United States

Department of

Agriculture

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i-nu s

W Southern Forest

Forest Service Research Note

SO-328

Experiment Station October 1988

The Relationship of Bole Diameters and Crown Widths of Seven

Bottomland Hardwood Species

John K. Francis

SUMMARY

Diameters, heights, and eight crown radii per tree

were measured on 75 individuals from each of seven

bottomland hardwood species in Mississippi. It was determined that the seven species could not be described

by a single regression equation. Crown class was tested

to see whether it significantly influenced the slope or

intercept of the linear relationship. Three of the species

were significantly affected. Total height was not a significant predictor of crown width. Regressions of average

crown radius on d.b.h. were calculated for each species

or species-crown class group. Roundness of crown was

not affected by species but average crown radius/d.b.h.

was. The crown width/d.b.h. relationship can be applied

to competition studies and in predicting d.b.h.‘s from

aerial photographs.

Additional keywords: Crown diameter, stem diameter, southern hardwoods.

A knowledge of the quantitative relationship between

bole diameter (d.b.h.) and crown width is necessary for

predicting diameters and volumes from aerial photos

and for structuring of competition studies and models.

Stocking and spacing studies can also benefit from an

understanding of this relationship.

The crown width/d.b.h. relationships for a number of

conifer species are given by Minor (1951) Smith and

Baily (1964) Wile (1964), Roberts and Ross (1965) and

Bonner (1968). The crown width/d.b.h. relationship of

tropical hardwoods has also been reported (Dawkins

1963, Curtin 1964, Kwan 1966, Perez 1970). All these

studies found a strong relationship between d.b.h. and

crown width (R* = .6 - .9). In one study, total height was

included as a variable. The crown width/d.b.h. relationship in temperate hardwoods has received a little attention. Krajicek and others (1961) found a very strong relationship (r = .98) between d.b.h. and crown width of

open-grown white oak (Quercus a/&), red oaks (Q. velutina and Q. r&a), and shagbark hickory (Carya

ovata). They concluded that the relationship was independent of stand age or site quality. From studies on

white oak, black oak (Q. velutina), Northern red oak (Q.

r&a), scarlet oak (Q. coccinea), and hickory (Carya

sp.). Minkler and Gingrich (1970) concluded that opengrown and forest-grown trees had the same crown width/

d.b.h. relationship and that the relationship for these

species appeared to be independent of site, crown class,

and species. The crown width/d.b.h. relationship of bottomland hardwood species, the subject of this paper,

has not been previously reported.

METHODS

Seven important local species were chosen for study.

They were: sweetgum (Liquidambar styraciflua), green

ash (Fraxhus pennsylvanica), sugarberry (Cekus laevigata), American elm (U/rnus americana), overcup oak

(Quercus Iyrata), Nuttal oak, (Q. nutallii), and willow oak

(Q. phellos). Seventy five trees of each species without

disease or major defect were selected for measurement.

About one-third of the trees of each species were in the

dominant, codominant, and intermediate crown classes.

All the trees were growing on the Delta Experimental

Forest near Stoneville, Mississippi, a 3,000-acre area

covered with a slack-water clay soil currently mapped as

the Sharkey series (very fine, montmorillonitic, nonacid,

thermic Vertic Haplaquepts).

Southern Forest Experiment StationIT-102lO U.S. Postal Services Bldg., 701 Loyola Avenue, New Orleans, La. 70113

Forest Service, U.S. Department of Agriculture.

Serving Alabama, Arkansas, Louisiana, Mississippi, E. Oklahoma, Tennessee, E. Texas, Puerto Rico, U.S. Virgin Islands

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Table 1 .-Means and ranges of diameter (d.b.h.), height, and average crown radius

for seven bottom/and hardwood species

D.b.h.

Species Average Range

- - - - _ Inches _ _ _ _ Sweetgum 14.9 6.0-28.4

Sugarberry 15.0 7.5-25.8

American elm 15.4 7.5-27.3

Green ash 15.4 6.0-28.5

Willow oak 19.9 8.2-35.9

Nuttall oak 18.8 6.8-35.3

Overcup oak 18.7 8.0-35.4

Height Crown radius

Average Range Average Range

-----------_____ Feet ________________

8 1 56-l 06 13.3 5.4-20.9

7 0 46-85 13.9 8.0-l 9.3

7 0 45-91 15.3 7.2-26.9

7 8 56-l 00 14.9 6.5-26.9

8 0 58-99 17.9 7.1-31.2

7 7 55-99 20.8 8.4-33.1

7 3 44-93 17.2 7.2-28.5

Each tree was measured for d.b.h., total height, and

average crown radius. Crown radius was measured

eight times per tree on the directions N., NE., E., SE., S.,

SW., W., and NW. This was done by stretching a tape

from the trunk, compensating for the distance to the

pitch, to a point visually located directly under the edge

of the crown. The resulting measurements were

summed and divided by eight.

