Evolutionary Dynamics Can be Chaotic: a First Example

We present in this paper the first example of chaotic evolutionary dynamics in biology. We consider a Lotka-Volterra tritrophic food chain composed of a resource, its consumer, and a predator species, each characterized by a single adaptive phenotypic trait, and we show that for suitable modeling and parameter choices the evolutionary trajectories approach a strange attractor in the three-dimensional trait space. The study is performed through the bifurcation analysis of the so-called canonical equation of Adaptive Dynamics, the most appropriate modeling approach to long-term evolutionary dynamics.