ࡱ> dfabc[@ bjbj44 ͱViVi/=ddd bbb8& "$}Rτdd   '([[[ :R(d[ [@[\{B"dڼ v8bG3#}"O<}3aV3Dx3d^[eL \   $>${[  >National Algorithms for Determining Stocking Class, Stand Size Class, and Forest Type for Forest Inventory and Analysis Plots Stanford L. Arner Sharon Woudenberg Shirley Waters John Vissage Colin MacLean Mike Thompson Mark Hansen February 13, 2001 Modified May 21, 2003 Abstract. Procedures to assign stocking values to individual trees, and forest type, stand size, and stocking class to all Forest Inventory and Analysis plots nationwide are presented. The stocking values are assigned using species specific functions of diameter developed from normal yield tables and stocking charts. These algorithms will be included as part of the set of standardized procedures being developed by Forest Inventory and Analysis that will result in consistent estimates without regard to political boundaries. Background Forest Inventory and Analysis (FIA) area and volume estimates are often summed across FIA unit boundaries using such plot classifications as forest type, stand size class, and stocking class. Much concern has been expressed that the methods used to determine these classifications be consistent among FIA units so that the estimates can be summed for large area analyses such as the periodic Resource Planning Act (RPA) assessments and for numerous other regional and national studies. Concern about the lack of complete consistency of FIA area classifications between states has been raised both internally within FIA and externally by user groups, particularly the American Forestry Council. In 1991, the FIA Project Leaders appointed an ad hoc committee to address this issue. Specifically, our mission was to develop procedures to determine stocking and related area classifications (forest type and stand size) that were acceptable to the scientific community and could be recommended for use by FIA projects nationwide. Prior to this all FIA units based most tree-related area classifications on stocking proportions; that is, they assigned a value to each tally tree that represents the trees contribution to stocking. The classification of a sample stand was based on various procedures that summed and compared these assigned stocking values across various classes of trees tallied in the stand. For example a stand could not be classified as a softwood forest type unless the stocking of all softwood species exceeded the total stocking of all hardwood species. The committee decided to continue with this approach of assigning a portion of the stand stocking to each tally tree and then base classification on these stocking values. Prior to the work of this committee, the various FIA projects had used somewhat different procedures to assign stocking and determine forest type and stand size. The methods for some of the units are described in published reports (Hansen and Hahn 1992, May 1991); for other units written descriptions are limited and the methods exist only as computer code (usually Fortran). The committees first task was to identify a method of assigning the stocking contribution to individual tally trees that was acceptable to all FIA projects, nationwide. Following this, common methods to assign forest type, stand size, and stocking class based on these stocking values would be developed. What is Stocking Stocking is an expression of stand density that may be expressed in absolute terms, such as basal area per acre, volume per acre, number of trees per acre, or in relative terms, as a percent of some previously defined standard. Absolute stocking is meaningful in the presence of other information, such as stand size, forest type, etc. Relative stocking, on the other hand, implies a standard that accounts for the effects of stage of development and species composition, and therefore would be a useful tool for interpreting the findings of extensive inventories, where a wide variety of stands are sampled. Past FIA Stocking Procedures Crown Closure early estimates of stocking were based on crown closure assessments from aerial photo interpretations. This procedure usually sorted stands into four crude categories well-stocked, moderately stocked, poorly stocked, and nonstocked. Because individual tree species and size classes could not be consistently identified, the usefulness of this classification as a tool for area classification was limited. Basal Area Standard in this procedure, tally trees are counted to determine the predominant species and age group. The basal area standard is the basal area expected in a normal stand of similar species, site index, and age group, as indicated by a normal yield table. The stocking contribution of a tally tree is the basal area per acre that the tree represents, expressed as a percent of the basal area standard of the stand. This method performs poorly in mixed and multi-aged stands. The selection of the predominant species and the determination of the average stand age may strongly affect the basal area standard. Thus, two stands, each with the same basal area and stand age and with similar species composition, but one with 51 percent conifer and 49 percent hardwood, and the other with 51 percent hardwood and 49 percent conifer, may be assigned very different stocking values. By the same token, stands with very different distribution of tree ages may get similar stocking assignments, not because their densities are really similar, but because their average age is the same. Field experience in trying to apply the basal area standard convinced most of us that the method would not satisfy our purposes. Basal Area some members of our committee felt that basal area could be used to determine forest type, stand size class, and other tree-based site classifications that require assessing the relative density of various stand components. This led to a discussion of objectives. Our conclusion was that FIA classifications should be based on site occupancy, the degree of site utilization by various stand components. Where light is the limiting factor, site occupancy is closely related to crown density. Where moisture is the limiting factor, site occupancy may be more closely related to the surface area of the trees root system. In either case, the relationship of site occupancy to cross-sectional bole area may vary substantially by species, by stage of development, and by social position. Thus, 100 ft2 of red alder may fully occupy a site with a capacity for growing 150 ft2 of similar-sized Douglas-fir. In our view, basal area might well be the variable most closely related to current timber volume. But it is inadequate as a descriptor of stand composition in a multi-resource inventory, and, in the absence of additional information, is inadequate as a measure of present site utilization. An additional problem with basal area as a measure of stocking is its inadequacy for rating of small-diameter stands. Saplings have very little basal area and seedlings have none. Basal area is of little use in describing regeneration stands. Relative Density for FIA Plots Because FIA inventories are extensive, covering a wide range of conditions, the committee decided that a relative measure of stand density would be most appropriate. Curtis (1970, 1971) has compared the usual measures of relative density. All use either normal stands or open-grown trees as a point of reference. All are developed for use with even-aged, uniformly stocked stands of a single species or forest type, and all give comparable results. How can such standards be applied to uneven-aged, mixed species stands with variable spacing? One way is to rate the density contribution of each tree individually, taking into account that trees individual characteristics. Using this approach, the density standard applied to the plot as a whole is a weighted average density that reflects the species, stage of development, and social position of trees present. A variant of this approach was adopted for the Timber Resources Review (TRR) in the 1950s (USDA Forest Service, 1958), where the stocking percent assigned to individual trees varies by tree diameter and forest type. This TRR approach is the basis for the stocking values previously used by several of the FIA units. At about the same time, Larson (1956) proposed that stocking in the East be based on the relationship between diameter at breast height (dbh) and the crown area of free-growing trees of each major species group. The stocking procedures in use in the Pacific Northwest Research Station for inventories of Washington, Oregon, and California, were a refinement of the TRR approach that attempts to account for the effects of species, stage of development, and social position on the area occupied by individual trees. The procedure is described in detail in MacLean (1979). Although stage of development is frequently defined by site and age, stands with the same quadratic mean diameter (D) have been found more alike in every way than stands of the same site and age (McArdle et al., 1961). Thus, two stands of the same average diameter, one a young stand on a good site and the other an old stand on a poor site, are usually more similar than stands of the same site and age but differing average diameters. Reineke (1933) has shown that the space occupied by average trees growing in normal stands increases exponentially with increasing quadratic mean diameter at a rate that is approximately proportional to D1.6. Chisman and Schumacher (1940) expressed the area occupied