p-- United States &] 3 Department of 

Agriculture D.b.h./Crown Diameter 

Forest Service Relationships in Mixed 

Northeastern Forest 

Experiment Station Appalachian Hardwood 

Research Pa~er NE-610 

Neil I. Lamson 

Stands 
Abstract 

Linear regression formulae for predicting crown diameter as a function of stem 

diameter are presented for nine species found in 50- to 80-year-old mixed hardwood stands in north-central West Virginia. Generally, crown diameter was closely 

related to tolerance; more tolerant species had larger crowns. 

The Author 

NEIL I. LAMSON received his B.S. and M.S. in silviculture and forest soils from 

the State University of New York College of Environmental Sciehce and Forestry. 

He joined the USDA Forest Service, State and Private Forestry, in 1972. Currently 

he is a research forester in timber management at the Timber and Watershed 

Laboratory, Northeastern Forest Experiment Station, Parsons, West Virginia. 

Manuscript received for publication 22 June 1987 

Northeastern Forest Experiment station 

370 Reed Road, Broomall, PA 19008 

December 1987 
Introduction 

In order to apply any silvicultural system, it is essential to 

understand how trees grow and react to various cultural 

treatments. Growth rates of trees are directly affected by 

the intensity of competition. Crown dimensions are feasible expressions of the cumulative effects of competition 

(Curtis 1970, Krajicek et al. 1961). This paper reports 

diameter breast height (d.b.h.)/crown diameter relationships for unmanaged, even-aged mixed hardwood stands 

in West Virginia. 

Methods 

Nine species were selected for study: hickory (Carya cordiformis and Carya ovata), northern red oak (Quercus 

rubra L.), scarlet oak (Quercus coccinea Muenchh.), 

white ash (Fraxinus americana L.), yellow-poplar (Liriodendron tulipifera L.), black cherry (Prunus serotina 

Ehrh.), sugar maple (Acer saccharum Marsh.), red maple 

(Acer rubrum L.), and beech (Fagus spp.). These are 

common species in mixed hardwood stands in the central 

Appalachian mountains. Data were collected from a total 

of 52 even-aged stands ranging in ages from 50 to 80 

years and located in north-central West Virginia. These 

were typical second-growth stands with scattered individual trees up to 150 years old. 

Northern red oak site index (SI) class ranged from 55 to 

85 feet in stands estimated by using height/age relationships (Schnur 1937). Within each stand, trees of the study 

species were randomly selected. All crown classes were 

included so long as the trees were reasonably healthy and 

had normal crowns that showed no signs of damage such 

as top breakage or disease. For each study tree, diameter 

outside bark at 4.5 feet (d.b.h.) and crown diameter along 

two axes were measured. Crown diameter was measured 

by two people using a 100-foot tape and ocularly estimating the crown edges. A total of 1,955 study trees were 

included with 98 to 549 trees for each of the nine study 

species. D.b.h. ranged from 3.0 to 36.3 inches, and crown 

width ranged from 5 to 70 feet. 

All data were grouped by species and 10-foot red oak site 

index class. For each group, the data were fit to the following equations: 

CD = a + b(D) 

CD = a + b(D2) 

CD = a + b(D) + C(D)2 

CD = a + b(log(D)) 

Log(CD) = a + b(D) 

LogCD = a + b(log(D)) 

11CD = a + b(D) 

1/CD = a + b(a/D) 

where CD = crown diameter 

D = d.b.h. 

Results 

Equation Selection 

None of the data transformations gave a better fit than the 

linear regression using only D. Therefore, the linear 

regression form of CD = a +b(D) was selected. 

Differences Due to Site Index 

Except for scarlet oak, which was observed only in SI 

class 60 stands, all species were observed in stands in 

which the SI class ranged from 60 to 70, 60 to 80, or 70 to 

80 feet. Differences due to SI class were tested by statistically comparing the slopes and intercepts of each specieslsite index class equation to those from a single 

species equation using the data from all trees for a species regardless of site index class. Significant differences 

were found among the SI classes only for red oak and 

yellow-poplar. For red oak, SI 70 and 80 were not 

different. 

