Mathematical modeling in semelparous biological species through two-sex branching processes

Manuel Molina; Manuel Mota; Alfonso Ramos; Manuel Molina; Manuel Mota; Alfonso Ramos

doi:10.3934/mbe.2024280

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 6: 6407-6424. doi: 10.3934/mbe.2024280

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Mathematical modeling in semelparous biological species through two-sex branching processes

1.
Department of Mathematics, University of Extremadura, Badajoz 06006, Spain
2.
Institute of Advanced Scientific Computation, University of Extremadura, Badajoz 06006, Spain
3.
Institute in Livestock and Cynegetic, University of Extremadura, Badajoz 06006, Spain

Received: 14 February 2024 Revised: 29 May 2024 Accepted: 12 June 2024 Published: 27 June 2024

This research focused its interest on the mathematical modeling of the demographic dynamics of semelparous biological species through branching processes. We continued the research line started in previous papers, providing new methodological contributions of biological and ecological interest. We determined the probability distribution associated with the number of generations elapsed before the possible extinction of the population in its natural habitat. We mathematically modeled the phenomenon of populating or repopulating habitats with semelparous species. We also proposed estimates for the offspring parameters governing the reproductive strategies of the species. To this purpose, we used the maximum likelihood and Bayesian estimation methodologies. The statistical results are illustrated through a simulated example contextualized with Labord chameleon (Furcifer labordi) species.
- mathematical modeling,
- branching processes,
- population dynamics,
- extinction probability,
- statistical inference,
- semelparous biological species
Citation: Manuel Molina, Manuel Mota, Alfonso Ramos. Mathematical modeling in semelparous biological species through two-sex branching processes[J]. Mathematical Biosciences and Engineering, 2024, 21(6): 6407-6424. doi: 10.3934/mbe.2024280

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Abstract

This research focused its interest on the mathematical modeling of the demographic dynamics of semelparous biological species through branching processes. We continued the research line started in previous papers, providing new methodological contributions of biological and ecological interest. We determined the probability distribution associated with the number of generations elapsed before the possible extinction of the population in its natural habitat. We mathematically modeled the phenomenon of populating or repopulating habitats with semelparous species. We also proposed estimates for the offspring parameters governing the reproductive strategies of the species. To this purpose, we used the maximum likelihood and Bayesian estimation methodologies. The statistical results are illustrated through a simulated example contextualized with Labord chameleon (Furcifer labordi) species.

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