Averages and ranges of height, d.b.h. and average

crown radius for each species are given in table 1. The

coefficient of variation of crown radius was calculated for

each tree as an index of uniformity in crown shape (a

perfect circle would equal zero percent). A crown/bole

index [average crown radius (in feet) divided by d.b.h. (in

inches)] was used in comparing species.

Analysis of covariance with dummy variables was employed to test whether a common regression equation

could accurately describe the relationship between

d.b.h. and crown width of all seven species. Tukey’s test

(Mendenhalll968) was used to compare ranked means

of crown/bole index of the seven species. Species as a

source of variation in roundness of crown was tested by

the analysis of variance of the coefficients of variation of

crown radius. A probability for error (0~) of 0.05 was used

in all cases. Linear regression models of average crown

radius on d.b.h. were calculated for each species. Because crown classes were known, it was necessary to

determine whether the relationship between crown radius and d.b.h. differed among crown classes of each

species. For each species, each of the three combinations of two crown classes were compared for significant

difference of variance, slope, and intercept. Where differences existed, separate regressions for each crown

class were calculated.

RESULTS

A comparison of crown/bole indexes of the seven

species shows that Nuttall oak had a significantly greater

crown/bole index, while the other species varied in two

overlapping groups (table 2). Sweetgum, often recogTable 2.-Average crown radius (in feet) divided by d.b.h. (in inches)

for seven bottom/and hardwood species as compared by

Tukey’s test (a = 0.05)’

Measurement NO AE GA SB 00 WiO SG

CR1d.b.h. -

1.133 -1.020 1.012 .963 .955 .907 .903

’ NO = Nuttall oak; AE = American elm; GA = Green ash; SB=

Sugarberry; 00 = Overcup oak; WiO = willow oak; SG = Sweetgum.

Lines under values for species indicate no significant difference.

Table 3.-Linear regression equations, coefficients of determination,

and coefficients of variation for seven bottom/and hardwood

species

John K. Francis is Research Forester, formerly at the Southern Hardwood Laboratory, USDA Forest Service, Stoneville, Mississippi; presently at

the Institute of Tropical Forestry, USDA Forest Service, Southern Forest Experiment Station, Rio Piedras, Puerto Rico.

Species Regression’ R2 C.V.

Sweetgum

Sugarberry

American elm

Green ash

Willow oak

Nuttall oak

Percent

Y = 2.35 t .735X .75 14.1

Y = 6.61 t .486X .61 12.5

Y = 3.36 t .776X .81 12.5

Y = 3.10 t .771x .82 14.2

Y = 1.33 t .832X .87 11.3

Y = 3.25 t .931X .86 13.3

Overcup oak Y = 3.95 t .709x .87 11.8

1 Y = average crown radius in feet; X = tree d.b.h. in inches.

nized for its narrow crown, had a crown/bole index about

25 percent smaller than that of Nuttall oak. Coefficient of

variation of crown radii, compared by analysis of variance, revealed no difference in species with respect to

roundness or uniformity of crown. Average coefficients

of variation by species ranged from 20.5 to 24.1 percent.

Linear regression models of average crown radius on

d.b.h. were calculated for each of the seven species

(table 3). Coefficients of multiple determination varied

from .87 for overcup and willow oaks to .61 for sugarberry. Contribution of the additional variables, d.b.h.

squared and height, were evaluated with the F-test and

found to be insignificant. A significant difference in

slopes of the regression lines prohibited the use of a

single equation to describe all seven species.

Crown classes within each species were tested by

analysis of covariance to determine whether separate

regression equations were needed within each species.

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Uniform variance and slope were found within the crown

classes of all species. However, green ash, Nuttall oak,

and overcup oak had at least two combinations of crown

classes with different intercepts. New linear regression

equations for each of the crown classes within these

species are presented in table 4. Because the crown

classes in this forest were closely tied to tree size, and

thus crown radius and d.b.h. range, R* values were considerably reduced.

DISCUSSION

An unexpected result of the crown radius/d.b.h. ratio

was that willow oak and overcup oak differed so little

from sweetgum and so much from Nuttall oak. The reason is unknown. Although sweetgum and willow oak appear to be more efficient in accumulating more d.b.h. per

unit of crown area than Nuttall oak or American elm,

nothing is implied about growth rates.

