Modeling the Effects of Cannibalistic Behavior in Zebra Mussel (Dreissena polymorpha) Populations

The threat of invasive species has increased with the expansion of global transportation. In the United States, zebra mussels became a problem by the early 1990’s when they were introduced by ballast water into Lake St. Clair in 1988. In 2007, a new deterministic discrete-time model for zebra mussel populations was proposed by Casagrandi. We show how this model produces periodic, stable, and chaotic population patterns. In addition, a parametric analysis corrects some results of Casagrandi concerning the effect of changes in the adult cannibalistic behavior through filter-feeding. Finally, a new stochastic continuous-time model is proposed, abstracted from the Casagrandi model and implemented via the Gillespie algorithm.