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

Area of Science:

• Theoretical Ecology
• Evolutionary Dynamics
• Mathematical Biology

Background:

• Coevolutionary dynamics in ecological communities are complex.
• Existing models often simplify stochastic evolutionary processes.
• Understanding individual-level ecological processes is key to coevolution.

Purpose of the Study:

• To develop a dynamical theory of coevolution in ecological communities.
• To explicitly incorporate stochasticity and individual-level processes.
• To derive and analyze the evolutionary paths and their underlying assumptions.

Main Methods:

• Derivation of a dynamical theory based on individual-level ecological processes.
• Modeling coevolutionary dynamics as a directed random walk in trait space.
• Quantitative description using a master equation and analysis of the first jump moment.

Main Results:

• The coevolutionary dynamic is described as a directed random walk.
• A master equation quantifies the stochastic process.
• Higher-order corrections reveal new effects like shifting isoclines and path slowing.

Conclusions:

• The derived theory recovers and refines existing models in evolutionary game theory.
• New evolutionary phenomena arise from stochasticity and higher-order dynamics.
• The framework is extendable to multi-trait and non-equilibrium coevolution.