404 The UMAP Journal 22. 4(2001) To improve upon Model l, we account for trends observed in the second data set from Lake A in constructing a more descriptive model to answer question(2) By including parameters for total phosphorus and total nitrogen, we account for the role of food availability on density. Following Ramcharan [1992], we employ the natural logarithms of total phosphorus and total nitrogen. Once again, by successively altering the coefficients, we determine an equation for the density of populations in the lake sites. We define high density as more than 400,000 juveniles/m on the settling plates collected at the peak of the reproductive season D=1.0 pH+0.2 [Ca]+0.1In [TP+0. 4In ITNI D<9.9, there will be no zebra mussels If 10<D<10.4, the site will support a low-density population; D>10.5 the site will support a high-density population By averaging the total phosphorus(TP) and total nitrogen(TN) values for each site in the second set of chemical data for Lake A, we calculated tpl and ITN]. USing those values in Model 2, we calculated the density D)for each site, as shown in table 2 Table 2 Density values in sites 1-10 in Lake A site In/TPI In[TN] D low/high mg/L mg/L 2.99-0.59812 hi 2 3.51-0.89211.8 g 079610.5high 4 4.47-0.81410.3 5-4400.87910.6 6|-4560.8529.5 absence 7-412-097110.2 8|-439-0.862103 9|-416-0965103 10-301-040598 absence Model 2 predicts that sites 1, 2, 3, and 5 should be able to support high density populations. The second set of population data used in Figure 2 is consistent with the first set of population data. Figure 2 shows that all four of the high-density sites have an average of more than 400,000 juveniles/m which agrees with the prediction made by our model. In the enlargement of Figure 2, sites 4, 7, 8, and 9 have an average of less than 400,000 juveniles/m2 while sites 6 and 10 have virtually no juvenile zebra mussels The most significant weakness of our model is that it does not predict pop- ulation versus time. Our model simply classifies an area's risk of invasion by examining the levels of critical chemicals to which the zebra mussels are sensitive404 The UMAP Journal 22.4 (2001) To improve upon Model 1, we account for trends observed in the second data set from Lake A in constructing a more descriptive model to answer question (2). By including parameters for total phosphorus and total nitrogen, we account for the role of food availability on density. Following Ramcharan [1992], we employ the natural logarithms of total phosphorus and total nitrogen. Once again, by successively altering the coefficients, we determine an equation for the density of populations in the lake sites. We define high density as more than 400,000 juveniles/m2 on the settling plates collected at the peak of the reproductive season. D = 1.0 pH + 0.2 [Ca] + 0.1 ln [TP] + 0.4 ln [TN]. If    D < 9.9, there will be no zebra mussels; 10 <D< 10.4, the site will support a low-density population; D > 10.5, the site will support a high-density population. By averaging the total phosphorus (TP) and total nitrogen (TN) values for each site in the second set of chemical data for Lake A, we calculated [TP] and [TN]. Using those values in Model 2, we calculated the density (D) for each site, as shown in Table 2. Table 2. Density values in sites 1–10 in Lake A. site ln[TP] ln[TN] D low/high mg/L mg/L 1 −2.99 −0.598 12.5 high 2 −3.51 −0.892 11.8 high 3 −4.30 −0.796 10.5 high 4 −4.47 −0.814 10.3 low 5 −4.40 −0.879 10.6 high 6 −4.56 −0.852 9.5 absence 7 −4.12 −0.971 10.2 low 8 −4.39 −0.862 10.3 low 9 −4.16 −0.965 10.3 low 10 −3.01 −0.405 9.8 absence Model 2 predicts that sites 1, 2, 3, and 5 should be able to support high density populations. The second set of population data used in Figure 2 is consistent with the first set of population data. Figure 2 shows that all four of the high-density sites have an average of more than 400,000 juveniles/m2, which agrees with the prediction made by our model. In the enlargement of Figure 2, sites 4, 7, 8, and 9 have an average of less than 400,000 juveniles/m2, while sites 6 and 10 have virtually no juvenile zebra mussels. The most significant weakness of our model is that it does not predict pop￾ulation versus time. Our model simply classifies an area’s risk of invasion by examining the levels of critical chemicals to which the zebra mussels are sensitive