by an individual tree, or tree area in terms of a quadratic function of the trees diameter, and expressed the density of a normal stand of unit area as a tree area ratio, the sum of individual tree areas. Curtis (1970, 1971) used Reinekes (1933) power function equation form to express tree area and tree area ratio. His exponent of 1.55 for Douglas-fir stands is very close to the 1.6 value of Reineke. Evidence from yield tables suggests that the relationship between tree area and diameter varies among species. For example a comparison of Normal yield tables for red alder (Worthington and others, 1960) with The yield of Douglas fir in the Pacific Northwest (McArdle and others, 1961) indicates that the space occupied by a 5-inch red alder is about 50% more than that occupied by a similar sized conifer. Considerations Used in Selecting the Recommended Stocking Curves The following is a summary of the committees considerations that led to the final recommended algorithm to assign stocking values to individual trees tallied on all forested FIA plots. We began with the common understanding that a measure of relative density was most appropriate. We found that normal yield tables and stocking guides are widely, although not universally, available for the wide variety of species encountered by FIA. These normal yield tables and stocking guides are based on natural stands and assume no particular management regime. The committee decided that the stocking values for our plots should be based on these normal yield tables and stocking guides because FIA plots represent a random sample of stands without regard to management or other factors. Stocking functions specific to a species or to a forest type were used to access the contribution of individual trees to stocking., The stocking functions relate the area occupied by an individual tree to the area occupied by a tree of the same size growing in a fully-stocked stand of like trees. Standards were determined using the normal value or A-line (Gingrich, 1967) of the stocking guides. The equation form that we selected was a power function approximating the 3/2 power, the so-called thee halves power function described by Reineke (1933) and others (Curtis 1970). Our reasons for this were two-fold: (1) The 3/2 thinning rule is widely accepted and well described in the literature; and (2) it is a model that extrapolates well, an important consideration when many of the existing yield tables and stocking guides cover less than the full range of diameters found on FIA plots. We also considered the quadratic tree area ratio used by Gingrich (1967) and Stout and Nyland (1986). We compared the two equations using 2944 plots of the most recent inventory of Pennsylvania. The results are presented in Table 1. When trees 5 and larger are used, the absolute difference in stocking between the power function and the quadratic function was no more than 4.7 on 98% of the plots. When trees at least 1 in diameter are used, a much higher proportion of the plots had much greater differences. Investigation revealed that most of the large differences were caused by one species group. For trees under 7 inches, the quadratic equation expressing tree area for this group is a decreasing instead of increasing function of diameter. Table 2 contains a list of equations that we developed to assign stocking values to trees. The column named species contains the predominant species or forest type used to develop the stocking guide or yield tables; b0 and b1 are the coefficients of the power function. The coefficients were estimated using the relationship between trees per acre and average stand diameter of the A-line of the stocking charts, or the level of average maximum competition as described by Curtis (1970,1971): S = (100/TPA) =  EMBED Equation.3  where D = average stand diameter TPA = trees per acre at average maximum density for a stand with average diameter D, and 100 = the reference level or density of a stand of average maximum competition. The equation for red maple, and cherry-ash-poplar are calculated by transforming the quadratic tree area ratio functions in Stout and Nyland (1986) to the power functions used here. The hemlock and basswood equations were determined from data in a report by Bragg (1992). He made adjustments to the trees per acre values of Tubbs (1977) to better fit the northern hardwoods equation of the Northeast Decision Model (Marquis 1991). The Northeast Decision Model uses the red maple equation for hardwoods and the jack pine equation for softwoods for species not used to develop any of the available stocking guides. With help from other members of the FIA staffs while considering the description in Silvics of North America (1990), we assigned a stocking equation to each species in our database, Table 3. All members of the committee thought that the density equations would overestimate the contribution of understory trees to a certain extent. PNW has developed discounting factors to adjust the density contribution of each tree according to stand position. In the northeast Hillebrand et al. (1991) have investigated the use of relative diameter as a weighting factor. Somewhat arbitrarily we decided to apply the crown position adjustment factors found in Table 4 to trees larger than 1 dbh. Using these weights could result in slight underestimation of total stocking on the plot. However their use will concentrate the classification procedures to the main canopy, which we believe will outweigh this deficiency. There is a wide range in the size of trees considered in the development of the yield tables. Some use all trees 1 and larger (Roach 1977). Others use only trees in the main canopy (Leak et al. 1987). Few consider stands with average diameter under 3 inches. All ignore seedlings. For these reasons we felt that the density equations would not work well in regeneration stands. Also, the density of the stand when it reaches some minimum size suitable for commercial thinning is of more interest than that of current seedlings and saplings. We therefore decided to apply a future-stand value to seedlings and saplings when the total stocking of 5+ trees was less than a specified limit, and to assign a stocking value based on the future diameter. We arbitrarily chose 5 inches as the future diameter. Because FIA will no longer rotate subplots into a uniform condition, a subplot as well as the plot may straddle two or more ecotypes. When this occurs FIA field crews differentiate the plot by condition and map the condition boundaries using the procedures outlined in Hahn et al. (1995). The conditions that are mapped are land use (forest, nonforest), forest type, stand size, and stand origin (natural, planted). A plot may also have limitations on its ability to support trees such as rock outcrops or small ponds. Low moisture is especially important in certain areas of the West. To account for these limitations a stockability proration can be applied expressing the ability to support trees as a proportion of the potential of the normal stands from which the stocking guides were developed. These proration values are determined by the individual units. Certain woodland species are measured at the root collar. These root collar diameters are used in our equations. On plots with multiple subplots we did not want a very high stocking of one subplot to completely compensate for very low stocking on other subplots. To account for this clumpiness we put a limit on the total stocking contribution of a subplot and adjust the stocking values on subplots that are above the limit. We also thought that the forest type classification algorithm should retain as much emphasis as possible on trees larger than 5 dbh when they are present. We did not want a high stocking total for seedlings and saplings to result in a reduction to the stocking values of the larger trees due to the clumpiness adjustment. We therefore put further limits on the stocking of seedlings and saplings by allowing a sapling total stocking only up to the remainder of the difference between the subplot maximum and the total for 5+ trees, and seedling total stocking up to the remainder after accounting for 5+ and sapling stocking. With these considerations in mind, the procedure to assign stocking values to individual trees is outlined below. Algorithm to Determine Stocking Values on Forested FIA Plots Plots with multiple subplots Let  EMBED Equation.3  = number of subplots in original design for plot  EMBED Equation.3 ,  EMBED Equation.3  = number of subplots of plot i in condition k  EMBED Equation.3  = diameter at breast height of tree j, subplot l, condition k of plot i = .1 for seedlings  EMBED Equation.3  = trees per acre expansion factor of tree j on subplot l , condition k of plot i, reflecting the plot size disregarding condition; i.e., condition does not enter into the computation of the expansion factor  EMBED Equation.3  = number of trees in condition k of subplot l , plot i  EMBED Equation.3  = proportion of subplot l of plot i that is condition k  EMBED Equation.3  = stockability proportion for condition k of plot i I = 100, the index reflecting maximum stocking for a plot  EMBED Equation.3  = 100/ EMBED Equation.3  , subplot index reflecting maximum stocking for subplot l of plot i  EMBED Equation.3  = stocking value for tree j in condition k of subplot l, plot i. Stocking values are assigned to live trees only. It is assumed that the proportion of each subplot in condition k,  EMBED Equation.3 , has been determined prior to the start of the algorithm. See Scott and Bechtold (1995) for the method FIA uses to calculate  EMBED Equation.3  for the fully mapped plot design as implemented by FIA (Hahn et al. 1995). 