Symmetric competition as a general model for single-species adaptive dynamics

Area of Science:

• Evolutionary Biology
• Theoretical Ecology
• Mathematical Biology

Background:

• Adaptive dynamics is a key framework for modeling the long-term evolution of continuous phenotypes.
• It relies on invasion fitness functions to determine selection gradients and the canonical equation of adaptive dynamics.
• Current insights from adaptive dynamics are often model-dependent due to the ecological model specification required for invasion fitness functions.

Purpose of the Study:

• To delineate the generality of results derived from adaptive dynamics models.
• To establish a precise connection between complex adaptive dynamics models and simpler competition models.
• To demonstrate how understanding symmetric competition models can illuminate broader evolutionary dynamics.

Main Methods:

• Analyzing the mathematical properties of invasion fitness functions.
• Transforming adaptive dynamics models with a specific gradient property into generalized symmetric competition models.
• Investigating the relationship between selection gradients and scalar function gradients.

Main Results:

• Any adaptive dynamics model based on an invasion fitness function with a specific gradient property can be transformed into a generalized symmetric competition model.
• This transformation clarifies the scope and limitations of evolutionary insights derived from competition models.
• A complete understanding of symmetric, frequency-dependent competition models is sufficient to understand a broad class of adaptive dynamics models.

Conclusions:

• The study provides a precise framework for understanding the generality of adaptive dynamics results.
• Results derived from competition models are more broadly applicable than previously assumed for models satisfying a certain gradient condition.
• This work simplifies the analysis of evolutionary dynamics by connecting diverse models to a common, well-understood framework.