Competition-colonization trade-off can explain any observed abundances and assumed competitive hierarchies

The competition-colonization trade-off is a possible explanation for coexistence of species in a metacommunity context that has been intensively studied for decades. Nonetheless, questions about the ubiquity and generality of the mechanism remain. The outcome of the model, equilibrium species abundances, are relatively easy to measure. However, the input into the basic model, the competitive hierarchy and the colonization rates, are not easy to measure in the field. We propose an approach that starts with an observed equilibrium configuration. We show that for any assumed competitive hierarchy we can find a corresponding set of colonization rates that would produce the observed equilibrium. We also find a simple formula for the colonization rates in terms of the observed abundances. This approach both shows that any observed set of abundances can result from a competition-colonization trade-off, and provides a method for future analyses. Additionally, generalizations of our approach can apply to generalizations of the basic competition-colonization model that avoid any biologically questionable assumptions.