Evolutionary Game Theory and Adaptive Dynamics of Continuous Traits

  title={Evolutionary Game Theory and Adaptive Dynamics of Continuous Traits},
  author={Brian J. McGill and Joel s. Brown},
  journal={Annual Review of Ecology, Evolution, and Systematics},
Continuous-trait game theory fills the niche of enabling analytically solvable models of the evolution of biologically realistically complex traits. Game theory provides a mathematical language for understanding evolution by natural selection. Continuous-trait game theory starts with the notion of an evolutionarily stable strategy (ESS) and adds the concept of convergence stability (that the ESS is an evolutionary attractor). With these basic tools in hand, continuous-trait game theory can be… 

Figures from this paper

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory

A dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability are derived by applying the Price equation to a multivariable Taylor polynomial.

Modeling social and evolutionary games.

  • A. Potochnik
  • Biology
    Studies in history and philosophy of biological and biomedical sciences
  • 2012

Difference equations as models of evolutionary population dynamics

  • J. Cushing
  • Mathematics, Biology
    Journal of biological dynamics
  • 2019
ABSTRACT We describe the evolutionary game theoretic methodology for extending a difference equation population dynamic model in a way so as to account for the Darwinian evolution of model

Evolutionary dynamics of continuous strategy games on social networks under weak selection: A preliminary study

The game dynamics in finite structured populations under weak selection is studied using the stochastic dynamics based on respectively the mutant fixation probability and the fixation probability ratio of mutant to resident (ρY/ρX).

Why Darwin would have loved evolutionary game theory

  • Joel s. Brown
  • Biology
    Proceedings of the Royal Society B: Biological Sciences
  • 2016
It is asserted that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations.

The Hitchhiker's Guide to Adaptive Dynamics

This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems, and how adaptive-dynamics techniques can be used in speciation research.

Instability of cooperation in finite populations

This work rigorously analyzes a standard model for the evolution of cooperation (the multi-player snowdrift game) and shows that in many situations in which there is a cooperative evolutionarily stable strategy if the population is infinite, there is no cooperative ESS if thepopulation is finite.

A bifurcation theorem for Darwinian matrix models and an application to the evolution of reproductive life-history strategies

  • J. Cushing
  • Mathematics
    Journal of biological dynamics
  • 2020
Bifurcation theorems for evolutionary game theoretic (Darwinian dynamic) versions of nonlinear matrix equations for structured population dynamics and a Darwinian model designed to investigate the evolutionary selection of reproductive strategies that involve either low or high post-reproductive survival (semelparity or iteroparity).

Evolutionary game theory

This chapter discusses in detail the main ingredients of a game-theoretical approach: strategies, payoffs and ‘solution concepts’ such as evolutionary stability, and introduces some of the classical models, including the Hawk–Dove game and the Prisoner’s Dilemma game.



Ecological stability, evolutionary stability and the ESS maximum principle

The concept of an ecological stable equilibrium (ESE) is used and the ESE concept is used to provide a very simple proof of the ESS maximum principle (which is a necessary condition for an ESS).

The dynamical theory of coevolution: a derivation from stochastic ecological processes

It is shown that the coevolutionary dynamic can be envisaged as a directed random walk in the community's trait space and a quantitative description of this stochastic process in terms of a master equation is derived.

Evolutionary Game Theory, Natural Selection, and

Whereas classic evolutionary game theory limits itself to behavioralinteractions and phenotypes, this book takes a very broad view of what constitutes a “game” and places natural selection itself within a game-theoretic framework.

Stability in an evolutionary game

Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits

A dynamic model of these adaptive scenarios in which the rate of change of the mean trait value is an increasing function of the fitness gradient is analyzed, arguing for greater attention to dynamical stability in models of the evolution of continuous traits.

Dynamics and evolution: evolutionarily stable attractors, invasion exponents and phenotype dynamics.

The mathematical formulation is used to analyse a non-reproductive form of evolution in which various learning rules compete and evolve and is given a very tentative economic application which has interesting ESAS and phenotype dynamics.

Random evolutionarily stable strategies.

Fitness minimization and dynamic instability as a consequence of predator–prey coevolution

The goal of the analysis is to determine conditions when the coevolutionary dynamics will be unstable and will generate population cycles, and to concentrate on the role of equilibrial fitness minima in producing cycles.

Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

A haploid version of Levene's ‘soft selection’ model is developed as a specific example to demonstrate evolutionary dynamics and branching in monomorphic and polymorphic populations.

Multi-species evolutionary dynamics

It is shown that under the above conditions an ESNIS has a better chance of being attained than a strategy coalition which is a CSS, and the theory developed is applied to a class of coevolutionary game models with Lotka–Volterra type interactions and shows that for such models, an ESS coalition will be dynamically attainable through mutations and natural selection if the E SS coalition is also an ESnIS coalition.