1. Assign an initial stocking value to each tree. Determine the stocking equation number; Table 3 contains the stocking code for each species code. Assign values to the coefficients b0 and b1 based on the stocking equation number determined in step A; Table 2 lists the coefficients for each equation. Assign an initial stocking value,  EMBED Equation.3  The diameter used for seedlings is .1 inch. Although not a reasonable value in most cases, .1 yields a non-zero value that has little effect on the classification algorithms in the presence of larger trees. 2. Adjust the initial values to reflect competitive position in relation to other trees on the subplot. For saplings, poletimber, and sawtimber trees, competitive position is based on crown class. However, FIA does not collect crown class on seedlings, and some units have not collected crown class on saplings in the past. In the absence of crown class we attempt to account for social position for these smaller trees through a ratio relating diameter of the tree to a maximum diameter on the subplot. Determine a crown competition factor CFiklj. For trees with a recorded crown class, CFiklj is assigned as in Table 4. For 5+ trees without crown class, set CFiklj to a default value of 1. For seedlings and saplings without a crown class, Sum the initial stocking multiplied by the crown competition factor as assigned in Table 4 of large (dbh>5) trees for each subplot in each condition,  EMBED Equation.3  where  EMBED Equation.3 = 1 if dbhiklj ( 5 = 0, otherwise. Calculate CF as a diameter ratio,  EMBED Equation.3  where  EMBED Equation.3  = 5 if  EMBED Equation.3  or  EMBED Equation.3  = maximum diameter of seedlings and saplings for condition k of subplot l, plot i if  EMBED Equation.3  . The 10% of subplot total stocking for 5+ trees is used as the cutoff in assigning Dmax with the reasoning that if the subplot total is greater than 10%, most of the time seedlings and saplings will have a lesser competitive position, while if the total stocking is less than 10%, most of the time the competitive position of the seedlings and saplings will not be affected by the larger trees. B. Multiply the initial stocking value by the crown competition factor  EMBED Equation.3  3. Decide whether future-stand or standard values are to be used for seedlings and saplings. First calculate several condition and subplot values to be used for the tests:  EMBED Equation.3   EMBED Equation.3  = proportion of whole plot i in condition k  EMBED Equation.3  = 20% of the subplot index adjusted for the proportion of subplot l in condition k  EMBED Equation.3  = 20 % of whole plot index adjusted for proportion of plot i in condition k  EMBED Equation.3  = condition total stocking of trees at least 5 dbh  EMBED Equation.3  = maximum total stocking allowed for condition k of subplot l, plot i. The 120 maximum value used in determining  EMBED Equation.3  allows for an overstocked condition when compared with the index of 100. b. Compare the total stocking of 5+ trees for the condition with the 20% condition index. The future-stand procedure is used if  EMBED Equation.3 . If there are enough subplots we feel that we should also try to account for distribution of stocking among the subplots when testing whether the future-stand procedure is to be used. Extensive testing indicated that the 20% condition total test, without consideration of subplot distribution, seemed to work best for the 4-subplot Forest Health Monitoring (FHM) plot layout (Scott 1993, Bechtold et al. 1992) that is currently being used by all FIA units, while consideration of subplot distribution seemed to improve the results of the 10-point variable radius plot that has been used by most of the FIA units prior to adoption of the FHM plot design. Therefore, with more than 4 subplots, the future-stand procedure is used if either  EMBED Equation.3  or the condition total stocking on a subplot is less than the 20% subplot index, i.e.,  EMBED Equation.3 on more than half of the subplots in the condition. 4. If future-stand procedure is used: a. Reassign the stocking values of seedlings and saplings using 5 as the diameter in the equation displayed in step 1-C. b. Adjust the recalculated values by multiplying by the competition factor, CFiklj, determined in step 2. 5. Future-stand and standard stocking values are further adjusted to account for clumpiness (unequal distribution among subplots) and to assure that seedlings and saplings do not reduce the stocking values of larger trees. Calculate a subplot total stocking for both saplings, EMBED Equation.3 and seedlings,  EMBED Equation.3 :  EMBED Equation.3   EMBED Equation.3  where  EMBED Equation.3  if 1 ( dbhiklj < 5 = 0, otherwise, and  EMBED Equation.3  1 if 0 ( dbhiklj < 1 = 0, otherwise. b. Determine an upper limit for both seedlings, EMBED Equation.3 , and saplings,  EMBED Equation.3 :  EMBED Equation.3   EMBED Equation.3  where max(a,b) is a function returning the larger of the values a and b. c. Calculate a proration ratio for 5+ trees ( EMBED Equation.3 ), saplings ( EMBED Equation.3 ), and seedlings ( EMBED Equation.3 );  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  where min(a,b) is a function returning the smaller of a and b. d. Multiply the stocking values by the appropriate adjustment,  EMBED Equation.3  where  EMBED Equation.3  if dbhiklj ( 5  EMBED Equation.3  if 1 ( dbhiklj ( 5  EMBED Equation.3  if 0 ( dbhiklj ( 1 and  EMBED Equation.3  if  EMBED Equation.3  and dbhiklj < 5 = 0.0 if  EMBED Equation.3  or dbhiklj ( 5. The small value,  EMBED Equation.3 , is added to saplings and seedlings to obtain a small positive value when the remainder adjustment results in zero. This is done so that the mere presence of any species can be recognized by the forest type algorithm. 6. Finally adjust the values for the proportion of the whole plot in the condition,  EMBED Equation.3 . This final adjustment recovers the index value of 100 for each condition. As an example, for a condition stocked at average maximum density but occupying 25% of the plot, the total stocking determined using steps 1 through 5 would be 25. Dividing by .25 yields a total stocking for the condition of 100. Single fixed radius plots with multiple regeneration subplots The Northeast FIA unit has used plots having a single fixed radius plot and multiple regeneration subplots. The procedure presented for multiple subplots needs to be modified slightly since we cannot account for unequal distribution of 5+ trees among several subplots. Let  EMBED Equation.3  = the number of regeneration subplots in condition k of plot i and  EMBED Equation.3 . The subplot index i is set to 1 for the single subplot with poletimber and sawtimber trees, with the subplot index for the regeneration subplots ranging from 2 to  EMBED Equation.3 . 1. For subplot i = 1 only, perform steps 1 through 4 of the multiple subplot procedure. Thus  EMBED Equation.3  of step 3 is the maximum total stocking for condition k. 2. For the regeneration subplots, l=2 through  EMBED Equation.3 , execute steps 5a and 5b of the multiple subplot procedure. In step 5b  EMBED Equation.3  = the upper limit of stocking allowed for seedlings and saplings for regeneration subplot l. 3. Determine the proration ratios as in step 5c. For 5+ trees, l = 1 and  EMBED Equation.3  For seedlings and saplings, l=2 through  EMBED Equation.3 ,  EMBED Equation.3  and  EMBED Equation.3 . 4. Execute steps 5d and 6. These procedures can be used for most of our old plots, including the 10-point variable radius plots, as well as the current national fully mapped design (Hahn et al. 1995) using the 4-subplot FHM layout (Scott 1993, Bechtold et al. 1992). However, for the variable radius subplots it is assumed that the plot occupies only one condition. Determination of Stocking Class, Stand Size Class, and Forest Type For each condition delineated on the plot with recorded boundaries, the stocking values are used to determine stocking class, stand size class, and forest type. When a plot is split so that a condition is represented by a small section of the plot, or the condition has a low tree count, the classification algorithms could return results that are not representative of the condition. Alternative procedures are compromises among time or cost, accuracy of classification, and consistency. We believe that the best classifications would be obtained with supplementary measurements in the condition. This would also be the most expensive and raises questions about the amount of additional measurement needed, the measurement procedure, and about a consistent but unbiased method of determining the location of the supplementary measurements. We also feel that the field crews can do a good job of classification using observation not restricted to the plot. The major concern with using field crew classification without additional measurement is consistency over time and among field crews. With these considerations, FIA will use field crew classifications, with or without supplemental measurements, when a condition occupies less than 25% of the plot. Stocking class for each condition For determination of stocking class, first sum the stocking values of all live trees in the condition. The class is assigned by comparing this total stocking with the following class boundaries: Stocking-class Class boundaries Nonstocked 0 - < 10 Poorly stocked 10 - < 35 Moderately stocked 35 - < 60 Fully stocked 60 - ( 100 Overstocked > 100 Stand size class Assign each tree to one of the following size classes based on dbh. Size class Class boundaries Seedling-sapling dbh <5 Poletimber 5 ( dbh ( 9 for hardwoods 5 ( dbh ( 11 for softwoods Sawtimber 9 ( dbh for hardwoods 11 ( dbh for hardwoods Sum the stocking values for each size class and for all classes combined. Assign the stand size class associated with the first condition that is met in the following table: Condition Stand size class Total stocking <10 Nonstocked Seedling-sapling stocking > 50% of total stocking Seedling-sapling Poletimber stocking > Sawtimber stocking Poletimber Poletimber stocking ( Sawtimber stocking Sawtimber Forest type An algorithm was developed that can be used to determine forest type by all FIA units. The forest types determined by the algorithm are, for the most part, the same as those previously reported by each FIA unit and are based on types presented by Eyre (1980). 