The stability of a community at equilibrium determines how it will respond to perturbations. Evolution can have important impacts on community stability; if populations evolve in response to perturbations, this will influence whether or not they return to their original state. In this work, we use matrix analysis to understand how feedbacks between ecological demographic responses and evolutionary trait changes affect community stability. In particular, we ask how do eco-evolutionary feedbacks impact stability when evolution is slow? When and how does this change with rapid evolution?
We derive an analytical condition to determine the stability of a community accounting for ecological and evolutionary dynamics. We find that a positive feedback between these two processes, i.e. directional trait changes lead to a demographic response that leads to selection for trait changes in the same direction, can destabilize a community that would be stable in the absence of the feedback. Conversely, a negative feedback, i.e. directional trait changes lead to a demographic response that leads to selection for traits to change in an opposing direction, can stabilize a community. Finally, the stability can change from rapid to slow evolution, where loss of stability results in cycles.