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The Mathematics of the Uncertain pp 319–328Cite as

Mathematical Modeling in Biological Populations with Reproduction in a Non-predictable Environment

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 142))

Abstract

In order to mathematically model the demographic dynamics of biological populations with sexual reproduction, we consider the more realistic situation where the reproductive process occurs in a non-predictable environment. We also assume that both biological processes, mating and reproduction, are influenced by the number of couples in the population. In this framework, a class of discrete-time two-sex branching models has been introduced in (A class of two-sex branching processes with reproduction phase in a random environment. Stochastics 88:147–161) [10]. In this work, we continue the research about such a class of stochastic models, investigating the time to extinction and some applications.

This work is my modest contribution to this volume edited as a tribute to Pedro Gil. He was an excellent professional and a great person. His wise advices were very useful for me (Manuel Molina).

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Notes

  1. 1.

    Given the variables X and Y, we say that X is stochastically smaller than Y if, for each real number t, \(P(X\le t)\ge P(Y\le t)\).

References

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Acknowledgements

This research has been supported by the Gobierno de Extremadura, Grant GR15105, the Ministerio de Economía y Competitividad of Spain, Grant MTM2015-70522-P, and the FEDER.

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Authors and Affiliations

  1. Faculty of Sciences, Department of Mathematics, University of Extremadura, 06006, Badajoz, Spain

    Manuel Molina & Manuel Mota

  2. Faculty of Veterinary, Department of Mathematics, University of Extremadura, 10003, Cáceres, Spain

    Alfonso Ramos

Authors
  1. Manuel Molina
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  2. Manuel Mota
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  3. Alfonso Ramos
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Corresponding author

Correspondence to Manuel Molina .

Editor information

Editors and Affiliations

  1. Liberbank, Oviedo, Spain

    Eduardo Gil

  2. Viajes El Corte Inglés, Oviedo, Spain

    Eva Gil

  3. Funl Media, Oxford, United Kingdom

    Juan Gil

  4. Departamento de Estadística e Investigación Operativa y Didáctica de la Matemática, Facultad de Ciencias, Universidad de Oviedo, Oviedo, Spain

    María Ángeles Gil

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Molina, M., Mota, M., Ramos, A. (2018). Mathematical Modeling in Biological Populations with Reproduction in a Non-predictable Environment. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_30

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  • DOI: https://doi.org/10.1007/978-3-319-73848-2_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73847-5

  • Online ISBN: 978-3-319-73848-2

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