122 METHODS Overview Annual costs and benefits are tracked and net gains or losses calculated over a 30-year period and summarized in graphical and tabular formats. The various elements of the model are pre- sented here in a sequential format. The full range of possible model outputs are demonstrated using default settings, for a small diameter at breast height (15 cm DBH), medium (30 cm), and large (45 cm) ash tree (with cost data and results in 2010 Canadian dollars). It should also be understood that consider- able uncertainty exists in the underlying data. Uncertainty does not eliminate the need for careful analysis of options and pos- sible outcomes. A relatively simple sensitivity analysis was carried out by running the model using three plausible values for each of six different parameters while holding the values of all other parameters at the default values for a medium-sized ash located on the west side of the property and within 10 m of the house. Although default settings were employed for the results presented here, all parameter values can be overridden by model users as required for their specific circumstances. Users can also choose whether or not to include the differ- ent benefit categories depending on their particular interests. Characterizing Existing and Replacement Trees To estimate many of the costs and benefits described here, it is necessary to briefly characterize both the existing ash tree, and if applicable, the tree that would replace it under the removal and replacement scenario. Thus, model users are required to identify the size (i.e., DBH) and location of the existing tree, as well as the planned location and type (conifer or decidu- ous) of the replacement tree (Table 1). This information is im- portant for determining default removal and treatment costs, and for calculating possible energy benefits as described below. Basic Analysis In its most basic form, the model simply tracks and compares the discounted flow of costs associated with treating an existing ash tree through time against the one-time costs associated with its removal and replacement. Both treatment and removal costs are expected to vary with the size of the existing tree. Default removal costs (including stump grinding) are calculated by mul- tiplying the user-supplied DBH value by the corresponding cost estimate (Table 1). Replacement costs are expected to be inde- pendent of the size of the tree removed; the default value used here, CAD $400, is for the purchase and establishment of a tree that is approximately five years old, 2 m high, and 4 cm DBH (Table 1). The default cost estimates for removal and replace- ment were obtained from discussions with city foresters and tree removal companies; actual costs are likely to vary considerably depending on local circumstances, such as the availability of ar- borists, tree condition, and proximity to houses and power lines. A default cost of $6.50/cm DBH is used for TreeAzin treat- ments (Table 1; Joe Meating, pers. comm.). This per cm cost may seem high relative to protection options in the United States but reflects the current situation in Canada. For treatment frequency, TreeAzin is currently considered to be effective when applied once every two years (Bioforest 2011; Table 1). Initial costs for treating ©2012 International Society of Arboriculture McKenney and Pedlar: An Economic Model for Threatened Ash Trees a tree are calculated by multiplying this value by the user-supplied DBH for the existing tree; however, per cm costs can be expected to increase over time as the tree grows. To account for this, the DBH of the existing ash tree was estimated for each year of the simulation. Since growth data were not available for Canadian ur- ban areas, a DBH-age equation developed from growth data col- lected at productive southern Ontario ash plantations with a wide spacing between trees was employed (McKenney et al. 2008): [1] DBH = 0.8015(age) - 0.0029(age)2 A parameter controlling what is called “removal lag” is also included in the model (Table 1). This value describes the number of years that a homeowner opting to remove and replace an ash tree may be able to delay these costs compared to treatment costs that would have to commence before a tree is too heavily infested. Clearly, this parameter involves some judgment regarding how quickly EAB may spread within a community. Given that it takes 3–5 years for EAB to kill a tree (Siegert et al. 2007), and given that insecticides have shown some potential to reverse light infestations (Bioforest 2011), a default lag value of two years was employed. The model makes use of the standard economic approach of discounting anticipated benefits and costs that occur at different points in time back to the present (Boardman et al. 2001; see also Scott and Betters 2000, for a discussion in the context of urban tree replacement). The discount rate can be thought of as representing the opportunity cost of borrowing and/or an impa- tience factor or price associated with the decision-maker’s view of the cost of time. Costs and benefits can be expected to oc- cur at different points in time, and discounting provides an ac- cepted approach to bring future values to the present. A default discount rate of 4% (Table 1) was employed—a value com- monly used in forest economics (see Portney and Weyant 1999, for discussions on discounting, ranging from an apparent pro- pensity of some individuals to implicitly employ very high dis- counting to arguments over the use of very low discount rates for issues that have long-term or intergenerational implications, such as climate change or species losses). Again, the discount rate can be changed by users to reflect their own time prefer- ence rate or varied to examine the importance of this factor. Extended Benefits and Costs Many benefits have been attributed to urban trees, including home value premiums, energy savings, pollution and runoff reduction, and human health benefits (Dwyer et al. 1992). However, urban trees also incur costs beyond the removal and replacement costs as previously outlined (e.g., pruning, debris cleanup, damage to infrastructure). The work of McPherson et al. (2007) quantifies many of these benefits and costs for urban trees in the northeast- ern United States. In particular, their values are used here to incor- porate annual energy benefits for suitably located trees (Table 1), annual pollution and runoff reduction benefits to society at large (accrued regardless of a tree’s location relative to the house), and costs associated with tree maintenance over time (not including initial planting costs, which are covered under basic costs above). In Table 9 and Table 10 of their work, McPherson et al. (2007) provide the annual benefit and cost estimates at five-year in- tervals through a tree’s life up to age 40. In order to use these values here, which characterizes benefits and costs in yearly
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