Evolution and Control of Ecological Communities

The Lotka-Volterra model for population dynamics is used to study the controllability and evolutionary trajectories of large, complex communities. A simple geometric interpretation for modifying interactions to displace the equilibrium abundance of communities towards some desired state is derived. It is possible to change communities with high specificity by modifying multiple interactions. On the slower evolutionary timescale, a mean-field adaptive dynamics model is used to predict the analytical trajectory of the community. This effective model averages over the noisy mutation-invasion events to provide an analytically tractable scheme representing local evolutionary behaviors. The two analytical frameworks presented can be used for (short) population dynamic and (long) evolutionary timescales.