424 Ford et al.: Use of Water by Eastern Hemlock Table 1. Predictive multiple-variable linear regression equations for eastern hemlock whole-tree daily water use (dwu, L water per day−1 ).z Model 1 2 Equation ln (dwu) –1.33 + 0.061 (dbh) + 0.027 (avg_T) + 0.003 (doy) + 0.676 (vpd) ln (dwu) –0.970 + 0.061 (dbh) + 0.071 (avg_T) Adjusted R2 0.83 0.78 F statistic 181.74 269.04 zIndependent variable descriptions and corresponding units are: 1) diameter at breast height (dbh, cm); 2) average daytime air temperature (avg_T, °C); 3) day of year (doy, julian); and 4) average daytime vapor pressure deficit (vpd, kPa). For all predictors, P > |t| was less than 0.01. Both models were significant at P < 0.001. expansion through time and sapwood growth through time) and evaporative demand. The more complex model predicting daily water use by eastern hemlock included tree diameter, average daytime air temperature, day of year, and daytime average vapor pressure deficit as variables (Table 1). The order of the variables in this model corresponds to their predictive ability. The simpler model included tree diameter and average daytime air tem- perature as predictor variables (Table 1; Figure 4). Although the more complex model had greater predictive ability than the less complex model (Table 1), both models performed well (adjusted R2 was 0.83 for the more complex model and 0.78 for the simpler model). Potential Application of Models The strongest predictor of whole-tree daily water use in east- ern hemlock was tree size (i.e., dbh). The exponential rela- tionship between mass flow of water and tree size (Figure 3) in eastern hemlock means that an exponential volume or mass of insecticide should also be applied to trees per unit diameter to achieve a consistent and known concentration in the tree xylem sap across tree sizes. Yet, most studies report using a constant dosage per unit diameter, consistent with the manu- facturer-recommended dosage (Fidgen et al. 2002; Webb et al. 2003; Doccola et al. 2005; McAvoy et al. 2005). The dosages used in all four studies previously mentioned would result in a higher concentration of imidacloprid for smaller diameter trees than for larger ones. For example, if the rec- ommended dosage is 0.55 g/cm−1 (1.4 g/in−1) dbh, an 80 cm (32 in) tree would receive 44 g (1.54 oz) of active ingredient (AI), whereas a 20 cm (8 in) tree would receive 11 g (0.39 oz) of AI. Based on our measurements and models of water use, an 80 cm (32 in) tree growing at 20°C (68°F) mean daytime temperature would use 200 L (52 gal) of water per day, resulting in a mean concentration of 0.22 g (0.01 oz) AI L−1 per day−1 (0.83 g [0.03 oz] AI gal−1 per day−1) (assuming that all of the chemical was released from the capsule in one day, concentrations would even lower if the chemical were re- leased over several days). By contrast, a 20 cm (8 in) tree would use 5 L (1.3 gal) of water per day, resulting in a mean concentration of 2.2 g (0.08 oz) AI L−1 per day−1 (8.3 g [0.29 oz] AI gal−1 per day−1). This 10-fold difference in imidaclo- prid concentration could affect the effectiveness of HWA treatments. The physio- and biochemical processes involved with root Figure 4. Estimated whole-tree daily water use of eastern hemlock trees of varying diameter at breast height (dbh, cm) as a function of mean daytime air temperature pre- dicted by model 2 in Table 1. ©2007 International Society of Arboriculture (from soil application) or stem uptake (from stem injection), dissolution in the xylem stream, movement to the leaves and twigs, and symplastic and apoplastic translocation of imida- cloprid are complex and beyond the scope of this study. How- ever, as recent studies show, the concentration of imidaclo- prid in the sap is highly correlated with HWA mortality. For example, varying the concentration of imidacloprid in water taken up by excised stems has been shown to directly affect HWA mortality (Cowles et al. 2006). Specifically, with each order of magnitude increase in concentration of AI in water taken up through the stems of excised infested branches, HWA mortality increased roughly 30%. A concentration of
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