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 sensitive
404 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 population 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
Waging War Against the Zebra Mussel 405 Graph 2. Comparing High and Low Density Popul 7194 196 l9771971/1I987F 1991/1/o 。eaon"t。 ation2Location3 ocation目 Figure 2. Comparison of high-and low-density populations. Another weakness of our model is that it relies on chemical and data from only one lake. By slightly varying the values of the coefficients observing whether the altered model more accurately predicts the density of the zebra mussels in the newly incorporated lakes, a better model can be achieved Information from other lakes could also be used to refine the value chosen for the division between low and high densities. Other factors, such as total ion concentration. could also be included in the model if the factor were shown in a variety of lakes to correspond to population densities We are not able to predict, using our model, how fast a population of ze bra mussels will spread from one site to another within a lake. However, by qualitatively examining the data from Lake A, it appears to take only a few years for the population to spread from one area to another as long as the new site is suitable for zebra mussels. For example, in site 5 in 1994 and 1995 there were no zebra mussels collected, but from 1996 to 1998, the population rapidly increased to a high density. Since zebra mussels can very quickly reach high density populations in a supportive environment, it seems that knowing whether a given site is a suitable habitat is a more useful piece of information than the rate at which the population grows Using Model for Lake a to Predict for Lake b and lake c Using the equations from our models, we can average pH, calcium concen- tration, total phosphorus concentration, and total nitrogen concentration for
Graph 2. Comparing High and Low Density Popula 0 500000 1000000 1500000 2000000 2500000 3000000 3500000 7/1/94 1/1/95 7/1/95 1/1/96 7/1/96 1/1/97 7/1/97 1/1/98 7/1/98 1/1/99 7/1/99 1/1/00 7/1/00 Date juveniles/m^2 Location 1 Location 2 Location 3 Location 5 Waging War Against the Zebra Mussel 405 Figure 2. Comparison of high- and low-density populations. Another weakness of our model is that it relies on chemical and population data from only one lake. By slightly varying the values of the coefficients and observing whether the altered model more accurately predicts the density of the zebra mussels in the newly incorporated lakes, a better model can be achieved. Information from other lakes could also be used to refine the value chosen for the division between low and high densities. Other factors, such as total ion concentration, could also be included in the model if the factor were shown in a variety of lakes to correspond to population densities. We are not able to predict, using our model, how fast a population of zebra mussels will spread from one site to another within a lake. However, by qualitatively examining the data from Lake A, it appears to take only a few years for the population to spread from one area to another as long as the new site is suitable for zebra mussels. For example, in site 5 in 1994 and 1995, there were no zebra mussels collected, but from 1996 to 1998, the population rapidly increased to a high density. Since zebra mussels can very quickly reach high density populations in a supportive environment, it seems that knowing whether a given site is a suitable habitat is a more useful piece of information than the rate at which the population grows. Using Model for Lake A to Predict for Lake B and Lake C Using the equations from our models, we can average pH, calcium concentration, total phosphorus concentration, and total nitrogen concentration for