1. Using the species code, determine an initial type group for each tree. Table 3 lists the initial type group for each species. 2. Sum the stocking values of individual trees comprising each initial type group to obtain a stocking total for each initial type. 3. For each combined type group listed in Table 5, sum the stocking of the initial type groups included in the combined type group. 4. The accumulated stocking of the combined types are then used in the decision tree depicted in Figure 1 to determine forest type. At each node, either the total stocking of an individual combined group is compared to a constant, or the total stocking of several combined groups are compared. When several groups are compared the algorithm proceeds down the branch with the predominant combined group, or the group with the highest stocking of those being compared, to the next decision node. The combined group names in the decision tree are those listed in Table 5. The groups compared at each node are preceded by the same letter in Table 5. With this approach logical combinations of species take precedence over a single species. If the true firs account for most of the stocking, the algorithm would yield one of the forest types in the true fir subgroup, even though the individual species with the largest value is not a true fir. In the case of ties, the first group listed is chosen. 5. Assign a national (RPA) forest type group based on the forest type determined. Table 6 lists the forest type group assignment for each forest type. Thus, after accumulating stocking into combined type groups, and determining that the condition is at least 10% stocked, the hierarchical process begins by comparing softwoods and hardwoods. If softwoods predominate, the true firs and spruce, doug fir-larch-western white pine, sitka spruce-hemlock, other western pines, redwoods, eastern pines, eastern spruce-fir, pinyon-juniper, and exotic softwoods are compared. If true firs-spruce predominate then spruce-subalpine fir, western hemlock, true firs, Alaska yellow-cedar, and western white pine are compared. If spruce-subalpine fir predominate then Engelmann spruce-subalpine fir is compared with blue spruce. In several instances, plurality only is not enough to determine type; additional conditions are required. In this discussion the terms predominance and plurality are used interchangeably when choosing among two or more species groups. The group with plurality, or the predominant group, is that which has the most stocking of those being compared. If Engelmann spruce-subalpine fir predominates blue spruce, then if the stocking of both subalpine fir and Engelmann spruce is between 5 and 50 percent of total stocking, the forest type is Engelmann spruce-subalpine fir. Otherwise the type is either Engelmann spruce or subalpine fir depending on which species predominates. The stepwise progression would proceed along other paths in a similar fashion. At each step the path proceeds to the next lower level of the group with the plurality of stocking. Special situations where this algorithm is not strictly adhered to are noted below. If the process has led to the red-white-jack pine group and white pine-hemlock is at least 50% of total stocking while individual contributions of white pine and hemlock are at least 5% but less than 50% of total stocking, then the forest type is white pine-hemlock. Likewise, if the algorithm has reached the upland spruce-fir combined group, balsam fir-red spruce is at least 50% of total stocking, and balsam fir and red spruce are each between 5 and 50 percent, the forest type is spruce-fir. The pine-hardwood mixed types occur if softwood stocking is less than half of the total, but the amount in the oak-pine group is at least 25% of total stocking. Oak-pine is the combined group (Table 5) composed of those pines and Eastern red-cedar that make up one of the mixed pine-hardwood types. Type is then based on plurality among the types within the oak-pine subgroup. Predominance of Eastern redcedar, shortleaf pine, eastern white pine, longleaf pine, Virginia pine, loblolly pine, and slash pine yield individual species types, while predominance of jack pine, red pine, sand pine, table mountain pine, pitch pine, or pond pine yield a type called other pine-hardwood. If hardwoods predominate and oak-pine is less than 25% of total stocking, several of the major hardwood groups have certain species added before determining the predominate group. Some of these species are included specifically in one or more forest types, but can occur over a wide range of conditions. Other associates are not mentioned specifically in a forest type. The addition of these associates to a particular group depends on physiographic class. In some cases non-zero stocking is also required before addition to prevent the situation where the algorithm reaches a major hardwood type in which the stocking is comprised of associates only. In particular note that Southern red oak is added to Post-blackjack oak and Chestnut oak only if these types already have a non-zero stocking. Although we wanted Southern red oak included in these types, we did not want these types determined by Southern red oak only. Similarly, Eyre (1980) lists black ash as the defining species in Black ash-American elm-red maple. We did not want to reach this forest type without some black ash. One exception to the addition of associates to the major groups depending on physiographic class occurs. With a lowland physiographic class, if both the elm-ash-cottonwood and oak-gum-cypress groups have zero stocking, then black cherry, beech, red maple, white ash, and green ash are added to one of the upland groups. This will prevent having types not being determined when all of the stocking is due to these species. With these additions, the major hardwood groups are compared for plurality of stocking. These include maple-beech-birch, oak-hickory, oak-gum-cypress, elm-ash-cottonwood, aspen-birch, alder-maple, western oaks, tan oak-laurel, other western hardwoods, tropical hardwoods, and exotic hardwoods. In several of these major hardwood groups, single species types are assigned only if certain conditions are met. In oak-hickory, if white oak, bur oak, chestnut oak, northern red oak, scarlet oak, yellow poplar, black walnut, red maple, or black locust is at least 50% of total stocking, the type assigned is that of the appropriate species. Otherwise type is assigned to one of the combination groups based on plurality. However, if the stocking of the type determined is less than 25% of the oak-hickory stocking, the mixed upland hardwood type is assigned. In the oak-gum-cypress group the first test determines whether Atlantic white cedar is at least half of total stocking. If not, the type is assigned based on plurality of the subgroups within oak-gum-cypress. If elm-ash-cottonwood is the predominant hardwood group, the cottonwood, willow, or red maple/lowland type is assigned if the stocking of one of these is at least half of the total. Otherwise plurality among the subgroups determines type. Within the maple-beech-birch hardwood group, type is decided by plurality unless the stocking of black cherry or red maple is at least 50% of the total. For the other hardwood groups, type is based on plurality of species groups at the lowest level of the decision tree. This level is reached in each case by one or more successive tests on plurality of stocking of groups at the same level. The final special situation occurs in California. In certain counties a California mixed conifer type is assigned if the forest type is Douglas fir. A California mixed confer type is also assigned if the forest type determined is sugar pine or incense cedar, or if the type determined is ponderosa pine, or Jeffrey pine and the stocking of ponderosa pine is less than 80% of the total, or the type determined is white fir or red fir and the stocking of true firs is less than 80% of the total. Future modifications So that there is consistency in procedures and estimates among all FIA units, FIA is reviewing all aspects of their program. One of the outcomes will be a standardized species list that could be slightly different than that presented in this report. Modification of the tree species list can affect stocking and attributes such as forest type, stand size, and stocking class that are determined using the stocking values. It will be necessary to assign a stocking equation, initial type, and other attributes to additional species. Also, it may be necessary to modify the algorithms to account for deletions from the species list. Improved stocking guides can be incorporated into the procedures by changing the coefficients or adding to the list of equations, which will also require changes to the stocking equation assignment for the affected species. Literature Cited Barnes, G.H. 1962. Yield of even-aged stands of western hemlock. Tech. Bull. 1273. Washington, DC: U.S. Department of Agriculture. Forest Service. 