On the Role of Spatial Aggregation in the Extinction of a Species

Schinazi, Rinaldo B.

doi:10.1007/978-3-7643-8786-0_26

Cited by 3 publications

(11 citation statements)

References 8 publications

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“…Since φ < 1, the chain is transient; therefore there is a positive probability q(φ) that starting at M > N A the chain will go on to infinity. The claim follows as in Step 3 of [21], proof of Theorem 2, since N 1/2 visits are enough for the probability to reach N − M + 1 at least one time to approach 1.…”

Section: Model IIImentioning

confidence: 74%

“…The rest of the proof is identical to Step 2 of [21], proof of Theorem 2: the key point is that conditioning on {R ξ N ≥ N 2 }, E N is larger than a binomial random variable V N with parameters N 2 and λ/(2d(λM + N φ)), such that (V N − E(V N ))/(N 1/2+a ) converges to 0 in probability for all a > 0. The claim follows by taking a ∈ (0, 1/2).…”

Section: Model IIImentioning

confidence: 93%

“…In [19] and [21], the author considers a metapopulation model to investigate the roles of mass death (i.e., the death of all individuals in a local population) and spatial aggregation in the extinction of a species. In [19] he shows that, in presence of mass death, animals living in large flocks are more susceptible to extinction than animals living in small flocks: for this model, mass death can be an alternative to the Allee effect in raising to the extinction of a species.…”

Section: Introductionmentioning

confidence: 99%

“…In [19] he shows that, in presence of mass death, animals living in large flocks are more susceptible to extinction than animals living in small flocks: for this model, mass death can be an alternative to the Allee effect in raising to the extinction of a species. The new results in [21] involve the role of spatial aggregation, which may be either bad or good for survival in a model respectively, with or without mass death. For these models the local population Allee effect was not taken into account.…”

Section: Introductionmentioning

confidence: 99%

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On the role of Allee effect and mass migration in survival and extinction of a species

Borrello¹

2012

Ann. Appl. Probab.

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We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of Z d . In each of the four models studied, an individual in a local population can reproduce, die or migrate to neighboring sites.We prove that an increase of the death rate when the local population density is small (the Allee effect) may be critical for survival, and that the migration of large flocks of individuals is a possible solution to avoid extinction when the Allee effect is strong. We use attractiveness and comparison with oriented percolation, either to prove the extinction of the species, or to construct nontrivial invariant measures for each model.

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Section: Model IIImentioning

confidence: 74%

Section: Model IIImentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the role of Allee effect and mass migration in survival and extinction of a species

Borrello¹

2012

Ann. Appl. Probab.

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“…The analysis in [7] and [8] shows that, for appropriate values of the birth rates and in the presence of catastrophic events modeled by the death of each local population independently at rate 1, the metapopulation survives if and only if the maximum number of individuals per patch is smaller than some critical value. In patches hosting a local population below the carrying capacity, individuals give birth at a fixed rate to offspring which stay in the parent's patch, whereas in patches at the carrying capacity, individuals give birth at another fixed rate to offspring which are sent to randomly chosen adjacent patches.…”

Section: Introductionmentioning

confidence: 99%

The Role of Dispersal in Interacting Patches Subject to an Allee Effect

Lanchier

2013

Adv. Appl. Probab.

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This article is concerned with a stochastic multipatch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch model that was recently introduced by Kang and the author. The main objective is to understand the effect of the geometry of the network of interactions, which represents potential migrations between patches, on the long-term behavior of the metapopulation. In the limit as the number of patches tends to ∞, there is a critical value for the Allee threshold below which the metapopulation expands and above which the metapopulation goes extinct. Spatial simulations on large regular graphs suggest that this critical value strongly depends on the initial distribution when the degree of the network is large, whereas the critical value does not depend on the initial distribution when the degree is small. Looking at the system starting with a single occupied patch on the complete graph and on the ring, we prove analytical results that support this conjecture. From an ecological perspective, these results indicate that, upon arrival of an alien species subject to a strong Allee effect to a new area, though dispersal is necessary for its expansion, fast long-range dispersal drives the population toward extinction.

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The Role of Dispersal in Interacting Patches Subject to an Allee Effect

Lanchier

2013

Advances in Applied Probability

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This article is concerned with a stochastic multi-patch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch model that has been recently introduced by Kang and the author. The main objective is to understand the effect of the geometry of the network of interactions, which represents potential migrations between patches, on the long-term behavior of the metapopulation. In the limit as the number of patches tends to infinity, there is a critical value for the Allee threshold below which the metapopulation expands and above which the metapopulation goes extinct. Spatial simulations on large regular graphs suggest that this critical value strongly depends on the initial distribution when the degree of the network is large whereas the critical value does not depend on the initial distribution when the degree is small. Looking at the system starting with a single occupied patch on the complete graph and on the ring, we prove analytical results that support this conjecture. From an ecological perspective, these results indicate that, upon arrival of an alien species subject to a strong Allee effect to a new area, though dispersal is necessary for its expansion, strong long range dispersal drives the population toward extinction.

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On the Role of Spatial Aggregation in the Extinction of a Species

Cited by 3 publications

References 8 publications

On the role of Allee effect and mass migration in survival and extinction of a species

On the role of Allee effect and mass migration in survival and extinction of a species

The Role of Dispersal in Interacting Patches Subject to an Allee Effect

The Role of Dispersal in Interacting Patches Subject to an Allee Effect

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