Linear Birth/Immigration-Death Process With Binomial Catastrophes

Kapodistria, Stella; Phung-Duc, Tuan; Resing, Jacques

doi:10.1017/s0269964815000297

Cited by 46 publications

(33 citation statements)

References 64 publications

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“…So called Catastrophe Models have been studied extensively and are quite close to our model, see Kapodistria et al (2016) for references on the subject. Particularly relevant is the birth and death process with binomial catastrophes, see Example 2 in Brockwell (1986).…”

Section: Non Spatial Modelsmentioning

confidence: 91%

Colonization and Collapse

Machado¹,

Roldán-Correa²,

Schinazi³

2017

ALEA

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Many species live in colonies that thrive for a while and then collapse. Upon collapse, very few individuals survive. The survivors start new colonies at other sites that thrive until they collapse, and so on. We introduce spatial and nonspatial stochastic processes for modeling such population dynamic. Besides testing whether dispersion helps survival in a model experiencing large fluctuations, we obtain conditions for the population to get extinct or to survive.

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Section: Non Spatial Modelsmentioning

confidence: 91%

Colonization and Collapse

Machado¹,

Roldán-Correa²,

Schinazi³

2017

ALEA

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“…They carried out an extensive analysis including first extinction time, number of individuals removed, survival time of a tagged individual, and maximum population size reached between two consecutive extinctions. For a nice literature overview and motivation see Kapodistria et al [5].…”

Section: Introductionmentioning

confidence: 99%

Dispersion as a Survival Strategy

2016

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Abstract. We consider stochastic growth models to represent population subject to catastrophes. We analyze the subject from different set ups considering or not spatial restrictions, whether dispersion is a good strategy to increase the population viability. We find out it strongly depends on the effect of a catastrophic event, the spatial constraints of the environment and the probability that each exposed individual survives when a disaster strikes.

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“…Transient distributions in discrete time discrete state space processes, e.g., a birth/immigration-death process with binomial catastrophes, have been studied in [20,28].…”

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confidence: 99%

Convergence rates for semistochastic processes

Ii¹,

Grigo²,

Petrov³

2019

Discrete &Amp; Continuous Dynamical Systems - B

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We study processes that consist of deterministic evolution punctuated at random times by disturbances with random severity; we call such processes semistochastic. Under appropriate assumptions such a process admits a unique stationary distribution. We develop a technique for establishing bounds on the rate at which the distribution of the random process approaches the stationary distribution. An important example of such a process is the dynamics of the carbon content of a forest whose deterministic growth is interrupted by natural disasters (fires, droughts, insect outbreaks, etc.).2010 Mathematics Subject Classification. Primary: 34F05, 60J25, 92D25; Secondary: 60Gxx, 92Bxx.

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Linear Birth/Immigration-Death Process With Binomial Catastrophes

Cited by 46 publications

References 64 publications

Colonization and Collapse

Colonization and Collapse

Dispersion as a Survival Strategy

Convergence rates for semistochastic processes

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