Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion

Li, Dan; Cui, Jinǵan; Song, Guohua

doi:10.1155/2014/249504

Cited by 1 publication

(1 citation statement)

References 31 publications

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“…Many other extensions of our model are possible. For example, the process component of the model could be adapted to accommodate other diffusion processes , such as jumpdiffusion (e.g., Li et al 2014 ). Given that the method is based on a Lagrangian implementation of a partial differential equation, it is also possible to use optimal mathematical solution methods such as "homogenization" when fi tting these models (e.g., Hooten et al 2013 ).…”

Section: Discussionmentioning

confidence: 99%

Dynamic occupancy models for explicit colonization processes

Broms

Hooten

Johnson

et al. 2016

Ecology

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The dynamic, multi‐season occupancy model framework has become a popular tool for modeling open populations with occupancies that change over time through local colonizations and extinctions. However, few versions of the model relate these probabilities to the occupancies of neighboring sites or patches. We present a modeling framework that incorporates this information and is capable of describing a wide variety of spatiotemporal colonization and extinction processes. A key feature of the model is that it is based on a simple set of small‐scale rules describing how the process evolves. The result is a dynamic process that can account for complicated large‐scale features. In our model, a site is more likely to be colonized if more of its neighbors were previously occupied and if it provides more appealing environmental characteristics than its neighboring sites. Additionally, a site without occupied neighbors may also become colonized through the inclusion of a long‐distance dispersal process. Although similar model specifications have been developed for epidemiological applications, ours formally accounts for detectability using the well‐known occupancy modeling framework. After demonstrating the viability and potential of this new form of dynamic occupancy model in a simulation study, we use it to obtain inference for the ongoing Common Myna (Acridotheres tristis) invasion in South Africa. Our results suggest that the Common Myna continues to enlarge its distribution and its spread via short distance movement, rather than long‐distance dispersal. Overall, this new modeling framework provides a powerful tool for managers examining the drivers of colonization including short‐ vs. long‐distance dispersal, habitat quality, and distance from source populations.

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Section: Discussionmentioning

confidence: 99%