How to fit nonlinear plant growth models and calculate growth rates: an update for ecologists

Authors

  • C. E. Timothy Paine,

    Corresponding author
    1. Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, CH-8057 Switzerland
      Correspondence author. E-mail: timothy.paine@ieu.uzh.ch
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  • Toby R. Marthews,

    1. Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, CH-8057 Switzerland
    2. Oxford University Centre for the Environment, South Parks Road, Oxford OX1 3QY, UK
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  • Deborah R. Vogt,

    1. Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, CH-8057 Switzerland
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  • Drew Purves,

    1. Computational Ecology and Environmental Science Group, Microsoft Research, Cambridge CB3 0FB, UK
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  • Mark Rees,

    1. Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield S10 2TN, UK
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  • Andy Hector,

    1. Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, CH-8057 Switzerland
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  • Lindsay A. Turnbull

    1. Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthurerstrasse 190, CH-8057 Switzerland
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Correspondence author. E-mail: timothy.paine@ieu.uzh.ch

Summary

1. Plant growth is a fundamental ecological process, integrating across scales from physiology to community dynamics and ecosystem properties. Recent improvements in plant growth modelling have allowed deeper understanding and more accurate predictions for a wide range of ecological issues, including competition among plants, plant–herbivore interactions and ecosystem functioning.

2. One challenge in modelling plant growth is that, for a variety of reasons, relative growth rate (RGR) almost universally decreases with increasing size, although traditional calculations assume that RGR is constant. Nonlinear growth models are flexible enough to account for varying growth rates.

3. We demonstrate a variety of nonlinear models that are appropriate for modelling plant growth and, for each, show how to calculate function-derived growth rates, which allow unbiased comparisons among species at a common time or size. We show how to propagate uncertainty in estimated parameters to express uncertainty in growth rates. Fitting nonlinear models can be challenging, so we present extensive worked examples and practical recommendations, all implemented in R.

4. The use of nonlinear models coupled with function-derived growth rates can facilitate the testing of novel hypotheses in population and community ecology. For example, the use of such techniques has allowed better understanding of the components of RGR, the costs of rapid growth and the linkage between host and parasite growth rates. We hope this contribution will demystify nonlinear modelling and persuade more ecologists to use these techniques.

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