Multiple attractors in host–parasitoid interactions: Coexistence and extinction

Kon, Ryusuke

doi:10.1016/j.mbs.2005.12.010

Cited by 29 publications

(30 citation statements)

References 19 publications

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“…As a result, solutions of Equation (1) satisfy lim t→∞ y(t) = 0 if al < 1 (cf. [10,15]). The proofs of the following theorem are straightforward and are not provided.…”

Section: The General Modelmentioning

confidence: 99%

Discrete-time host–parasitoid models with pest control

Jang

2012

Journal of Biological Dynamics

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“…As a result, solutions of Equation (1) satisfy lim t→∞ y(t) = 0 if al < 1 (cf. [10,15]). The proofs of the following theorem are straightforward and are not provided.…”

Section: The General Modelmentioning

confidence: 99%

Discrete-time host–parasitoid models with pest control

Jang

2012

Journal of Biological Dynamics

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“…In this case, the system has no permanence due to existing attractors on the x-axis. There are many models (Kon, 2006;Kang et al, 2008;Kuang and Chesson, 2008) presenting this scenario under some proper parameter ranges. The uniform invasibility criterion A1 and A2 requires both (12) and (15) to be positive for all initial positive initial states of the resident.…”

Section: Relative Nonlinearitymentioning

confidence: 99%

“…For instance, a plant-herbivore model in Kang et al (2008) shows bistability between interior attractors and boundary attractors as a consequence of fluctuating dynamics of the plant population. Also, Kon (2006) shows that there are multiple attractors between interior attractors and boundary attractors caused by the fluctuating dynamics of the host in a hostparasitoid model.…”

Section: Lemma 51 (Dissipativity) If the System (1)-(2) Satisfies Cmentioning

confidence: 99%

“…In this subsection, we give an example of when fluctuating dynamics associated with a nonpoint attractor undermine permenance because they make the invasion rate negative while the invasion rate from the resident fixed point is positive. Both models studied in Kon (2006) and Kang et al (2008) provide examples. Here we use following host-parasitoid interaction model studied by Kon (2006):…”

Section: Resident Population Fluctuations Leading To a Negative Invasmentioning

confidence: 99%

“…Both models studied in Kon (2006) and Kang et al (2008) provide examples. Here we use following host-parasitoid interaction model studied by Kon (2006):…”

Section: Resident Population Fluctuations Leading To a Negative Invasmentioning

confidence: 99%

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Relative nonlinearity and permanence

Kang

Chesson

2010

Theoretical Population Biology

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a b s t r a c tWe modify the commonly used invasibility concept for coexistence of species to the stronger concept of uniform invasibility. For two-species discrete-time competition and predator-prey models, we use this concept to find broad easily checked sufficient conditions for the rigorous concept of permanent coexistence. With these results, permanent coexistence becomes a tractable concept for many discretetime population models. To understand how these conditions apply to nonpoint attractors, we generalize the concept of relative nonlinearity and use it to show how population fluctuations affect the long-term low-density growth rate (''the invasion rate'') of a species when it is invading the system consisting of the other species (''the resident'') at a single-species attractor. The concept of relative nonlinearity defines circumstances when this invasion rate is increased or decreased by resident population fluctuations arising from a nonpoint attractor. The presence and sign of relative nonlinearity is easily checked in models of interacting species. When relative nonlinearity is zero or positive, fluctuations cannot decrease the invasion rate. It follows that permanence is then determined by invasibility of the resident's fixed points. However, when relative nonlinearity is negative, invasibility, and hence permanent coexistence, can be undermined by resident population fluctuations. These results are illustrated with specific twospecies competition and predator-prey models of generic forms.Published by Elsevier Inc.

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