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Natural selection—probably the most well-known evolutionary mechanism—increases the prevalence of traits that enhance survival and reproduction. However, evolution does not merely propagate favorable traits, nor does it always benefit populations.
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Related Experiment Video

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Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

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Published on: February 3, 2023

Evolutionary dynamics and strong Allee effects.

J M Cushing1, Jarred T Hudson

  • 1Department of Mathematics, 617 N Santa Rita, University of Arizona, Tucson, AZ 85721, USA. cushing@math.arizona.edu

Journal of Biological Dynamics
|August 14, 2012
PubMed
Summary
This summary is machine-generated.

Evolutionary dynamics with a strong Allee effect show that trait evolution can shrink or eliminate the Allee basin, impacting population survival. Stable equilibria emerge at trait-dependent carrying capacity maxima and growth rate minima.

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Area of Science:

  • Evolutionary Biology
  • Population Dynamics
  • Mathematical Biology

Background:

  • The Allee effect describes reduced per capita growth at low population densities.
  • Evolutionary processes can interact with population dynamics, influencing species persistence.
  • Understanding these interactions is crucial for predicting population viability and evolutionary trajectories.

Purpose of the Study:

  • To investigate the dynamics of an evolutionary model incorporating a strong Allee effect.
  • To analyze how evolving phenotypic traits influence population carrying capacity, growth rate, and Allee threshold.
  • To determine the impact of evolution on population stability and extinction risk.

Main Methods:

  • Developed a plane autonomous system modeling coupled population and mean phenotypic trait dynamics.
  • Analyzed the model to identify conditions for bounded orbits and equilibrium states.
  • Investigated the influence of trait-dependent parameters (k(u), r(u), a(u)) on population dynamics.

Main Results:

  • Evolutionary changes can lead to a shrinking or disappearance of the Allee effect basin.
  • Stable non-extinction equilibria are found at local maxima of the carrying capacity function k(u).
  • Stable extinction equilibria are associated with local minima of the inherent growth rate function r(u).
  • Multiple evolutionarily stable strategies (ESS) and the potential to evolve away from an ESS were demonstrated.

Conclusions:

  • Trait evolution significantly alters population dynamics under a strong Allee effect.
  • Evolution can both stabilize populations at high densities and increase extinction risk by shrinking the Allee basin.
  • The model provides insights into complex evolutionary-population dynamics, including multiple stable states and evolutionary escape from ESS.