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Bayesian analysis for controlled branching processes. (English) Zbl 1354.60092
del Puerto, Inés M. (ed.) et al., Branching processes and their applications. Proceedings of the workshop, WBPA, Badajoz, Spain, April 7–10, 2015. Cham: Springer (ISBN 978-3-319-31639-0/pbk; 978-3-319-31641-3/ebook). Lecture Notes in Statistics 219, 185-205 (2016).
Summary: The branching model considered in the present work is the controlled branching process. This model is a generalization of the standard Bienaymé-Galton-Watson (BGW) branching process, and, in the terminology of population dynamics, is used to describe the evolution of populations in which a control of the population size at each generation is needed. This control consists of determining mathematically the number of individuals with reproductive capacity at each generation through a random process. In practice, this branching model can describe reasonably well the probabilistic evolution of populations in which, for various reasons of an environmental, social, or other nature, there is a mechanism that establishes the number of progenitors which take part in each generation. For example, in an ecological context, one can think of an invasive animal species that is widely recognized as a threat to native ecosystems, but there is disagreement about plans to eradicate it, i.e., while the presence of the species is appreciated by a part of the society, if its numbers are left uncontrolled it is known to be very harmful to native ecosystems. In such a case, it is better to control the population to keep it within admissible limits even though this might mean periods when animals have to be culled. Another practical situation that can be modelled by this kind of process is the evolution of an animal population that is threatened by the existence of predators. In each generation, the survival of each animal (and therefore the possibility of giving new births) will be strongly affected by this factor, making the introduction of a random mechanism necessary to model the evolution of this kind of population.
For the entire collection see [Zbl 1354.60003].

MSC:
 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 62C10 Bayesian problems; characterization of Bayes procedures 60J85 Applications of branching processes 92D25 Population dynamics (general)
Software:
CODA; R; Rmpi; snow; Snow
Full Text:
References:
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