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Determinism, noise, and spurious estimations in a generalised model of population growth

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  • de Vladar, Harold P.
  • Pen, Ido

Abstract

We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two sources of multiplicative noise. The stationary probability distributions have two characteristic power-law scales. Numerical simulations show that noise suppresses the explosion of the growth rate which occurs in the deterministic counterpart. Instead, in different parameter regimes populations will grow with “anomalous” stochastic rates and (i) stabilise at “random carrying capacities”, or (ii) go extinct in random times. Using logistic fits to reconstruct the simulated data, we find that even highly significant estimations do not recover or reflect information about the deterministic part of the process. Therefore, the logistic interpretation is not biologically meaningful. These results have implications for distinct model-aided calculations in biological situations because these kinds of estimations could lead to spurious conclusions.

Suggested Citation

  • de Vladar, Harold P. & Pen, Ido, 2007. "Determinism, noise, and spurious estimations in a generalised model of population growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 477-485.
    • Handle: RePEc:eee:phsmap:v:373:y:2007:i:c:p:477-485
    DOI: 10.1016/j.physa.2006.06.025
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    References listed on IDEAS

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    1. Geoffrey B. West & James H. Brown & Brian J. Enquist, 2001. "A general model for ontogenetic growth," Nature, Nature, vol. 413(6856), pages 628-631, October.
    2. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

    1. Barker, Daniel & Sibly, Richard M., 2008. "The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation," Ecological Modelling, Elsevier, vol. 219(1), pages 170-177.

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