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The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density

Emanuel A. Fronhofer, Lynn Govaert, Mary I. O’Connor, Sebastian J. Schreiber, Florian Altermatt
doi: https://doi.org/10.1101/485946
Emanuel A. Fronhofer
1ISEM, Université de Montpellier, CNRS, IRD, EPHE, Montpellier, France
2Eawag: Swiss Federal Institute of Aquatic Science and Technology, Department of Aquatic Ecology, Überlandstrasse 133, CH-8600 Dübendorf, Switzerland
3Department of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthur-erstrasse 190, CH-8057 Zürich, Switzerland
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  • For correspondence: emanuel.fronhofer@umontpellier.fr
Lynn Govaert
2Eawag: Swiss Federal Institute of Aquatic Science and Technology, Department of Aquatic Ecology, Überlandstrasse 133, CH-8600 Dübendorf, Switzerland
3Department of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthur-erstrasse 190, CH-8057 Zürich, Switzerland
4University Research Priority Programme (URPP) on Global Change and Biodiversity, University of Zurich, Winterthurerstrasse 190, CH-8057 Zrich, Switzerland
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Mary I. O’Connor
2Eawag: Swiss Federal Institute of Aquatic Science and Technology, Department of Aquatic Ecology, Überlandstrasse 133, CH-8600 Dübendorf, Switzerland
5Department of Zoology and Biodiversity Research Centre, University of British Columbia, 2370-6270 University Blvd, Vancouver, BC Canada, V6T 1Z4
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Sebastian J. Schreiber
6Department of Evolution & Ecology and the Center for Population Biology, One Shields Avenue, University of California, Davis, CA 95616, USA
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Florian Altermatt
2Eawag: Swiss Federal Institute of Aquatic Science and Technology, Department of Aquatic Ecology, Überlandstrasse 133, CH-8600 Dübendorf, Switzerland
3Department of Evolutionary Biology and Environmental Studies, University of Zurich, Winterthur-erstrasse 190, CH-8057 Zürich, Switzerland
4University Research Priority Programme (URPP) on Global Change and Biodiversity, University of Zurich, Winterthurerstrasse 190, CH-8057 Zrich, Switzerland
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Abstract

The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated.

Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer-resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density-regulation functions are usually non-linear and may exhibit convex or both concave and convex curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the continuous-time Beverton-Holt model. More complex consumer dynamics show similarities to a Maynard Smith-Slatkin model.

Importantly, we show how population-level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. As a solution, we propose simple and general relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer-resource systems.

Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time-series from microbial food chains to fit population growth models and validate theoretical predictions.

Our results show that density-regulation functions need to be chosen carefully as their shapes will depend on the study system’s biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions.

Competing Interest Statement

The authors have declared no competing interest.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license.
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Posted June 02, 2020.
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The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density
Emanuel A. Fronhofer, Lynn Govaert, Mary I. O’Connor, Sebastian J. Schreiber, Florian Altermatt
bioRxiv 485946; doi: https://doi.org/10.1101/485946
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The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density
Emanuel A. Fronhofer, Lynn Govaert, Mary I. O’Connor, Sebastian J. Schreiber, Florian Altermatt
bioRxiv 485946; doi: https://doi.org/10.1101/485946

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