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Maternal effects and the stability of population dynamics in noisy environments

Authors

  • Tim G. Benton,

    Corresponding author
    1. Institute of Biological Sciences, University of Stirling, Stirling, FK9 4LA, Scotland, UK;
      §Correspondence author: Dr T.G. Benton, Institute of Biological Sciences, University of Stirling, Stirling, FK9 4LA, Scotland, UK. Tel: + 44(0)1786 467809. Fax: + 44(0)1786 464994. E-mail:t.g.benton@stir.ac.uk
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  • Esa Ranta,

    1. Integrative Ecology Unit, Division of Population Biology, Department of Ecology and Systematics, PO Box 17 (Arkadiankatu 7), FIN-00014 University of Helsinki, Finland; and
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  • Veijo Kaitala,

    1. Department of Biological and Environmental Science, University of Jyväskylä, PO Box 35, FIN-40351 Jyväskylä, Finland
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  • Andrew P. Beckerman

    1. Institute of Biological Sciences, University of Stirling, Stirling, FK9 4LA, Scotland, UK;
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§Correspondence author: Dr T.G. Benton, Institute of Biological Sciences, University of Stirling, Stirling, FK9 4LA, Scotland, UK. Tel: + 44(0)1786 467809. Fax: + 44(0)1786 464994. E-mail:t.g.benton@stir.ac.uk

Summary

  • 1It is widely appreciated that complex population dynamics are more likely in systems where there is a lag in the density dependence. The transmission of maternal environmental conditions to offspring phenotype is a potential cause of such a lag. Maternal effects are increasingly found to be common in a wide range of organisms, and might thus be a frequent cause of nonequilibrium population dynamics.
  • 2We show that a maternal effects’ lag generally increases population variability. This may result from the lag inducing cycles (or more complex dynamics) in a deterministic environment or, in a stochastic environment, from the lag interacting with environmental noise to produce more variable dynamics than would otherwise occur. This may happen whether the underlying dynamics are equilibrium, periodic or more complex.
  • 3Although maternal effects may generally destabilize dynamics there are a clear set of exceptions to this. For example, including a maternal lag may convert cycles to equilibrium dynamics, which may revert to cycles when external noise is added.
  • 4The influence of the maternal effect depends importantly on the details of the model, whether it is structured or unstructured, the life-history traits which are maternally affected, and the type of density dependence.
  • 5Our results indicate that, if maternal effects are possible, failure to include them in models used predictively may result in quantitatively, and perhaps qualitatively, poor predictions.

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