Figure 2.

Comparison between models using zebra mussel invasions in Michigan for parameterization (1992–2001). (a) Projected relation between invasibility and environmental conditions (pH and calcium), $P(I|{\mathit{x}}_l)$, when we use the joint model (open circles) versus only the invasibility sub-model (filled circles). Invasibility is estimated to be much lower if propagule pressure is not considered. (b) Projected relation between probability of establishment and propagule pressure, P(E|N_l,t), when we use the joint model (open squares) versus only the propagule pressure sub-model (filled squares). The effect of propagule pressure is estimated to be much lower if invasibility is not included. (c) Forecasting risk of invasion. We used data from 1992 to 1996 to parameterize the models. For each model, we predicted the most probable lakes to be invaded, using the top ranked 100 lakes at risk. We compared predictions of the models (null model, only invasibility, only propagule pressure, and joint model) to observations of actual invasions occurring in our validation dataset, from 1997 to 2001 (i.e. how many of the 100 lakes identified as high risk became invaded).