76 Sadof et al.: Restoration Capacity and Costs of Managing the Emerald Ash Borer in Urban Forests where Vn = the value at the end of the investment period, Vo = value at the beginning of the investment, i = interest rate, and n = number of periods (years) (Rose et al. 1988). Evaluating Cost and Reforestation Capacity Projections of costs and tree size of 11 management strategies (Appendix), were compared under an arbitrary assumption that the discount rate would be 3%. Effects of the discount rate on strategy costs are explored in a sensitivity analysis that will be described later. Trees were treated every three years in an- ticipation that insecticide applications are likely to be effective for three years (Herms et al. 2009). The first three management scenarios—remove all ash trees, replace all ash trees, treat all ash trees—are the simplest cases. The next four management strategies are based on recent research that indicates ash trees with a DBH of up to 63.5 cm can be protected with insecticides. Under the assumption of the normal growth, trees with a DBH > 30 cm in 25 years are likely to grow beyond the point where protection has been demonstrated (Herms et al. 2009; Sadof 2009b). The first two of these strategies protect all trees smaller than this critical size and remove or replace the larger ash trees. The next two strategies only protect trees with an initial DBH between 15 and 30 cm while removing or replacing the rest. In these strategies, recently planted trees with a DBH < 15 cm are removed in attempt to take advantage of their ease of removal and relatively low investment in maintenance. This size class also happens to be the median size of ash trees in Indianapolis. The last four strategies have been contrived under the optimis- tic scenario that technology will be developed to compensate for trees with a DBH > 61 cm. Examined here is the cost of protecting the historical investment in larger trees and replacing the smaller trees. The first two strategies compare using a minimum size of 30 cm to select trees that will be treated with insecticides with the remainder being removed or replaced. The last two strategies were selected from a recent study of urban ash trees in North America that suggest protecting trees with a minimum DBH of 61 cm would optimize the value of the standing forest and minimize control and removal costs for city managers (Kovacs et al. 2010). Reforestation capacity of each management strategy was evaluated by calculating the size of the resulting forest relative to the initial size of the ash forest. The projected forest size in any year is expressed as the sum of the DBH of all trees. The initial size of ash forest was estimated from inventory data by multiplying the midpoint value of each size range by the num- ber of trees in each size class, and calculating the sum (Table 1). Reforestation capacity at each time step was expressed as a percentage of the initial forest size and plotted over time. The relative cost of each management strategy was evaluated by comparison to the strategy of removing all ash trees and re- placing them with a resistant tree. In this way, each strategy was compared to a simple approach toward reforestation that would eventually eliminate the need for managing trees for EAB. Rela- tive cost of each management strategy was expressed as a per- centage of the cost of replacing all ash trees and plotted over time. To demonstrate graphics provided by the calculator, the cal- culator was used to construct plots of annual and cumulative costs, and forest size over time for the three simple management strategies of treating, removing and replacing all trees. Plots that evaluate reforestation capacity and relative costs of each manage- ©2011 International Society of Arboriculture ment strategy were obtained from tabular values of cost and for- est size provided by the calculator for each year of the simulation. Impacts of Variable Factors on 25-year Strategy Projections Later compared were the expected variations in treatment cost, discount rates, median tree size, and cost of tree removal, and their impact on the 25-year costs of each of the seven default strategies on the EAB calculator website. Treatment costs were reduced by extending the number of years between insecticide treatments from one to four years. Discount rates were var- ied between zero and 6% to determine effects of the variable cost of money. Median tree size of the Indianapolis data set was shifted one size class up or down to determine projected costs for an urban forest with younger trees (median size tree size 7–15 cm DBH) or older trees (median tree size 15–30 cm DBH). Finally, to determine how the price of ash removal costs could alter future costs, the program was run with initial removal costs as well as at two, four, and eight times the rate. Tradeoffs Between Insecticide Treatment and Tree Replacement In order to generalize beyond the 11 strategies, alterations to the proportion of ash trees replaced or treated with insecticide affects forest regeneration after 25 years were examined. Two approaches were used to reduce the proportion of trees treated with insecticide. The first gradually increased the percentage of trees in each size category that would be treated with insecticide rather than to be replaced. The second specified a maximum caliper size to select trees that would be protected with insec- ticide and not replaced. According to this scheme, if the maxi- mum DBH is 0 cm, then all trees would be replaced and no trees would be treated; whereas if the minimum was 107 cm, then all trees would be treated. Forest regeneration was measured as a percentage change from the initial size of the ash forest. Results were plotted and curves fit to a linear model for comparisons. RESULTS Comparison of simple management programs for the City of In- dianapolis based on single tactics indicate that treating each ash tree every third year had the lowest annual cost, but the highest total cost in current dollars after 25 years (Figure 1). Cumula- tive costs for treatment reached the costs of removing all ash trees in seven years, and replacing all trees in 17 years. As ex- pected, successfully protecting standing trees with insecticide produced a forest larger than what would be expected if all ash trees were removed and replaced with 5 cm trees. The size of the replacement forest was at its minimum in year five but reached the size of the initial Indianapolis ash forest after 25 years. Examination of reforestation capacity of each of the 11 strate- gies indicate that at its minimum, the size of the forest produced by replacing all Indianapolis ash trees was 27% the initial size of the initial ash forest (Figure 2). Growth of these replacement trees produced a forest that was 50% the initial size by year twelve, 75% by year eighteen, and 100% after 25 years (Fig- ure 2a). Those strategies which combined the replacement and treating of ash trees produced a forest that was intermediate in size when compared to that of simply treating or replacing all
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