root scale, e.g., Cushing et al [2003]. All of these methods lead to stochastic difference or differential equations, where environmental stochasticity is treated as a general quantity but not necessarily determined from a single, specific mechanism.…”

Section: Introduction Global Climate Change Is a Central Issue In Ecmentioning

confidence: 99%

Accounting for Temperature in Predator Functional Responses

Logan

Wolesensky

2007

Natural Resource Modeling

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ABSTRACT. A rational mechanism that integrates temperature-mediated activity cycles into standard predator functional responses is presented. Daily temperature variations strongly influence times that predators can search for prey, and they affect the activity periods of prey, thereby modifying their detection by predators. Thus, key parameters in the functional response, the search time and the detection, become temperature-dependent. These temperature mediated responses are included in discrete-time population growth models, and it is shown how environmental temperature variations, such as those that may occur under global climate change, can affect population levels. As an illustration, a logistic growth model with a stochastic, temperature-dependent predation term is examined, and the response to both average temperature levels and temperature variability is quantified. We infer, through simulations, that predation and prey abundance are strongly affected by mean temperature, temperature amplitudes, and increasing uncertainty in predicting temperature levels and variation, thus confirming many qualitative conclusions in the ecological literature. In particular, we show that increased temperature variability increases oscillations in the system and leads to increased probability of extinction of the prey.

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Chaos

Cited by 47 publications

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Stable bifurcations in semelparous Leslie models

Stable bifurcations in semelparous Leslie models

Some Discrete Competition Models and the Competitive Exclusion Principle^†

Accounting for Temperature in Predator Functional Responses

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Chaos

Cited by 47 publications

References 0 publications

Stable bifurcations in semelparous Leslie models

Stable bifurcations in semelparous Leslie models

Some Discrete Competition Models and the Competitive Exclusion Principle†

Accounting for Temperature in Predator Functional Responses

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Some Discrete Competition Models and the Competitive Exclusion Principle^†