PREDICTION OF LONG-DISTANCE DISPERSAL USING GRAVITY MODELS: ZEBRA MUSSEL INVASION OF INLAND LAKES

Abstract

Gravity models are commonly used by geographers to predict migration and interaction between populations and regions. Even though rarely used by ecologists, gravity models allow estimation of long-distance dispersal between discrete points in heterogeneous landscapes. We developed a production-constrained gravity model to forecast zebra mussel (Dreissena polymorpha) dispersal into inland lakes of Illinois, Indiana, Michigan, and Wisconsin (USA) based on the site and location of lakes and the number and location of boats within 364 counties. A deterministic form of this model was used to estimate best-fit parameters for distance coefficient, Great Lakes boat-ramp attractiveness, and colonization cutoff threshold. A stochastic model thus developed from these parameters allows for random changes in colonization likelihood. The results of our model are highly correlated with the actual pattern of colonized lakes in southern Michigan and southeastern Wisconsin at the end of 1997. Areas of central Wisconsin and western Michigan, where zebra mussel colonies have not been documented, were also predicted to be colonized, suggesting that future invasions may be imminent in these locations. These analyses suggest that gravity models may be useful in predicting long-distance dispersal when dispersal abilities of species and the attractiveness of potential habitats are known.