Differences Among Species 

Differences among species were tested by statistically 

comparing slopes and intercepts of individual species 

equations to those from equations which included all 

trees from two or more species. No significant differences 

were found among hickory, red oak SI 70 and 80, scarlet 

oak, and white ash. Also red oak SI 60, red maple and 

black cherry were not significantly different. Th'erefore, 

equations for the white ash, hickory, red oak SI 70 and 80, 

and scarlet oak group and the red oak SI 60, red maple, 

black cherry group were calculated. The resultant six 

equations are shown in Table 1. Coefficients of determination (R2) ranged from 0.59 to 0.68 for the six equations. 

Intercepts (a) ranged from 4.951 feet for yellow-poplar, 

site index 80, to 17.845 for sugar maple, while slopes (b) 

ranged from 1.022 for sugar maple to 2.030 for the yellowpoplar, SI 80 (Table 1). 
Table 1.-Slopes (b) and intercepts (a) for linear regression 

equations crown diameter =a +b(d.b.h.) 

Table 2.-Estimated crown diameter by 2-inch d.b.h. classes 

calculated using the formulae from Table 1. 

Equa- No. of 

tion obserNo. Species vations a b r2 SE(a) 

1 Beech 98 16.734 1.291 0.61 1.665 

2 Sugar maple 241 17.845 1.022 0.68 0.691 

3 White ash/ 

oak groupl 607 13.571 1.318 0.59 0.768 

4 Red maple, 

black cherry2 566 12.596 1.073 0.62 0.518 

5 Yellow-poplar, 

S1 70 109 5.203 1.383 0.61 1.753 

6 Yellow-poplar, 

S180 334 4.951 2.030 0.59 1.530 

10ak group contains hickory, scarlet oak, and red oak SI 

70 and 80. 

%so includes red oak SI 60. 

Validation of Equations 

The six equations were validated by splitting the data into 

a regression data set and a test data set. The regression 

equations for the six species and SI classes were calculated using the regression data set and these equations 

were used to calculate predicted values and residuals for 

the test data set. The SAS procedure PROC MEANS (SAS 

1985) was used on the residuals to test whether there 

were differences for each group and for the data set as a 

whole. The variance estimates of the residuals were also 

compared to the variances obtained with the regression 

data set. Since the variances of the two procedures were 

nearly identical and the tests indicated that none of the 

mean residuals were significantly different from zero, the 

equations were assumed to be valid. 

Crown Diameters 

Crown diameters calculated using the formulae from 

Table 1 are shown in Table 2. Yellow-poplar SI 70 and red 

maplelblack cherry have the smallest crowns, while 

yellow-poplar SI 80 and beech have the largest. It is interesting to note that yellow-poplar SI 80 has the largest 

crowns for trees over 16 inches d.b.h. However, yellowpoplar over 16 inches d.b.h. have crowns only about 3 to 

8 feet larger than beech. 

D.b.h. class 

Species 6 8 10 12 14 16 18 20 22 24 26 

Feet 

Beech 25 27 30 32 35 37 40 43 45 48 50 

Sugar maple 24 26 28 30 32 34 36 38 40 42 44 

White ash/oak groupl 22 24 27 29 32 35 37 40 43 45 48 

Red maple/black cherry 19 21 23 26 28 30 32 34 36 38 40 

group2 

Yellow-poplar SI 70 14 16 19 22 25 27 30 33 36 38 41 

Yellow-poplar SI 80 17 21 25 29 33 37 42 46 50 54 58 

lOak group contains hickory, scarlet oak, and red oak SI 

70 and 80. 

2lncludes red oak SI 60. 

Discussion 

These equations and tables are based on data collected 

from even-aged stands that were 50 to 80 years old. 

Therefore, most of the 4- and 6-inch trees were overtopped, as were many of the 8-inch trees. These equations may not accurately describe d.b.h./crown diameter 

relationships of trees in stands less than 50 years old. For 

example, 6-inch SI 70 yellow-poplar trees in a 25-year-old 

stand will most likely be codominant and may not have 

crowns that are 14 feet in diameter as estimated in Table 

2. 

Generally, the intolerant species, black cherry and yellowpoplar SI 70, have the smallest crowns. Beech has the 

largest crowns for diameters up to 16 inches. Sugar 

maple has larger crowns than the white ash/oak group up 

to 14 inches d.b.h. However, for trees 20 inches d.b.h. and 

larger, the white ash/oak group, beech and sugar maple 

have crowns about the same size. Since most of the study 

trees at least 20 inches d.b.h. were codominant, it can be 

concluded that for these 50- to 80-year-old stands, 

codominant white ashloak group species beech and 

sugar maple have about the same size crowns. 
These crown diameter data suggest that there are three 

major species groups for trees at least 16 inches d.b.h. 

