Evolution and Mutualism in Fundamental Models for Ecological Interactions

I will present an investigation of adaptive evolutionary change in Lotka-Volterra and closely related systems, including long-term development of properties of the interaction matrix. I will present some mathematical results both in the case that interaction terms (entries in the interaction matrix) evolve independently of each other and in the case of interactions constrained to a low-dimensional tradeoff surface. In the presentation of the mathematics, we will discover a sense in which the system ‘gravitates’ toward mutualism — ecological cooperation — in each case. Additionally I will discuss how the presence of mutualism appears to change the overall system dynamics qualitatively.