Two-sex Branching Models with Random Control on the Number of Progenitor Couples

Molina, Mario García; Mota, M.; Ramos, Alfonso

doi:10.1007/s11009-010-9167-x

Cited by 4 publications

(1 citation statement)

References 24 publications

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“…Thus, this model represents a combination of the two-sex branching process and the controlled branching process with random control functions on the total number of individuals. Moreover, this model differs from the one introduced in [38] in the fact that in our case the control is not made on the number of couples, but on the total number of individuals, which seems to be a more reasonable assumption. First, we shall give an intuitive insight of the model.…”

Section: A Controlled Two-sex Branching Processmentioning

confidence: 96%

A Predator–Prey Two-Sex Branching Process

Gutiérrez

Minuesa

2020

Mathematics

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In this paper, we present the first stochastic process to describe the interaction of predator and prey populations with sexual reproduction. Specifically, we introduce a two-type two-sex controlled branching model. This process is a two-type branching process, where the first type corresponds to the predator population and the second one to the prey population. While each population is described via a two-sex branching model, the interaction and survival of both groups is modelled through control functions depending on the current number of individuals of each type in the ecosystem. In view of their potential for the conservation of species, we provide necessary and sufficient conditions for the ultimate extinction of both species, the fixation of one of them and the coexistence of both of them. Moreover, the description of the present predator–prey two-sex branching process on the fixation events can be performed in terms of the behaviour of a one-type two-sex branching process with a random control on the number of individuals, which is also introduced and analysed.

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Section: A Controlled Two-sex Branching Processmentioning

confidence: 96%

A Predator–Prey Two-Sex Branching Process

Gutiérrez

Minuesa

2020

Mathematics

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Mathematical modeling in biological populations through branching processes. Application to salmonid populations

2014

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This work deals with mathematical modeling through branching processes. We consider sexually reproducing animal populations where, in each generation, the number of progenitor couples is determined in a non-predictable environment. By using a class of two-sex branching processes, we describe their demographic dynamics and provide several probabilistic and inferential contributions. They include results about the extinction of the population and the estimation of the offspring distribution and its main moments. We also present an application to salmonid populations.

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