52p. Bechtold, W.A., Labau, V.J., McLain, W., and Rogers, P. 1992. Site classification, growth, and regeneration. In Forest health monitoring field methods guide (national guide), Conkling, B.L., and G.E. Byers (eds.). U.S. Environmental Protection Agency, Office of Research and Development, internal rep. Research Triangle Park, NC. 434p. Benzie, J.W. 1977. Managers handbook for jack pine in the North Central States. Gen. Tech. Rep. NC-32. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Experiment Station. 18p. Benzie, J.W. 1977. Managers handbook for red pine in the North Central States. Gen. Tech. Rep. NC-33. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Experiment Station. 22p. Bickford, C.A., F.S. Baker, and F.B. Wilson. 1957. Stocking, normality, and measurement of stand density. J. For. 55(2):99-104. Bragg, W.C. Northeast decision model relative density algorithm. Unpublished. Burns, R.M. and B.H. Honkala, tech. Cords. 1990. Silvics of North America: 1. Conifers. Agriculture Handbook 654. U. S. Department of Agriculture. Forest Service, Washington, DC. Vol. 1, 675p. Burns, R.M. and B.H. Honkala, tech. Cords. 1990. Silvics of North America: 2. Hardwoods. Agriculture Handbook 654. U. S. Department of Agriculture. Forest Service, Washington, DC. Vol. 1, 675p. Chisman, H.H. and F.X. Schumacher. 1940. On the tree-area ratio and certain of its applications. J. For. 38:311-317. Cochran, P.H. 1985. Site index, height growth, normal yields and stocking levels for larch in Oregon and Washington. Res. Pap. PNW-424. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station. 24p. Curtis, R.O. 1970. Stand density measures: an interpretation. For. Sci. 16:403-414. Curtis, R.O. 1971. A tree area power function and related stand density measures for Douglas-fir. For. Sci. 17:146-159. Dahms, W.G. 1964. Gross and net yield tables for lodgepole pine. Res. Pap. PNW-8 Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station. 14p. Eyre, F.H., ed. 1980. Forest cover types of the United States and Canada. Soc. Am. For., Bethesda, MD. 148p. Gingrich, S.F. 1967. Measuring and evaluating stocking and stand density in upland hardwood forests in the Central States. Forest Science. Vol. 13, No. 1:38-53. Hahn, J.T., MacLean, C.D., Arner, S.L., Bechtold, W.A. 1995. Procedures to handle inventory cluster plots that straddle two or more conditions. Forest Science Monograph. 31:12-25. Hansen,M.H. and J.T. Hahn. 1992. Determining stocking, forest type and stand-size class from Forest Inventory data. Northern Journal of Applied Forestry, Vol. 9, No. 3, p. 82-89. Haig, I.T. 1932. Second growth yield, stand, and volume tables for western white pine type. Tech. Bull. 323. Washington DC: U.S. Department if Agriculture, Forest Service. 65p. Hillebrand, J.J., R.L. Earnst, S.L. Stout, and S. Fairweather. 1992. Using relative diameter to improve density measures in Allegheny hardwood stands. Forest Ecology Management. 55:225-232. Johnston, W.F. 1977. Managers handbook for Northern white cedar in North Central States. Gen. Tech. Rep. NC-35. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Experiment Station. Larson, R.W. 1956. Standards and procedures for classification of stocking. Unpublished office report. On file at the Southern Forest Experiment Station. U.S. Department of Agriculture, Forest Service. Ashville, NC. Leak, W.B., D.S. Solomon, and P.S. Debald. 1987. Silvicultural guide for northern hardwood types in the Northeast(revised). Res. Pap. NE-603. Broomall, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. 36p. McArdle, R.E., W.H. Meyer, and D. Bruce. 1961. The yield of Douglas-fir in the Pacific Northwest. USDA Tech. Bull. 201. (revised). U.S. Department of Agriculture, Forest Service, Washington, DC. 74p. MacLean, C.D. Emperical data on redwoods using FIA plots in Northern California. Unpublished. Maclean, C.D. 1979. Relative density: The secret to stocking assessment in regional analysis a Forest Survey viewpoint. Gen. Tech. Rep. PNW-78. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station. MacLean, C.D., Bolsinger, C.L. 1973. Estimating productivity on sites with a low stocking capacity. Res. Pap. PNW-152. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experimental Station. 18p. Marquis, D.A. 1991. The Northeast decision Model; a multi-resource silvicultural decision model for forests of the Northeastern United States. In: Systems Analysis in Forestry, Symposium, Charlston, SC, 5-7 March, 1991. 419-431. May, D.M. 1991. Stocking, forest type, and stand size class- the Southern Forest Inventory and Analysis units calculation of three important stand descriptors. Gen. Tech. Rep. SO-77. New Orleans, LA: U. S. Department of Agriculture, Forest Service, Southern Forest Experiment Station. 7p. Meyer, W.H. 1961. Yield of even-aged stands of ponderosa pine. Tech. Bull. 630(revised). Washington, DC: U.S. Department of Agriculture, Forest Service. 59p. Meyers, C.C. and R. Buchman. 1984. Managers handbook for elm-ash-cottonwood in the North Central States. Gen. Tech. Rep. NC-98. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Experiment Station. 11p. Osbourne, J.G., and R. K. Winters. 1935. Growth and yield of second growth red gum in fully stocked stands on alluvial lands in the south. USFS SOFES occasional paper 54. 34p. Perala, D.A. 1997. Managers handbook for aspen in the North Central States. Gen. Tech. Rep. NC-36. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Experiment Station. 30p. Philbrook, J.S., J.P. Barrett, and W.B. Leak. 1973. A stocking guide for Eastern White Pine. Res. Note NE-168. Upper Darby, PA: U.S. Department of Agriculture, Forest Service, Northeast Forest Experiment Station. 3p. Plonski, W.L. 1960. Normal yield tables for black spruce, jack pine, tolerant hardwoods, white pine, and red pine. Ontario Department of Lands and Forests Sivicultural Series. Bull. No. 2. 39p. Reineke, L.H. 1933 Perfecting a stand-density index for even-aged forests. J. Agric. Res. 46:627-638. Roach, B.A. and S.F. Gingrich. 1962. Timber management guide for upland central hardwoods. U.S. Department of Agriculture, Forest Service, Central States Forest Experiment Station and North Central Region. 33p. Roach, B.A. 1977. A stocking guide for Allegheny hardwoods and its use in controlling intermediate cuttings. Res. Pap. NE-373. Upper Darby, PA: U.S. Department of Agriculture, Forest Service, Northeast Forest Experiment Station. 30p. Scott, C.T. 1993. Optimal design of a plot cluster for monitoring. In:Rennolls, K.; Gertner, G.. eds. The optimal design of forest experiments and forest surveys. London: University of Greenwich, School of Mathematics, Statistics and Computing: 233-242. Scott, C.T. and W.A. Bechtold. 1995. Techniques and computations for mapping plot clusters that straddle stand boundaries. Forest Science Monograph. 31: 46-61. Safford, L.O. 1983. Silvicultural guide for paper birch in the Northeast (revised). Res. Pap. NE535. Broomall, PA: U.S. Department of Agriculture, Forest Service, Northeast Forest Experiment Station. 29p. Schlesinger, R.C. and D.T. Funk. 1977. Managers guide for black walnut. Gen Tech. Rep. NC-38. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Experiment Station. Schumacher, F.X., and T.S. Coile. 1960. Growth and yield of natural stands of the southern pines. T.S. Coile, Inc., Durham, NC 115p. Solomon, D.S., R.A. Hosmer, and H.T. Hayslett, Jr. 1987. Fiber Handbook: A growth model for spruce-fir and northern hardwood forest types. Res. Pap. NE-602. Broomall, PA: U.S. Department of Agriculture, Forest Service, Northeast Forest Experiment Station. 19p. Stout, S.L. and R.D. Nyland. 1986. Role of species composition in relative density measurement in Allegheny hardwoods. Can. J. For. Res. Vol. 16:574-579. Tubbs, C.H. 1977. Managers handbook for northern hardwoods in the North Central States. Gen. Tech. Rep. NC-39. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Experiment Station. USDA Forest Service. 1929. (re. 1976) Volume, yield, and stand tables for second-growth southern pines. USDA Misc. Pub. 50. 202p. USDA Forest Service. 1958. Timber resources for Americas Future. USDA For. Serv. Res. Rep. No. 14. Washington, DC. 713p. Worthington, N.P., F.A. Johnson, G.R. Staebler, and W.J. Lloyd. 1960. Normal yield tables for red alder. Res. Paper 36. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range Experiment Station.  EMBED Excel.Sheet.8   Table 3. Initial types with species assignment and stocking equation assignment to species.  