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Mathematical Modeling of Extinction of Inhomogeneous Populations

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Abstract

Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed of clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity,” i.e., the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception.

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Acknowledgments

This research was partially supported by the Intramural Research Program of the NCBI, NIH. The authors would also like to thank the anonymous reviewers, whose comments and suggestions contributed to significant improvement of the manuscript.

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Authors and Affiliations

  1. National Center for Biotechnology Information, National Institutes of Health - Bldg. 38A, 8600 Rockville Pike, Bethesda, MD, 20894, USA

    G. P. Karev

  2. Floating Hospital for Children at Tufts Medical Center, Boston, MA, 02111, USA

    I. Kareva

  3. Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Engineering Center A, Arizona State University, Tempe, AZ, 85287, USA

    I. Kareva

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  1. G. P. Karev
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  2. I. Kareva
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Correspondence to G. P. Karev.

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Karev, G.P., Kareva, I. Mathematical Modeling of Extinction of Inhomogeneous Populations. Bull Math Biol 78, 834–858 (2016). https://doi.org/10.1007/s11538-016-0166-0

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  • DOI: https://doi.org/10.1007/s11538-016-0166-0

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