The first is beech and yellow-poplar SI 80, with the largest 

crowns. The second group, with intermediate-size crowns 

contains sugar maple, white ash, and the oaks. The third 

group, with the smallest crowns includes red maple, 

yellow-poplar SI 70, and black cherry. Growth and yield 

researchers working in these stands are investigating various even-age management strategies. If relative stand 

density (Marquis et al. 1984) proves to be a viable management tool in Appalachian hardwood stands, these 

three species groups may prove to be useful. 

Leak (1983) reported that in New Hampshire beech also 

had larger crowns than sugar maple or red maple. Hough 

(1935) also found that young beech had the largest 

crowns in Pennsylvania hardwood stands. Lake States 

northern hardwoods have about the same size crowns as 

the Appalachian red maple/black cherry group (Godman 

and Tubbs 1973). 

Conclusions 

D.b.h. is a reasonably good predictor of crown diameter 

in 50- to 80-year-old even-aged Appalachian hardwood 

stands. In these mixed stands, beech has the largest 

crowns, while yellow-poplar SI 70 and black cherry have 

the smallest. Three general crown width groups are evident. Beech and yellow-poplar SI 80 have the largest 

crowns, followed by a second group of sugar maple, 

white ash, red oak, scarlet oak, and hickory. Red maple, 

yellow-poplar SI 70, and black cherry form the third 

group with the smallest crowns. 

Literature Cited 

Curtis, R. 0. 1970. Stand density measures: an interpretation. Forest Science 16:403-414. 

Godman, R. M.; Tubbs, C. H. 1973. Establishing even-age 

northern hardwood regeneration by the shelterwood 

method-a preliminary guide. Res. Pap. NC-99. St. Paul, 

MN: US. Department of Agriculture, Forest Service, North 

Central Forest Experiment Station. 9 p. 

Hough, A. F. 1935. Crown spread of Allegheny hardwoods. 

Tech. Note No. 7. Philadelphia, PA: US. Department of 

Agriculture, Forest Service, Allegheny Forest Experiment 

Station. 1 p. 

Krajicek, J. E.; Brinkman, K. A.; Gingrich, S. F. 1961. Crown 

competition-a measure of density. Forest Science 

7:35-42. 

Leak, W. B. 1983. Stocking, growth and habitat relations in 

New Hampshire hardwoods. Res. Pap. NE-523. Broomall, 

PA: US. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. 11 p. 

Marquis, David A,; Ernst, Richard L.; Stout, Susan L. 1984. 

Prescribing silvicultural treatments in hardwood stands of 

the Alleghenies. Res. Pap. NE-96. Broomall, PA: U.S. 

Department of Agriculture, Forest Service, Northeastern 

Forest Experiment Station. 90 p. 

SAS Institute, Inc. 1985. SAS Users Guide: Basics, Version 5 

Edition. Cary, NC: SAS Institute Inc. 1290 p. 

Schnur, G. L. 1937. Yield, stand, and volume tables for evenaged upland oak forests. Tech. Bull. 560. Washington, DC: 

US. Department of Agriculture, Forest Service. 88 p. 

3 

U. S. GOVERNMENT PRINTING OFFICE: 1987/548466/60009 
Lamson, Neil 1. 1987. D.b.h./crown diameter relationships in mixed Appalachian hardwood stands. Res. Pap. NE-610. Broomall, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment 

Station. 3 p. 

Linear regression formulae for predicting crown diameter as a function of 

stem diameter are presented for nine species found in 50- to 80-year-old 

mixed hardwood stands in north-central West Virginia. Generally, crown 

diameter was closely related to tolerance; more tolerant species had larger 

crowns. 

Keywords: Crown diameter 

ODC: 531 (Appalachian hardwoods):176.1 
Headquarters of the Northeastern Forest Experiment Station are in Broomall, Pa. 

Field laboratories are maintained at: 

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Hamden, Connecticut, in cooperation with Yale University. 

Morgantown, West Virginia, in cooperation with West Virginia University, 

Morgantown. 

Orono, Maine, in cooperation with the University of Maine, Orono. 

Parsons, West Virginia. 

Princeton, West Virginia. 

Syracuse, New York, in cooperation with the State University of New York 

College of Environmental Sciences and Forestry at Syracuse University, 

Syracuse. 

University Park, Pennsylvania, in cooperation with the Pennsylvania State 

University. 

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