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Consequences of Environmental Fluctuations on Taylor’s Power Law and Implications for the Dynamics and Persistence of Populations

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Abstract

Conservation Biologists have found that demographic stochasticity causes the mean time to extinction to increase exponentially with population size. This has proved helpful in analyses determining extinction times and characterizing the pathway to extinction. The aim of this investigation is to explore the possible interactions between environmental/demographic noises and the scaling effect of the mean population size with its variance, which is expected to follow Taylor’s power law relationship. We showed that the combined effects of environmental/demographic noises and the scaling of population size variability interact with the population dynamics and affect the mean time to extinction.

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Abbreviations

CV:

Coefficient of variation

F d :

Size of the fluctuations in population size caused by demographic processes

F e :

Size of the fluctuations in population size caused by environmental processes

HM:

Harmonic mean

K :

Constant

log :

Logarithm

N E :

Effective population size

p:

Phase between sinusoidal fluctuations

r:

Instantaneous growth rate

SD:

Standard deviation

β:

Scaling coefficient

ρ :

Correlation

\( \bar{\mu } \) :

Aritmetic mean

\( \bar{\mu }_{pop} \) :

Arithmetic mean of population size

σ 2tot :

Variance of the population size in the presence of environmental noise

σ2 :

Variance of the population size in absence of environmental noise

σ 2e :

Demographic noise

σ 2e :

Environmental noise

ρ(σσe):

Covariance between the environmental noise and the population fluctuation

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Acknowledgments

This study has been partly supported by the Danish Natural Science Research Council for financial support to CP (grant number: #11-103926, #09-065999 and 95095995) and the Carlsberg Foundation (grant number 2011-01-0059). We thank three anonymous Reviewers and the Associate Editor Lia Hemerik, for invaluable suggestions and help.

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Authors and Affiliations

  1. Department of Biosciences, Aarhus University, Ny Munkegade 114, 8200, Aarhus, Denmark

    C. Pertoldi

  2. Department 18/Section of Environmental Engineering, Aalborg University, Sohngårdsholmsvej 57, 9000, Aalborg, Denmark

    C. Pertoldi

  3. Aalborg Zoo, Mølleparkvej 63, 9000, Aalborg, Denmark

    C. Pertoldi

  4. Department of Ecology and Evolutionary Biology, University of California Los Angeles, 621 Charles E. Young Dr. South, Los Angeles, CA, 90024, USA

    S. Faurby

  5. Department of Biological Sciences, University of Aarhus, Ny Munkegade 114, 8000, Aarhus C, Denmark

    C. Pertoldi

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  1. C. Pertoldi
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  2. S. Faurby
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Correspondence to C. Pertoldi.

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Pertoldi, C., Faurby, S. Consequences of Environmental Fluctuations on Taylor’s Power Law and Implications for the Dynamics and Persistence of Populations. Acta Biotheor 61, 173–180 (2013). https://doi.org/10.1007/s10441-012-9167-z

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