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This study explores how cooperation evolves in populations where individuals adjust their investments based on local density. Different cost models reveal that cooperation can be highest in intermediate populations, challenging simple assumptions.

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Area of Science:

  • Evolutionary Biology
  • Behavioral Ecology
  • Mathematical Biology

Background:

  • Cooperation is prevalent despite exploitation by defectors, posing an evolutionary puzzle.
  • Defectors benefit from public goods without contributing, making cooperation appear irrational.
  • Understanding the evolution of cooperation is crucial in various biological and social systems.

Purpose of the Study:

  • To investigate the evolution of plastic, quantitative cooperation.
  • To model how individuals adjust investments in public goods based on local population density.
  • To analyze the impact of different cost-of-cooperation mechanisms on cooperative strategies.

Main Methods:

  • Utilized the adaptive dynamics framework for evolutionary analysis.
  • Modeled populations with stochastic demographic events (births and deaths).
  • Incorporated costs of cooperation by affecting birth or death rates.

Main Results:

  • Density-dependent cooperation evolved as a decreasing function of population size when costs reduced birth rates.
  • When costs increased death rates, density-dependent cooperation showed a qualitatively different form, peaking in intermediate populations.
  • Model details, such as how cooperation costs are applied, significantly impact evolutionary outcomes.

Conclusions:

  • The evolution of cooperation is sensitive to the ecological context and the specific mechanisms of cost realization.
  • Plastic cooperation, adjusting investment with density, can lead to complex evolutionary trajectories.
  • Intermediate population densities can favor higher levels of cooperation under certain cost structures.