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Incorporating environmental stochasticity within a biological population model

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  • Varughese, M.M.
  • Fatti, L.P.

Abstract

The birth and death transition rates for a population are modelled as functions of both the population size and the environmental condition. An assortment of important theoretical results and techniques that can be utilized to analyze such a population’s behaviour is covered. Consequently, these results and techniques are used to study two examples. Firstly, we study a population with a stable equilibrium state, whose per capita birth and death rates are linearly related to the environmental condition. (The environmental condition in turn is modelled as an Ornstein–Uhlenbeck process.) Secondly, we study a population affected by two interdependent environmental factors.

Suggested Citation

  • Varughese, M.M. & Fatti, L.P., 2008. "Incorporating environmental stochasticity within a biological population model," Theoretical Population Biology, Elsevier, vol. 74(1), pages 115-129.
    • Handle: RePEc:eee:thpobi:v:74:y:2008:i:1:p:115-129
    DOI: 10.1016/j.tpb.2008.05.004
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    References listed on IDEAS

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    1. Valenti, D. & Fiasconaro, A. & Spagnolo, B., 2004. "Stochastic resonance and noise delayed extinction in a model of two competing species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 477-486.
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    Cited by:

    1. Varughese, Melvin M., 2009. "On the accuracy of a diffusion approximation to a discrete state–space Markovian model of a population," Theoretical Population Biology, Elsevier, vol. 76(4), pages 241-247.
    2. Bretó, Carles, 2014. "Trajectory composition of Poisson time changes and Markov counting systems," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 91-98.
    3. Varughese, Melvin M., 2013. "Parameter estimation for multivariate diffusion systems," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 417-428.
    4. Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.
    5. Kostić, Vladimir R. & Cvetković, Ljiljana & Cvetković, Dragana Lj., 2016. "Improved stability indicators for empirical food webs," Ecological Modelling, Elsevier, vol. 320(C), pages 1-8.
    6. Bretó, Carles & Ionides, Edward L., 2011. "Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2571-2591, November.

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