376 The UMAP Journal 22. 4(2001) data point for each lake, we must extrapolate. Thus, the model's predictions might not hold in areas where the concentration or pH differs significantly from this value The model clearly indicates that there is no chance of zebra mussel infes- tation in Lake C, consistent with the fact that the ph in the lake is far too low to support a mussel population. The literature indicates zero growth at a ph below about 7.3: the highest measurement of pH in Lake C is 6.0, which is clearly far too acidic. In addition, the calcium concentration must be greater than 12 mg/L for larvae survival; Lake C is far below this cutoff, with a mere 1.85 mg/L at maximum The chemical data for Lake B are less clear cut. The pH is in the required range but the calcium concentration is too low for adult survival. Our model and the literature both indicate that it would take a significant shift in the lakes calcium content for it to support zebra mussels Although taken over the course of several years, the data for lakes B and C are not spread out spatially. It is possible that some region in either lake has much higher pH and calcium concentrations. For example, Lake george in the Adirondacks was initially thought to be immune to zebra mussels because of the water chemistry, but they were later discovered in a small region near a cul- vert with elevated calcium concentrations. Scientists are now concerned about Dreissena's potential to spread to other parts of lake George, as the mussels have an amazingly ability to adapt once they have settled [Revkin 2000 Other models strongly agree with our conclusions about Lakes b and c Hincks and Mackies model [1997] also found that zebra mussel populations depend only on pH and calcium concentration. Their formula, where L=1347-3659[a2+1-15.868pH+0.43ICa2+lpH, predicts 100% mortality in Lake C and 99% in Lake B; a population might be able to make some headway if it could establish itself in Lake b Ramcharan et al. [1992] modeled the probability of a population becoming established, finding through discriminant analysis that only ph and calcium levels are significant factors. The discriminant function is A=1246pH+0.045Ca2+]-11.696 where A must be greater than.638 for a population to exist. This equation which is nearly a constant multiple of our (1), suggests that no populations would establish themselves in either lake376 The UMAP Journal 22.4 (2001) data point for each lake, we must extrapolate. Thus, the model’s predictions might not hold in areas where the concentration or pH differs significantly from this value. The model clearly indicates that there is no chance of zebra mussel infes￾tation in Lake C, consistent with the fact that the pH in the lake is far too low to support a mussel population. The literature indicates zero growth at a pH below about 7.3; the highest measurement of pH in Lake C is 6.0, which is clearly far too acidic. In addition, the calcium concentration must be greater than 12 mg/L for larvae survival; Lake C is far below this cutoff, with a mere 1.85 mg/L at maximum. The chemical data for Lake B are less clear cut. The pH is in the required range but the calcium concentration is too low for adult survival. Our model and the literature both indicate that it would take a significant shift in the lake’s calcium content for it to support zebra mussels. Although taken over the course of several years, the data for Lakes B and C are not spread out spatially. It is possible that some region in either lake has much higher pH and calcium concentrations. For example, Lake George in the Adirondacks was initially thought to be immune to zebra mussels because of the water chemistry, but they were later discovered in a small region near a cul￾vert with elevated calcium concentrations. Scientists are now concerned about Dreissena’s potential to spread to other parts of Lake George, as the mussels have an amazingly ability to adapt once they have settled [Revkin 2000]. Other models strongly agree with our conclusions about Lakes B and C. Hincks and Mackie’s model [1997] also found that zebra mussel populations depend only on pH and calcium concentration. Their formula, p = eL 1 + eL , where L = 134.7 − 3.659 [Ca2+] − 15.868 pH + 0.43 [Ca2+]pH, predicts 100% mortality in Lake C and 99% in Lake B; a population might be able to make some headway if it could establish itself in Lake B. Ramcharan et al. [1992] modeled the probability of a population becoming established, finding through discriminant analysis that only pH and calcium levels are significant factors. The discriminant function is A = 1.246 pH + 0.045[Ca2+] − 11.696, where A must be greater than −0.638 for a population to exist. This equation, which is nearly a constant multiple of our (1), suggests that no populations would establish themselves in either lake