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


Fronhofer, Emanuel A; Govaert, Lynn; O'Connor, Mary I; Schreiber, Sebastian J; Altermatt, Florian (2024). The shape of density dependence and the relationship between population growth, intraspecific competition and equilibrium population density. Oikos, 2024(2):e09824.

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 concave curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the Schoener model. More complex consumer dynamics show similarities to a Maynard Smith–Slatkin model. 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. We propose simple 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 as a test case for our 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.

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 concave curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the Schoener model. More complex consumer dynamics show similarities to a Maynard Smith–Slatkin model. 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. We propose simple 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 as a test case for our 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Evolutionary Biology and Environmental Studies
08 Research Priority Programs > Global Change and Biodiversity
Dewey Decimal Classification:590 Animals (Zoology)
570 Life sciences; biology
Scopus Subject Areas:Life Sciences > Ecology, Evolution, Behavior and Systematics
Uncontrolled Keywords:Ecology, Evolution, Behavior and Systematics
Language:English
Date:February 2024
Deposited On:20 Jan 2024 16:31
Last Modified:30 Jun 2024 01:37
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0030-1299
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1111/oik.09824
Project Information:
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 3.0 Unported (CC BY 3.0)