Singular point implies coexistence in adaptive dynamics

Adaptive dynamics is a relatively new mathematical framework for studying evolution(~1990s). Under the influence of the mathematical ecology and the game theory, adaptive dynamics considers the effect of resident populations on the fitness landscape. As a result, it explains a possible mechanism of evolutionary branching. In this talk, I introduce adaptive dynamics and Pairwise Invasibility Plot (PIP) analysis, a standard method for understanding the adaptive dynamics. Then, I propose a new approach to analyze the adaptive dynamics which enable us to understand higher dimensional systems than PIP does.