Initial Species Stocking equation  type group code common name code name  1 11 Pacific silver fir 18 Western hemlock 2 14 Santa lucia fir 18 Western hemlock 15 White fir 15 Douglas fir 3 17 Grand fir 18 Western hemlock 4 18 Corkbark fir 1 Spruce-fir 19 Subalpine fir 1 Spruce-fir 5 20 California red fir 18 Western hemlock 21 Shasta red fir 18 Western hemlock 6 120 Bishop pine 10 Ponderosa pine 7 22 Noble fir 18 Western hemlock 8 41 Port-Orford-cedar 18 Western hemlock 9 42 Alaska-yellow-cedar 18 Western hemlock 10 81 Incense-cedar 18 Western hemlock 11 242 Western redcedar 18 Western hemlock 12 50 Cypress 10 Ponderosa pine 51 Arizona cypress 10 Ponderosa pine 52 Baker cypress 10 Ponderosa pine 53 Tecate cypress 10 Ponderosa pine 54 Monterey cypress 10 Ponderosa pine 55 Sargent cypress 10 Ponderosa pine 13 73 Western larch 2 Western larch 14 93 Engelmann spruce 1 Spruce-fir 15 96 Blue spruce 1 Spruce-fir 16 90 Spruce sp. 1 Spruce-fir 94 White spruce 1 Spruce-fir 99 Lutz spruce 1 Spruce-fir 17 95 Black spruce 3 Black spruce 18 98 Sitka spruce 18 Western hemlock 19 101 Whitebark pine 10 Ponderosa pine 20 102 Bristlecone pine 10 Ponderosa pine 104 Foxtail pine 8 Western white pine 142 Gr.Basin brstlcone pine 10 Ponderosa pine 21 103 Knobcone pine 8 Western white pine 22 112 Apache pine 10 Ponderosa pine 114 Southwestern white pine 10 Ponderosa pine 118 Chihuahua pine 10 Ponderosa pine 137 Washoe pine 10 Ponderosa pine 138 Four-leaf pine 10 Ponderosa pine 139 Torreya pine 10 Ponderosa pine 141 Arizona pine 10 Ponderosa pine 23 108 Lodgepole pine 5 Lodgepole pine 24 109 Coulter pine 10 Ponderosa pine 25 113 Limber pine 10 Ponderosa pine Table 3. Initial types with species assignment and stocking equation assignment to species.(cont.)   Initial Species Stocking equation type group code common name code name  26 122 Ponderosa pine 10 Ponderosa pine 135 Arizona pine 10 Ponderosa pine 27 117 Sugar pine 10 Ponderosa pine 28 119 Western white pine 8 Western white pine 29 124 Monterey pine 10 Ponderosa pine 30 201 Bigcone douglas-fir 15 Douglas fir 31 202 Douglas-fir 15 Douglas fir 32 211 Redwood 19 Redwood 33 212 Giant sequoia 19 Redwood 34 263 Western hemlock 18 Western hemlock 35 264 Mountain hemlock 18 Western hemlock 36 116 Jeffrey pine 10 Ponderosa pine 38 64 Western juniper 10 Ponderosa pine 40 72 Subalpine larch 2 Western larch 92 Brewer spruce 18 Western hemlock 231 Pacific yew 18 Western hemlock 232 Florida yew 18 Western hemlock 251 Calif. torreya(nutmeg) 18 Western hemlock 252 Florida nutmeg 18 Western hemlock 41 105 Jack pine 4 Jack pine 42 125 Red pine 11 Red pine 44 107 Sand pine 4 Jack pine 45 110 Shortleaf pine 6 Shortleaf pine 46 111 Slash pine 7 Slash pine 47 115 Spruce pine 4 Jack pine 48 121 Longleaf pine 9 Longleaf pine 49 123 Table Mountain pine 4 Jack pine 50 126 Pitch pine 4 Jack pine 51 128 Pond pine 12 Pond pine 52 131 Loblolly pine 14 Loblolly pine 53 129 Eastern white pine 13 Eastern white pine 54 132 Virginia pine 4 Jack pine 55 10 Fir sp. 1 Spruce-fir 12 Balsam fir 1 Spruce-fir 16 Fraser fir 1 Spruce-fir 58 97 Red spruce 1 Spruce-fir 59 43 Atlantic white-cedar 16 Northern white cedar 60 241 Northern white-cedar 16 Northern white cedar 61 221 Baldcypress 31 Sweetgum 222 Pondcypress 31 Sweetgum 223 Montezuma baldcypress 31 Sweetgum 63 66 Rocky Mountain juniper 10 Ponderosa pine Table 3. Initial types with species assignment and stocking equation assignment to species.(cont.)   Initial Species Stocking equation type group code common name code name  64 67 Southern redcedar 4 Jack pine 68 Eastern redcedar 4 Jack pine 65 71 Tamarack (native) 1 Spruce-fir 66 260 Hemlock sp. 17 Eastern hemlock 261 Eastern hemlock 17 Eastern hemlock 262 Carolina hemlock 17 Eastern hemlock 70 70 Larch (introduced) 1 Spruce-fir 91 Norway spruce 1 Spruce-fir 136 Austrian pine 11 Red pine 145 Italian stone pine 4 Jack pine 71 130 Scotch pine 4 Jack pine 72 144 Japanese black pine 4 Jack pine 81 802 White oak 29 Oaks and hickory 82 806 Scarlet oak 29 Oaks and hickory 83 823 Bur oak 10 Ponderosa pine 84 832 Chestnut oak 29 Oaks and hickory 85 833 Northern Red oak 29 Oaks and hickory 86 809 Northern pin oak 29 Oaks and hickory 835 Post oak 29 Oaks and hickory 840 Dwarf(sand) post oak 29 Oaks and hickory 87 813 Cherrybark oak,Swamp Rd 29 Oaks and hickory 825 Swamp chestnut oak 29 Oaks and hickory 834 Shumard oak 29 Oaks and hickory 836 Delta post oak 29 Oaks and hickory 88 812 Southern red oak 29 Oaks and hickory 89 808 Durand oak 29 Oaks and hickory 816 Bear oak, Scrub oak 29 Oaks and hickory 819 Turkey oak 29 Oaks and hickory 841 Dwarf live oak 29 Oaks and hickory 842 Bluejack oak 29 Oaks and hickory 90 401 Water hickory 29 Oaks and hickory 405 Shellbark hickory 29 Oaks and hickory 91 404 Pecan 29 Oaks and hickory 92 400 Hickory sp. 29 Oaks and hickory 402 Bitternut hickory 29 Oaks and hickory 403 Pignut hickory 29 Oaks and hickory 406 Nutmeg hickory 29 Oaks and hickory 407 Shagbark hickory 29 Oaks and hickory 408 Black hickory 29 Oaks and hickory 409 Mockernut hickory 29 Oaks and hickory 410 Sand hickory 29 Oaks and hickory 93 521 Common persimmon 29 Oaks and hickory 931 Sassafras 29 Oaks and hickory Table 3. Initial types with species assignment and stocking equation assignment to species.(cont.)   Initial Species Stocking equation type group code common name code name  94 972 American elm 36 Elm,ash,cottonwood 975 Slippery elm 36 Elm,ash,cottonwood 977 Rock elm 36 Elm,ash,cottonwood 95 316 Red maple 25 Red maple 96 314 Black maple 27 Maple,beech,birch 318 Sugar maple 27 Maple,beech,birch 97 317 Silver maple 25 Red maple 98 370 Birch sp. 27 Maple,beech,birch 371 Yellow birch 27 Maple,beech,birch 372 Sweet birch 27 Maple,beech,birch 99 375 Paper birch 28 Paper birch 376 Western paper birch 28 Paper birch 377 Alaska paper birch 28 Paper birch 378 NW paper birch 28 Paper birch 379 Gray birch 28 Paper birch 100 461 Sugarberry 36 Elm,ash,cottonwood 101 500 Hawthorn 29 Oaks and hickory 501 Hawthorn crus-galli 29 Oaks and hickory 502 Hawthorn mollis 29 Oaks and hickory 552 Honeylocust 27 Maple,beech,birch 571 Kentucky coffeetree 25 Red maple 641 Osage-orange 29 Oaks and hickory 102 531 American beech 27 Maple,beech,birch 103 541 White ash 33 Cherry,ash,yellow poplar 104 543 Black ash 33 Cherry,ash,yellow poplar 105 544 Green ash 36 Elm,ash,cottonwood 106 591 American holly 25 Red maple 107 601 Butternut 30 Black walnut 108 602 Black walnut 30 Black walnut 109 611 Sweetgum 31 Sweetgum 110 621 Yellow-poplar 33 Cherry,ash,yellow poplar 111 653 Sweetbay 25 Red maple 112 691 Water tupelo 31 Sweetgum 113 693 Blackgum 31 Sweetgum 114 694 Swamp tupelo 31 Sweetgum 115 460 Hackberry sp. 36 Elm,ash,cottonwood 462 Hackberry 36 Elm,ash,cottonwood 463 Netleaf hackberry 36 Elm,ash,cottonwood 116 731 Sycamore 36 Elm,ash,cottonwood 117 741 Balsam poplar 32 Aspen Table 3. Initial types with species assignment and stocking equation assignment to species.(cont.)   Initial Species Stocking equation type group code common name code name  118 740 Cottonwood sp. 36 Elm,ash,cottonwood 742 Eastern cottonwood 36 Elm,ash,cottonwood 744 Swamp cottonwood 36 Elm,ash,cottonwood 745 Plains cottonwood 36 Elm,ash,cottonwood 748 Rio Grande cottonwood 36 Elm,ash,cottonwood 749 Narrowleaf cottonwood 36 Elm,ash,cottonwood 752 Silver poplar 36 Elm,ash,cottonwood 119 743 Bigtooth aspen 32 Aspen 746 Quaking aspen 32 Aspen 120 837 Black oak 29 Oaks and hickory 121 762 Black cherry 33 Cherry,ash,yellow poplar 122 901 Black locust 29 Oaks and hickory 123 920 Willow 25 Red maple 921 Peachleaf willow 25 Red maple 922 Black willow 25 Red maple 924 Scouler willow 25 Red maple 927 White willow 25 Red maple 929 Weeping willow 25 Red maple 124 950 Basswood sp. 35 Basswood 951 American basswood 35 Basswood 952 White basswood 35 Basswood 953 Carolina basswood 35 Basswood 125 831 Willow oak 29 Oaks and hickory 127 555 Loblolly-bay 25 Red maple 721 Redbay 33 Cherry,ash,yellow poplar 128 822 Overcup oak 29 Oaks and hickory 129 373 River birch 28 Paper birch 130 312 Bigleaf maple 25 Red maple 131 351 Red alder 26 Red alder 132 361 Pacific madrone 29 Oaks and hickory 362 Arizona madrone 29 Oaks and hickory 363 Texas madrone 29 Oaks and hickory 133 431 Golden chinkapin 29 Oaks and hickory 134 807 Blue oak 29 Oaks and hickory 135 542 Oregon ash 33 Cherry,ash,yellow poplar 136 631 Tanoak 25 Red maple 137 747 Black cottonwood 36 Elm,ash,cottonwood 138 801 Coast live oak 29 Oaks and hickory 139 818 California black oak 29 Oaks and hickory 140 815 Oregon white oak 29 Oaks and hickory 141 981 California laurel 29 Oaks and hickory 142 805 Canyon live oak 29 Oaks and hickory 839 Interior live oak 29 Oaks and hickory Table 3. Initial types with species assignment and stocking equation assignment to species.(cont.)   Initial Species Stocking equation type group code common name code name  143 828 Nuttall oak 29 Oaks and hickory 144 712 Paulownia, Empress tree 27 Maple,beech,birch 145 992 Melaluca 1 Spruce-fir 146 355 European alder 26 Red alder 974 Siberian elm 36 Elm,ash,cottonwood 993 Chinaberry 33 Cherry,ash,yellow poplar 994 Chinese tallowtree 25 Red maple 995 Tung-oil tree 25 Red maple 147 911 Sabal palm 29 Oaks and hickory 148 510 Eucalyptus 15 Douglas fir 149 989 Mangrove 25 Red maple 151 311 Florida maple 25 Red maple 341 Ailanthus 25 Red maple 374 Water birch 28 Paper birch 381 Chittamwood,Gum bumelia 25 Red maple 551 Waterlocust 25 Red maple 692 Ogechee tupelo 31 Sweetgum 722 Water elm,Planer tree 33 Cherry,ash,yellow poplar 804 Swamp white oak 29 Oaks and hickory 152 310 Maple sp. 25 Red maple 315 Striped maple 27 Maple,beech,birch 319 Mountain maple 25 Red maple 320 Norway maple 25 Red maple 356 Serviceberry 25 Red maple 367 Pawpaw 25 Red maple 391 Am.hornbeam,musclewood 25 Red maple 421 American chestnut 25 Red maple 422 Allegheny chinkapin 29 Oaks and hickory 423 Ozark chinkapin 29 Oaks and hickory 450 Catalpa sp. 27 Maple,beech,birch 451 Southern catalpa 27 Maple,beech,birch 452 Northern catalpa 27 Maple,beech,birch 471 Eastern redbud 25 Red maple 650 Magnolia sp. 33 Cherry,ash,yellow poplar 651 Cucumbertree 33 Cherry,ash,yellow poplar 652 Southern magnolia 33 Cherry,ash,yellow poplar 654 Bigleaf magnolia 33 Cherry,ash,yellow poplar 655 Mountain magnolia 33 Cherry,ash,yellow poplar 656 Ashe's magnolia 33 Cherry,ash,yellow poplar 657 Pyramid magnolia 33 Cherry,ash,yellow poplar 658 Umbrella magnolia 33 Cherry,ash,yellow poplar 660 Apple sp. 29 Oaks and hickory 661 Oregan crabapple 29 Oaks and hickory 662 Southern crabapple 29 Oaks and hickory 663 Sweet crabapple 29 Oaks and hickory 664 Prarie crabapple 29 Oaks and hickory 665 Apple 29 Oaks and hickory Table 3. Initial types with species assignment and stocking equation assignment to species.