372 The UMAP Journal 22.4( 2001) Actual and Model growth Rates for an"Average Year 分30000 25000 15000 10000 Time(fraction of average year) Figure 3. The derivative of the population growth model, along with data for an average year at Lake A (at site 2, the most populous site). The peak height of 38,000 is the quantity that best characterizes the populations success, so it is used in the regression analysis Influence of the Environment: Multiple Regression Analysis To determine the effect of environmental conditions on growth rates, we lust correlate the peak growth rates in the logistic model with the chemical concentrations at each site. To this end, we perform a multiple regression with peak growth rate as the dependent variable and some or all of the chemical concentrations as independent variables There are only 10 data points, far fewer than needed to separate the effects of all 1l variables. Fortunately, the literature provides guidance in selecting which variables to use. The dominant factors influencing the success of a Dreissena population are the concentration of calcium and the pH. Although alkalinity seems to be somewhat important, it is included in only the first data set; more- over, it also appears to be closely correlated with calcium concentration,so we exclude it. Another marginally important factor, dissolved oxygen,was not measured in the first data set. According to the literature other chemical perform the regression on just two variables: calcium concentration andpt o factors are negligible as long as they are present in trace amounts. Thus, w The equation we obtain is maximum rate= 1687 [Ca2+]+55703 pH-454995 where the maximum growth rate is in juveniles settling per day and [Ca2+372 The UMAP Journal 22.4 (2001) Actual and Model Growth Rates for an “Average Year” Growth Rate (juveniles/day) 0.2 0.4 0.6 0.8 1 5000 10000 15000 20000 25000 30000 35000 Time (fraction of average year) Figure 3. The derivative of the population growth model, along with data for an average year at Lake A (at site 2, the most populous site). The peak height of 38,000 is the quantity that best characterizes the population’s success, so it is used in the regression analysis. Influence of the Environment: Multiple Regression Analysis To determine the effect of environmental conditions on growth rates, we must correlate the peak growth rates in the logistic model with the chemical concentrations at each site. To this end, we perform a multiple regression with peak growth rate as the dependent variable and some or all of the chemical concentrations as independent variables. There are only 10 data points, far fewer than needed to separate the effects of all 11 variables. Fortunately, the literature provides guidance in selecting which variables to use. The dominant factors influencing the success of a Dreissena population are the concentration of calcium and the pH. Although alkalinity seems to be somewhat important, it is included in only the first data set; more￾over, it also appears to be closely correlated with calcium concentration, so we exclude it. Another marginally important factor, dissolved oxygen, was not measured in the first data set. According to the literature, other chemical factors are negligible as long as they are present in trace amounts. Thus, we perform the regression on just two variables: calcium concentration and pH. The equation we obtain is maximum rate = 1687 [Ca2+] + 55703 pH − 454995, (1) where the maximum growth rate is in juveniles settling per day and [Ca2+]