4.3 Biological applications: evolutionary stable strategies

Evolutionary stable strategies (ESS) blend game theory with biology to explain animal behavior. They represent strategies that, when adopted by a population, can't be overtaken by alternatives. This concept helps us understand how certain behaviors persist in nature.

ESS ties into the broader applications of Nash equilibrium in biology. It shows how game theory principles can illuminate evolutionary processes, explaining phenomena like cooperation, aggression, and communication in animal populations. This approach bridges economics, politics, and biology through shared game theory concepts.

Evolutionary Stable Strategies

Concept and Relevance

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• An evolutionary stable strategy (ESS) is a strategy that, if adopted by a population, cannot be invaded by any alternative strategy
• ESS is a key concept in evolutionary game theory combines game theory with evolutionary biology to study the behavior of populations over time
• In biological systems, an ESS represents a behavioral strategy that, once adopted by a majority of individuals, provides them with a fitness advantage over individuals using alternative strategies

Examples in Nature

• The hawk-dove game models aggressive vs. passive behavior
• The prisoner's dilemma models cooperation vs. defection
• ESS helps explain the evolution and maintenance of various behavioral traits in animal populations
  • Altruism
  • Cooperation
  • Aggression

Conditions for Evolutionary Stability

Nash Equilibrium and Resistance to Invasion

• For a strategy to be evolutionarily stable, it must be a Nash equilibrium meaning that no individual can benefit by unilaterally changing their strategy
• An ESS must also be resistant to invasion by mutant strategies, ensuring that it remains stable over evolutionary time

Factors Influencing Stability

• The stability of an ESS depends on the frequency of individuals adopting the strategy in the population
• In some cases, multiple ESSs can coexist in a population, leading to a mixed ESS where individuals adopt different strategies
• The evolutionary stability of a strategy can be influenced by factors such as:
  • Population size
  • Mutation rates
  • Environmental conditions

Game Theory in Animal Evolution

Studying Cooperation and Conflict

• Game-theoretic models can be used to study the evolution of cooperation and conflict in animal populations
  • Prisoner's dilemma
  • Hawk-dove game
• These models help explain the conditions under which cooperative behavior can evolve and be maintained, despite the apparent benefits of selfish behavior

Communication and Biological Systems

• The evolution of communication in animal populations can be studied using game-theoretic models, such as the signaling game models the interaction between signalers and receivers
• Game-theoretic models can be applied to various biological systems
  • Predator-prey interactions
  • Mating strategies
  • Social behavior in group-living animals
• Empirical studies in animal behavior and ecology can be combined with game-theoretic models to test predictions and gain insights into the evolution of complex behavioral strategies

Frequency-Dependent Selection vs Mutation

Frequency-Dependent Selection

• Frequency-dependent selection occurs when the fitness of a strategy depends on its frequency in the population relative to other strategies
• Positive frequency-dependent selection favors common strategies, while negative frequency-dependent selection favors rare strategies
• Frequency-dependent selection can lead to the coexistence of multiple strategies in a population, as the fitness of each strategy varies with its frequency

Mutation and Evolutionary Dynamics

• Mutation introduces new strategies into a population, which can potentially invade and replace existing strategies if they have a fitness advantage
• The rate of mutation can influence the evolutionary dynamics of a population, with higher mutation rates leading to faster evolution and greater diversity of strategies
• The interplay between frequency-dependent selection and mutation can result in complex evolutionary dynamics
  • Cyclic dominance
  • Fluctuating selection