Community Composition in a Changing World: Using a Circuit Equation to Predict Invasion Dynamics*

Ecological communities are often composed of multiple species competing for the same resources.  Traditional Lotka-Volterra models would predict survival of only the species with the highest fitness. However, migration from outside the system permits species with lower fitness to stably persist, allowing them to quickly proliferate when conditions become more favorable. Thus, understanding the basis for invasive species persistence in suboptimal environments is important for predicting ecological dynamics under climate change.

Using a simple Lotka-Volterra equation modified to include migration, we show that the fitness of a less-fit species can be solved for based on its steady state survival when migration occurs. The equation is analogous to that describing an electrical circuit, I=V/R with the current, I, equivalent to the migration rate, the inverse of resistance, 1/R, equivalent to the steady state population of the invader, and the volatege, V, equivalent to the difference in fitness between the resident and the less fit invader. 

Here, we test this prediction by invading a population of E. Coli with 20 different mutants with known fitness defects. 

The approach provides a predictor of steady-state community composition, a potential tool for measuring in vivo fitness in invasive populations,  as well as predicting populations with the potential to become invasive due to stochastic variation and climate change.