(cont.)   Initial Species Stocking equation type group code common name code name  152 680 Mulberry sp. 25 Red maple 681 White mulberry 25 Red maple 682 Red mulberry 25 Red maple 683 Texas mulberry 25 Red maple 684 Black mulberry 25 Red maple 701 Eastern hophornbeam 25 Red maple 702 Knowlton hophornbean 25 Red maple 711 Sourwood 25 Red maple 760 Prunus sp. 25 Red maple 761 Pin cherry 25 Red maple 763 Chokecherry 25 Red maple 764 Peach 25 Red maple 765 Canada plum 25 Red maple 766 Wild plum 25 Red maple 768 Bitter cherry 25 Red maple 851 Mountain ash 25 Red maple 900 Locust sp. 29 Oaks and hickory 935 American mountain-ash 25 Red maple 936 European mountain-ash 25 Red maple 937 Northern mountain-ash 25 Red maple 938 Greene mountain-ash 25 Red maple 939 Western mountain-ash 25 Red maple 970 Elm sp. 36 Elm,ash,cottonwood 976 September elm 36 Elm,ash,cottonwood 153 330 Buckeye,horsechestnut 27 Maple,beech,birch 331 Ohio buckeye 27 Maple,beech,birch 332 Yellow buckeye 27 Maple,beech,birch 333 California buckeye 27 Maple,beech,birch 334 Texas buckeye 27 Maple,beech,birch 335 Bottlebrush buckeye 27 Maple,beech,birch 336 Red buckeye 27 Maple,beech,birch 337 Painted buckeye 27 Maple,beech,birch 345 Mimosa, silktree 36 Elm,ash,cottonwood 346 Woman's tongue 36 Elm,ash,cottonwood 350 Alder sp. 26 Red alder 352 White alder 26 Red alder 353 Mountain alder 26 Red alder 481 Yellowwood 25 Red maple 490 Dogwood sp. 25 Red maple 491 Flowering dogwood 25 Red maple 492 Pacific dogwood 26 Red alder 540 Ash sp. 33 Cherry,ash,yellow poplar 545 Pumpkin ash 33 Cherry,ash,yellow poplar 546 Blue ash 33 Cherry,ash,yellow poplar 547 Velvet ash 33 Cherry,ash,yellow poplar 548 Carolina ash 33 Cherry,ash,yellow poplar 549 Singleleaf ash 33 Cherry,ash,yellow poplar 580 Silverbell 25 Red maple Table 3. Initial types with species assignment and stocking equation assignment to species.(cont.)   Initial Species Stocking equation type group code common name code name  600 Walnut 30 Black walnut 603 Calif. black walnut 30 Black walnut 604 S. Calif. black walnut 30 Black walnut 605 Texas walnut 30 Black walnut 606 Arizona walnut 30 Black walnut 730 California sycamore 36 Elm,ash,cottonwood 732 Arizona sycamore 36 Elm,ash,cottonwood 991 Salt cedar 25 Red maple 996 Smoketree 25 Red maple 997 Russian olive 25 Red maple 999 Other, unknown 25 Red maple 156 475 Curlleaf mtn. mahogany 10 Ponderosa pine 476 Alder-Leaf mtn.mahogany 33 Cherry,ash,yellow poplar 477 Hairy mountain-mahogany 33 Cherry,ash,yellow poplar 157 755 Mesquite 10 Ponderosa pine 756 W. honey mesquite 10 Ponderosa pine 757 Velvet mesquite 10 Ponderosa pine 758 Screwbean mesquite 10 Ponderosa pine 158 800 Oak-deciduous 10 Ponderosa pine 814 Gambel oak 10 Ponderosa pine 821 Calif.(valley) wht.oak 25 Red maple 919 Western soapberry 25 Red maple 159 321 Rocky mountain maple 10 Ponderosa pine 322 Bigtooth maple 10 Ponderosa pine 323 Chalk maple 10 Ponderosa pine 324 Vine maple 10 Ponderosa pine 325 Amur maple 10 Ponderosa pine 160 300 Acacia 25 Red maple 902 New Mexico locust 10 Ponderosa pine 990 Tesota,Arizona ironwood 10 Ponderosa pine 161 57 Redcedar/juniper 3 Black spruce 58 Pinchot juniper 10 Ponderosa pine 59 Redberry juniper 10 Ponderosa pine 60 Common juniper 3 Black spruce 61 Ashe juniper 3 Black spruce 62 California juniper 10 Ponderosa pine 63 Alligator juniper 10 Ponderosa pine 65 Utah juniper 10 Ponderosa pine 69 Oneseed juniper 10 Ponderosa pine 162 106 Common pinyon 10 Ponderosa pine 133 Singleleaf pinyon 10 Ponderosa pine 134 Border pinyon 10 Ponderosa pine 140 Mexican pinyon pine 10 Ponderosa pine 143 Arizona pinyon pine 10 Ponderosa pine 163 127 Gray pine 10 Ponderosa pine Table 3. Initial types with species assignment and stocking equation assignment to species.(cont.)   Initial Species Stocking equation type group code common name code name  201 820 Laurel oak 29 Oaks and hickory 202 817 Shingle oak 29 Oaks and hickory 203 838 Live oak 29 Oaks and hickory 204 827 Water oak 29 Oaks and hickory 205 830 Pin oak 29 Oaks and hickory 206 824 Blackjack oak 29 Oaks and hickory 207 826 Chinkapin oak 10 Ponderosa pine 208 313 Boxelder 36 Elm,ash,cottonwood 209 971 Winged elm 36 Elm,ash,cottonwood 973 Cedar elm 36 Elm,ash,cottonwood 210 803 Ariz. white oak,Gray oak 10 Ponderosa pine 810 Emery oak 10 Ponderosa pine 811 Engelmann oak 10 Ponderosa pine 829 Mexican blue oak 10 Ponderosa pine 843 Silverleaf oak 10 Ponderosa pine 850 Oak-evergreen 10 Ponderosa pine    Table 5. Initial type assignment to combined type groups  Combined type groups Initial type group  A. Softwoods 1-58,60,62-79,161,162 B. True firs and spruce 1-5,7,9,14,15,28,34,35 C. Spruce-subalpine fir 4,14,15 D. Engelmann spruce-subalpine fir 4,14 E. Subalpine fir 4 E. Engelmann spruce 14 D. Blue spruce 15 C. Western hemlocks 34,35 D. Western hemlock 34 D. Mountain hemlock 35 C. True firs 1-5,7 D. Pacific silver fir 1 D. White fir 2 D. Grand fir 3 D. Subalpine fir 4 D. Red fir 5 D. Noble fir 7 C. Alaska yellow cedar 9 C. Western white pine 28 B. Doug fir-larch-western white pine 8,10,11,13,23,24,26,27,30,31,36 C. Doug fir-western larch 11,13,31 D. Doug fir 31 D. Western larch 13 D. Western redcedar 11 C. Doug fir-western pines 8,10,23,24,26,27,30,31,36 D. Doug fir 31 D. Ponderosa pine 26,36 D. Port-orford cedar 8 D. Lodgepole pine 23 D. Sugar pine 27 D. Incense cedar 10 D. Jeffrey-Coulter pine-Bigcone Doug fir 24,30,36 C. Western larch-pine 13,23,26,36 D. Western larch 13 D. Ponderosa pine 26,36 D. Lodgepole pine 23 B. Sitka spruce-hemlock 11,18,34 C. Western hemlock 34 C. Sitka spruce 18 C. Western redcedar 11 B. Other western pines 6,12,19,20,21,22,25,29,40 C. Knobcone pine 21 C. Southwest white pine 22 C. Bishop pine 6 C. Monterey pine 29 C. Foxtail-bristlecone pine 20 C. Limber pine 25 C. Whitebark pine 19 C. Miscellaneous western softwoods 12,40 B. Redwoods 31,32,33 C. Redwood 32 C. Gian sequoia 33 C. Doug fir 31 B. Eastern pines 41,42,44-54,66 C. Red-white-jack pine 41,42,53,66 D. White pine-hemlock 53,66 E. Eastern white pine 53 E. Eastern hemlock 66 D. Red pine 42 D. Jack pine 41 C. Longleaf-slash pine 46,48 D. Longleaf pine 48 D. Slash pine 46 C. Loblolly-shortleaf pine 44,45,47,49-52,54 D. Loblolly pine 52 D. Shortleaf pine 45 D. Virginia pine 54 D. Sand pine 44 D. Table mountain pine 49 D. Pond pine 51 D. Pitch pine 50 D. Spruce pine 47 B. Pinyon-juniper 38,63,64,161,162 C. Eastern redcedar 64 C. Rocky mountain juniper 63 C. Western juniper 38 C. Juniper woodland 161 C. Pinyon-juniper woodland 161,162 B. Eastern spruce-fir 16,17,55,58,60,65 C. Upland spruce-fir 16,55,58 D. Balsam fir-red spruce 55,58 E. Balsam fir 55 E. Red spruce 58 D. White spruce 16 C. Lowland spruce-fir 17,60,65 D. Black spruce 17 D. Tamarack 65 D. Northern white cedar 60 B. Exotic softwoods 70,71,72 C. Scotch pine 71 C. Australian pine 72 C. Other exotic softwoods 70 A. Hardwoods 59,61,81-153,156-160,163,201-210 B. Oak-pine 41,42,44-54,64 C. Eastern redcedar 64 C. Shortleaf pine 45 C. Eastern white pine 53 C. Longleaf pine 48 C. Virginia pine 54 C. Loblolly pine 52 C. Slash pine 46 C. Jack pine 41 C. Red pine 42 C. Sand pine 44 C. Spruce pine 47 C. Table mountain pine 49 C. Pitch pine 50 C. Pond pine 51 B. Oak-hickory 81-86,88,89,92,93,101,108,110,120, 122,202,206,207 C. White oak 81 C. Bur oak 83 C. Chestnut oak 84 C. Northern red oak 85 C. Scarlet oak 82 C. Yellow poplar 110 C. Black walnut 108 C. Black locust 122 C. Red maple 95 COMBINATION GROUPS C. Post-blackjack oak 86,206 C. Chestnut-black-scarlet oak 82,84,120 C. Yellow poplar-white oak-red oak 81,85,110 C. White oak-red oak-hickory 81,85,92,94,120,207 C. Southern scrub oak 89,203,206 C. Sweetgum-yellow poplar 109,110 C. Sassafras-persimmon 93 C. Mixed upland hardwoods 83,88,94,101,106,108,113,122,125, 201,202,203,204 B. Oak-gum-cypress 59,61,87,90,111,112,114,127,128,143 C. Swamp chestnut-cherrybark oak 87 C. Sweetgum-nuttall-willow oak 109,125,143,201,203,204 C. Cypress-water tupelo 61,112 C. Overcup oak-water hickory 90,128 C. Atlantic white cedar 59 C. Sweetbay-swamp tupelo-red maple 95,111,113,114,127 B. Elm-ash-cottonwood 91,97,100,104,115,116,118,123,129 135,137,208 C. Cottonwood 118,137 C. Willow 123 C. Red maple 95 C. River birch-sycamore 108,116,123,129 C. Sycamore-pecan-elm 91,94,109,116 C. Black ash-elm-maple 104 C. Silver maple-American elm 94,97 C. Sugarberry-elm-green ash 94,100,105,115,208,209 C. Cottonwood-willow 118,123,130,131,137 C. Oregon ash 135 B. Maple-beech-birch 66,96,98,107,110,122,124 C. Black cherry 121 C. Red maple 95 C. Black cherry-white ash 103,110,121 C. Maple-basswood 96,124 C. Elm-ash-locust 94,105,122 C. Maple beech-yellow birch 66,94,95,96,98,102,105,107,108 B. Aspen-birch 99,117,119 C. Aspen 119 C. Balsam poplar 117 C. Paper birch 99 B. Alder-maple 130,131 C. Red alder 131 C. Bigleaf maple 130 B. Western oaks 134,138,139,140,142,158,163,210 C. California black oak 139 C. Oregon white oak 140 C. Blue oak 134 C. Gray pine 163 C. Coast live oak 138 C. Canyon-interior live oak 142 C. Deciduous oak-woodland 158 C. Evergreen oak-woodland 210 B. Tan oak-laurel 133,136,141 C. Tan oak 136 C. California laurel 141 C. Giant chinkapin 133 B. Other western hardwoods 132,156,157,159,160 C. Pacific madrone 132 C. Mesquite woodland 157 C. Mountain brush woodland 156 C. Intermountain maple woodland 159 C. Miscellaneous western hardwoods 160 B. Tropical hardwoods 147,149 C. Sable pine 147 C. Mangrove 149 B. Exotic hardwoods 144,145,146,148 C. Paulownia 144 C. Melaluca 145 C. Eucalyptus 148 C. Other exotic hardwoods 146 SPECIAL COMBINED GROUPS AND ASSOCIATE SPECIES Upland-lowland oaks 125,201,203,204 Upland-lowland hardwoods 95,103,105 Southern red oak 88 American elm 94 Winged-cedar elm 209 Silver maple 97 White ash 103 Eastern cottonwood 118 Black cherry 121 Black gum 113 Beech 102 Holly 106 Sweetgum 109 Pin oak 205 Total 1-163,201-210  Table 6. Local forest type composition of national forest type groups.  