Logistic growth population models based on controlled branching processes

M. González Velasco, C. Minuesa Abril, I. M. del Puerto García

The logistic growth of populations is characterized by an initial approximately exponential growth of the number of individuals till they reach an equilibrium value around which they fluctuate. This equilibrium value mainly depends on the carrying capacity of the population. In this work we propose a controlled branching process (CBP) to model population logistic growths by considering control laws defined by binomial distributions with a success probability depending on the current population size, the carrying capacity and the offspring mean. Stochastic versions of well-known deterministic models are obtained as particular cases.

Our aim is to estimate the posterior distributions of the main parameters of such a CBP using approximate Bayesian computation. We analyze real data sets.

Acknowledgements:
This research has been supported by the Junta de Extremadura (grant GR21050) and by grant PID2019-108211GB-I00 funded by MCIN/AEI/10.13039/501100011033, by “ERDF A way of making Europe”

Keywords: controlled branching processes, logistic growth population models, Bayesian inference, ABC

Scheduled

GT17 Stochastic Processes and their Applications IV
June 7, 2022  6:40 PM
A26

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