Apparently, for the number of samples taken, no

species produced rounder or smoother crowns than

others. And evidently, natural hazards, such as storm

breakage of limbs, not species differences, were the

cause of deviations from roundness of crown.

The conclusion that height used in combination with

d.b.h. was an insignificant predictor of crown width

agreed with the findings of Cur-tin (1964) for eucalyptus

but differed with the results reported by Bonner (1968)

for northern conifers. Species may have had something

to do with these differences.

The inadvisability of combining the data from different

crown classes in three of the seven species indicates

differences among crown classes, at least in Nuttall oak,

green ash, and overcup oak. Even differences between

crown classes within these species was not always consistent. A better comparison might have resulted if a

broader range of diameters within each crown class had

been sampled. Minkler and Gingrich (1970) reported that

crown width1d.b.h. relationships of well stocked, unevenaged stands of upland oak and hickories were independent of site, crown class, and species.

The crown width/d.b.h. relationship can now be used

to predict stem diameters from crown widths on aerial

photographs. Although basal area will continue to be

used as the principal stocking guide and index of competition, crown width/d.b.h. relationships can be used to

refine competition and stocking studies involving crown

expansion where d.b.h. is known or can be predicted.

Bonner, G.M. Stem diameter estimates from crown width

and tree height. Commonwealth Forestry Review.

47(1):8-13; 1968.

Curtin, R.A. Stand density and the relationship of crown

Table 4.-Linear regression equations, coefficients of determination,

and coefficients of variation for regression to predict average crown radius from d.b.h. for three bottom/and hardwood

species

Identification Regression’ Iv C.V.

Green ash

Dominant

Codominant

Intermediate

Nuttall oak

Dominant

Codominant

Intermediate

Overcup oak

Dominant

Y=11.82 + .454X .41 16.5

Y = 1.27 + .963X .51 17.1

Y = ,641 + .852X .48 24.5

Y = 2.41 + .821X .43 21.6

Y = 5.38 + .679X .41 19.6

Y = 1.27 + .752X .42 33.3

Y = .526 + 1.185X .60 30.7

Y = 6.27 + .686X .41 16.2

brcent

Intermediate Y = 1.76 + .829X .39 17.5

lX = tree d.b.h. in inches; Y = average crown radius in feet.

width to diameter and height in Eucalyptus obliqua.

Australian Forestry. 28(2):91-l 05; 1964.

Dawkins, H.C. Crown diameters: their relation to bole

diameter in tropical forest trees. Commonwealth

Forestry Review. 42(4):318-333; 1963.

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

competition-a measure of density. Forest Science.

7( 1):35-42; 1961.

Kwan, W.Y. Crown diameter/bole diameter relationship

of Dyera costulafe and its planting distance and crop

density. Malayan Forester. 29(3):163-l 69; 1966.

Mendenhall, W. Introduction to linear models and the

design and analysis of experiments. Wadsworth Publishing Company, Inc., Belmont, CA; 1968. 465 p.

Minkler, L.S.; Gingrich, S.F. Relation of crown width to

tree diameter in some upland hardwood stands of

Southern Illinois. Research Note NC-99. St. Paul, MN:

U.S. Department of Agriculture, Forest Service, North

Central Forest Experiment Station; 1970. 4 p.

Minor, C.O. Stem-crown diameter relations in southern

pine. Journal of Forestry. 49(7):490-493; 1951.

Perez, J.W. Relation of crown diameter to stem diameter

in forests of Puerto Rico, Dominica, and Thailand. In:

Odum, H.T; Pigeon, R.F., eds. A Tropical rain foresta study of irradiation and ecology at El Verde. U.S.

Atomic Energy Commission, Division of Technical Information; 1970: B105-8122.

Roberts, E.G.; Ross, R.D. Crown area of free-growing

loblolly pine and its apparent independence of age

and site. Journal of Forestry. 63(6):462-463; 1965.

Smith, J.H.; Baily, G.R. Influence of stocking and stand

density on crown widths of Douglas fir and lodgepole

pine. Commonwealth Forestry Review. 43(3):243-

246; 1964.

Wile, B.C. Crown size and stem diameter in red spruce

and balsam fir. Forestry Pub. No. 1056. Ottawa, Ont.:

Canada Department of Forestry, Forestry Research

Branch; 1964. 9 p.

StU.S.GOV~MENTP~GOFL1~:1966 -761 466, 60001

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