Forest Local type forest group type code National forest type group code Local forest type  100 White-red-jack pine 101 Jack pine 102 Red pine 103 Eastern White pine 104 White pine-hemlock 105 Eastern Hemlock 120 Spruce-fir 121 Balsam fir 122 White spruce 123 Red spruce 124 Red spruce-balsam fir 125 Black spruce 126 Tamarack 127 Northern white cedar 140 Longleaf-slash pine 141 Longleaf pine 142 Slash pine 160 Loblolly-shortleaf pine 161 Loblolly pine 162 Shortleaf pine 163 Virginia pine 164 Sand pine 165 Table-mountain pine 166 Pond pine 167 Pitch pine 168 Spruce pine 180 Pinyon-Juniper 181 Eastern redcedar 182 Rocky mountain juniper 183 Western Juniper 184 Juniper-woodland 185 Pinyon-juniper woodland 200 Douglas fir 201 Douglas fir 202 Port orford cedar 220 Ponderosa pine 221 Ponderosa pine 222 Incense cedar 223 Jeffry-Coulter-bigcone douglas fir 224 Sugar pine 240 Western white pine 241 Western white pine 260 Fir-spruce-Mountain hemlock 261 White fir 262 Red fir 263 Noble fir 264 Pacific silver fir 265 Engelmann spruce 266 Engelmann spruce-subalpine fir 267 Grand fir 268 Subalpine fir 269 Blue spruce 270 Mountain hemlock 271 Alaska yellow cedar Table 6. Local forest type composition of national forest type groups (cont.)  Forest Local type forest group type code National forest type group code Local forest type  280 Lodgepole pine 281 Lodgepole pine 300 Hemlock-Sitka spruce 301 Western hemlock 304 Western redcedar 305 Sitka spruce 320 Western larch 321 Western larch 340 Redwood 341 Redwood 342 Giant Sequoia 360 Other western softwoods 361 Knobcone pine 362 Southwest white pine 363 Bishop pine 364 Monterey pine 365 Foxtail-Bristlecone pine 366 Limber pine 367 Whitebark pine 368 Misc. Western softwoods 370 California mixed conifer 371 California mixed conifer 380 Exotic softwoods 381 Scotch pine 383 Other exotic softwoods 400 Oak-pine 401 White pine-red oak-white ash 402 Eastern redcedar-hardwood 403 Longleaf pine-oak 404 Shortleaf pine-oak 405 Virginia pine-southern red oak 406 Loblolly pine-hardwood 407 Slash pine-hardwood 409 Other pine-hardwood 500 Oak-hickory 501 Post-blackjack oak 502 Chestnut oak 503 White oak-red oak-hickory 504 White oak 505 Northern red oak 506 Yellow poplar-white oak-red oak 507 Sassafras-persimmon 508 Sweetgum-Yellow poplar 509 Bur oak 510 Scarlet oak 511 Yellow poplar 512 Black walnut 513 Black locust 514 Southern scrub oak 515 Chestnut-black-scarlet oak 519 Red maple-oak 520 Mixed upland hardwoods Table 6. Local forest type composition of national forest type groups (cont.)  Forest Local type forest group type code National forest type group code Local forest type  600 Oak-gum-cypress 601 Swamp chestnut-cherrybark oak 602 Sweetgum-Nuttall-willow oak 605 Overcup oak-water hickery 606 Atlantic white-cedar 607 Bald cypress-water tupelo 608 Sweetbay-swamp tupelo-red maple 700 Elm-ash-cottonwood 701 Black ash-American elm-red maple 702 River birch-sycamore 703 Cottonwood 704 Willow 705 Sycamore-pecan-American elm 706 Sugarberry-hackberry-elm-green ash 707 Silver maple-American elm 708 Red maple-lowland 709 Cottonwood-willow 722 Oregan ash 800 Maple-beech-birch 801 Sugar maple-beech-Yellow birch 802 Black cherry 803 Cherry-ash-yellow poplar 805 Hard maple-basswood 807 Elm-ash-locust 809 Red maple-upland 900 Aspen-birch 901 Aspen 902 Paper birch 904 Balsam poplar 910 Alder-maple 911 Red alder 912 Bigleaf maple 920 Western oak 921 Gray pine 922 California black oak 923 Oregon white oak 924 Blue oak 925 Deciduous oak woodland 926 Evergreen oak woodland 931 Coast live oak 932 Canyon-interior live oak 940 Tan oak-laurel 941 Tan oak 942 California laurel 943 Giant chinkapin 950 Other western hardwoods 951 Pacific madrone 952 Mesquite woodland 953 Mountain brush woodland 954 Intermountain maple woodland 955 Misc. western hardwoods 980 Tropical hardwoods 981 Sable Palm 982 Mangrove 990 Exotic hardwoods 991 Paulownia 992 Melaluca 993 Eucalyptus 995 Other exotic hardwoods         PAGE  PAGE 1  EMBED Word.Document.8 \s   EMBED Excel.Sheet.8  ~   LY ,!-!,,'<(<;<<<=<><NNNNNN O OO O!O"O*O+O=O>O|j#c= h)UVjh)EHUj#c= h)UVjh)EHUj#c= h)UVjh)EHU!j< h)CJOJQJUVjh)U h)H*h)5CJ\HhӪufh)5\ h)5\ h)CJ$h)/~   # $ % & ' ( ) * + , 7 8 <D%D%D%D%D%D%D%D%D%D%D%D%D%D%D% D%YD%YD%YD%YD%YD%YD%YD%YD%YD%I=D%YD%!:ddd/H<= -.KLa#b###Z*[*..T0U000&7D%YD%*D%YD%*D%YD%I=D%YD%o%D%YD%I=D%YD%D%YD%UED%YD%8PD%YD%I=D%D%eD%YD%;-@D%YD%D%YD%I=D%YD%C`d&7'7::<<?<@<h<i<<<A=B=>>g@h@4C5C_F`FHHIIpKqKMD%YD%*D%YD% D%YD%D%YD%YD%YD%YD%YD%YD%YD%D%YD%idD%YD%*D%YD%!0D%YD%D%YD%D%YD%D%YD%o%  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Percentiles of the distribution of-differences in plot density between the powerand quadratic functions  I@  dMbP?_*+%M FIA_Lexpr#Jw,,⤗C0Lexmark Optra S 18559Lexmark Optra S 1855  eXNw @⤗X,,X⤗"d,,??U}   8 8 8 , , , , , , , , ,          ~ X@~ `@~ `}@ ~ W@ ~ @u@ ~ `s@  ~ ? ~ @` ~ >@  ~ @ ~ 4 ~   ~ ? ~ 8 ~ `}    ***4RRRRRR (  dB  s *D@&3]`nrjB  0D@jJ]`LnrjB  0D@jJ  ]`nrjB  0D@jJ ]`dnrjB   0D@jJ 3=] `nll   s *Pl  @] `Pln >@7 I@  dMbP?_*+%"??U>@7 I@  dMbP?_*+%"??U>@7 USDA FOREST SERVICEUSDA FOREST SERVICEMicrosoft Excel@<m!@@R19U՜.+,0 PXt | USDA Forest Service Sheet1Sheet2Sheet3  Worksheets  FMicrosoft Word Document MSWo1TableCRCompObj\_jObjInfoObjectPool^av8v8 i<@< NormalCJOJQJ_HmH sH tH <A@< Default Paragraph Font8Z@8 Plain TextCJOJQJ^J ;=>o?~Ed+w^6tM\1 }  M 000000000000000000000000000000000000000000000 t   8@"(  HB  C DNB  S DoHB  C DHB  C DNB  S DoNB  S DoB S  ?;>op tx%xt,P,Pt%t,<,<t%tpw6: X]#kp OSN_ ! 2 : b j N ` $/cn)it <GOZZe&1S_PV  U ` ' 2 Q ` 333333333333333333333333333333333USDA FOREST SERVICE)D:\stocking\tech report tables\table2.doc@L L wL L  @@UnknownG:Times New Roman5Symbol3& :Arial71CourierG MS Mincho-3 fg3Times?5 :Courier New"qhiDOjD!'20d 27 Table 2: Stocking equation coefficients and referencesUSDA FOREST SERVICEUSDA FOREST SERVICErdDocWord.Document.89q+ :    &' """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3fWordDocumentN"SummaryInformation(`b\DocumentSummaryInformation8d_1030275563g Fv8v87 bjbjUU "7|7| l  # % % % % % % $N nI I ^  ~# # # #  cRJ # # t 0 # R R#   Table 2: Stocking equation coefficients and references   Equation Coefficients  Species number b0 b1 References Spruce-fir 1 .00869 1.48 Solomon, Hosmer, Hayslett(1987) Western larch 2 .00454 1.73 Cochran(1985) Black spruce 3 .01691 1.05 Plonski(1960) Jack pine 4 .00946 1.59 Benzie(1977a) Lodgepole pine 5 .00422 1.70 Dahms(1964) Shortleaf pine 6 .00509 1.81 USDA Misc. Publ. 50(1976) Slash pine 7 .00458 1.91 Schumacher and Coile(1960) USDA Misc. Publ. 50(1976) Western white pine 8 .00335 1.73 Haig(1932) Longleaf pine 9 .01367 1.44 Schumacher and Coile(1960) USDA Misc. Publ. 50(1976) Ponderosa pine 10 .00250 2.00 Meyer(1961) Red pine 11 .00609 1.67 Benzie(1977b) Pond pine 12 .00914 1.67 Schumacher and Coile(1960) Eastern white pine 13 .00900 1.51 Philbrook, Barrett, Leak(1973) Loblolly pine 14 .00680 1.72 Schumacher and Coile(1960) USDA Misc. Publ. 50(1976) Douglas fir 15 .00769 1.54 McArdle, Meyer, Bruce (1961) Northern white cedar 16 .00433 1.80 Johnston(1977) Eastern hemlock 17 .00313 2.11 Bragg(1992), Tubbs(1977) Western hemlock 18 .00427 1.67 Barnes(1962) Redwood 19 .00333 1.68 MacLean(unpublished) Red maple 25 .01105 1.53 Stout and Nyland(1986) Red alder 26 .01671 1.41 Worthington, et al.(1960) Maple,beech,birch 27 .00694 1.86 Bragg(1992) Stout and Nyland(1986) Leak, Solomon, Debald(1987) Roach(1977) Paper birch 28 .00635 1.89 Safford(1983) Oaks and hickory 29 .01119 1.63 Roach and Gingrich(1962) Black walnut 30 .01546 1.50 Schlesinger and Funk(1977) Sweetgum 31 .00429 1.87 Osbourne and Winters(1935) Aspen 32 .01429 1.46 Perala(1977) Cherry,ash,yellow poplar 33 .02197 1.13 Stout and Nyland(1986) Basswood 35 .00442 2.02 Bragg(1992), Tubbs(1977) Elm,ash,cottonwood 36 .00688 1.86 Meyers and Buckman(1984)  ;<>?bnoq>*OJPJQJ jOJPJQJUmHnHu OJPJQJ ;=>o?~Ed+w ^ 6 t t  M  \ 1 } M 1h/ =!'"'#$%Oh+'0 , HT p | 8 Table 2: Stocking equation coefficients and referencesTabUSDA FOREST SERVICESDASDA Normal.dot USDA FOREST SERVICE3DAMicrosoft Word 9.0@q@k?@cEJ՜.+,00 hp  USDA Forest Service  8 Table 2: Stocking equation coefficients and references TitleOle PRINTdf|CompObjfObjInfoeif333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___www45'  ' %' %Times New Roman,- "Systemn-'- x%? 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