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Frequency dependence 3.0: an attempt at codifying the evolutionary ecology perspective.

Johan A J Metz1,2,3, Stefan A H Geritz4

  • 1Mathematical Institute and Institute of Biology, Leiden University, 2333 CA, Leiden, The Netherlands. j.a.j.metz@biology.leidenuniv.nl.

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|February 3, 2016
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Summary

This study redefines frequency independence in eco-evolutionary models, focusing on competitive ability rather than strict population genetics definitions. It introduces weak frequency dependence for more realistic ecological scenarios.

Keywords:
Adaptive dynamicsESS theoryFeedback environmentFrequency dependenceFrequency independenceInvasion fitnessMeso-evolutionary staticsOptimisation principlePessimisation principleWeak frequency dependence

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Area of Science:

  • Evolutionary biology
  • Population genetics
  • Theoretical ecology

Background:

  • Traditional population genetics defines frequency-independent fitnesses using discrete time models with non-overlapping generations.
  • Evolutionary ecologists often use per capita invasion speed in complex life histories, diverging from strict definitions.
  • Existing definitions of frequency independence may not fully capture practical ecological applications.

Purpose of the Study:

  • To develop a new concept of frequency independence applicable to eco-evolutionary models used by ecologists.
  • To establish criteria for frequency independence based on competitive hierarchies (invasion fitness signs).
  • To introduce and analyze a concept of weak frequency dependence for more realistic models.

Main Methods:

  • Defining frequency independence based on the ability to rank phenotypes by competitive strength (who can invade whom).
  • Analyzing the conditions for frequency independence, such as the absence of priority effects and rock-scissor-paper dynamics.
  • Comparing the proposed definition with existing concepts, particularly Heino et al.'s framework based on feedback environments.
  • Introducing and analyzing the concept of weak frequency dependence.

Main Results:

  • Frequency independence is achieved when phenotypes can be ranked by competitive strength, equivalent to avoiding specific ecological configurations.
  • The new definition relies solely on the signs of invasion fitnesses, differing from feedback environment-based approaches.
  • Eco-evolutionary models exhibit frequency independence if feedback effects on fitness signs are summarized by a single monotonic scalar.
  • Weak frequency dependence is defined to capture near-frequency-independent scenarios in realistic models.

Conclusions:

  • The proposed definition of frequency independence offers a more practical framework for evolutionary ecology.
  • The concept of weak frequency dependence allows for analysis of models that approximate frequency independence.
  • Understanding these fitness concepts is crucial for predicting evolutionary trajectories in complex ecological systems.