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Coevolutionary dynamics: from finite to infinite populations.
Arne Traulsen1, Jens Christian Claussen, Christoph Hauert
1Institut für Theoretische Physik und Astrophysik, Christian-Albrechts Universität, Olshausenstrasse 40, 24098 Kiel, Germany. traulsen@fas.harvard.edu
Physical Review Letters
|December 31, 2005
Summary
This study clarifies the link between deterministic and stochastic evolutionary dynamics in large populations. It shows how individual-level variations and population size impact evolutionary trajectories, even reversing them.
Area of Science:
- Evolutionary dynamics
- Theoretical ecology
- Population genetics
Background:
- Deterministic replicator dynamics assume infinite populations.
- Stochastic processes are increasingly used for finite populations.
- The relationship between these approaches was previously unclear.
Purpose of the Study:
- To clarify the relationship between deterministic and stochastic evolutionary dynamics.
- To identify microscopic stochastic processes underlying replicator dynamics.
- To investigate the impact of individual differences and population size on evolutionary outcomes.
Main Methods:
- Analysis of evolutionary dynamics in large populations.
- Identification of microscopic stochastic processes.
- Comparison of standard and adjusted replicator dynamics.
Main Results:
- Identified microscopic stochastic processes leading to standard or adjusted replicator dynamics.
- Demonstrated that individual-level differences can cause qualitatively different dynamics.
- Showed that population size can invert the direction of evolutionary processes, especially in asymmetric conflicts.
Conclusions:
- Explicitly considered large populations to bridge deterministic and stochastic evolutionary dynamics.
- Provided a framework for understanding how finite population effects emerge from microscopic processes.
- Highlighted the crucial role of population size and individual variation in shaping evolutionary trajectories.