Some discrete competition models and the competitive exclusion principle

A difference equation model, called that Leslie/Gower model, played a key historical role in laboratory experiments that helped establish the competitive exclusion principle in ecology. We show that this model has the same dynamic scenarios as the famous Lotka/Volterra (differential equation) competition model. It is less well known that some anomalous results from the experiments seem to contradict the exclusion principle and Lotka/Volterra dynamics. We give an example of a competition model that has non-Lotka/Volterra dynamics that are consistent with the anomalous case.