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Urban Forestry & Urban Greening 12 (2013) 144–153

Contents lists available at SciVerse ScienceDirect

Urban Forestry & Urban Greening

journa l homepage: www.elsevier .de/ufug

Relationships between bole and crown size for young urban trees

in the northeastern USA

Blake Troxel a,b,∗, Max Piana a,b, Mark S. Ashton a, Colleen Murphy-Dunninga,b

a Yale School of Forestry & Environmental Studies, 195 Prospect Street, New Haven, CT 06511, United Statesb Urban Resources Initiative, Hixon Center for Urban Ecology, 301Prospect Street, First Floor, NewHaven,CT 06511, United States

a r t i c l e i n f o

Keywords:

AllometryGrowth projection

New Haven

Street tree management

Urban ecology

Urban forestry

a b s t r a c t

Knowledge of allometric equations can enable urban forest managers to meet desired economic, social,

andecological goals. However, there remains limited regional data on young tree growth within the urban

landscape. The objective of this study is to address this research gap and examine interactions between

age, bole size and crown dimensions of young urban trees in New Haven, CT, USA to identify allometric

relationships and generate predictive growth equations useful for the region. This study examines the

10 most common species from a census of 1474 community planted trees (ages 4–16). Regressions were

applied to relate diameter at breast height (dbh), age (years since transplanting), tree height, crown diam-

eter and crown volume. Across all ten species each allometric relationship was statistically ( p < 0.001)

significant at an˛-level of 0.05. Consistently, shade trees demonstrated stronger relationships than orna-

mental trees. Crown diameter and dbh displayed the strongest fit with eight of the ten species having

an R2 > 0.70. Crown volume exhibited a good fit for each of the shade tree species (R2 > 0.85), while the

coefficients of determination for the ornamentals varied (0.38 < R2 < 0.73). In the model predicting height

from dbh, ornamentals displayed the lowest R2 (0.33 < R2 < 0.55) while shade trees represented a much

better fit (R2 > 0.66). Allometric relationships can be used to develop spacing guidelines for commonly

planted urban trees. These correlations will better equip forest managers to predict the growth of urban

trees, thereby improving the management and maintenance of New England’s urban forests.

© 2013 Elsevier GmbH. All rights reserved.

Introduction

The composition and arrangement of trees within a city can

provide a range of benefits for the urban community. Urban trees

moderate micro-climate (Rosenfeld et al., 1998; Simpson, 1998;

Akbariet al., 2001; Akbari, 2002; Donovan andButry, 2009); reduce

energy use and atmospheric carbon dioxide (McPherson, 1998;

McPherson and Simpson, 2000); improve air, soil, and water qual-

ity (Beckett et al., 1998; Nowak et al., 2002; Donovan et al., 2005;

Yang et al., 2005; Nowak, 2006; Escobedo and Nowak, 2009); miti-

gate stormwater runoff (Sanders, 1986; Xiao et al., 1998, 2000a,b);

reduce noise, increase property values, and enhance the social

and aesthetic environment of a city (Nowak et al., 2001; Maco

and McPherson, 2002; Nowak, 2006). These social, economic, and

ecological benefits are often correlated with tree and crown size.

Numerous studies illustrate a direct relationship between the asso-

ciated benefits of trees and their leaf-atmosphere interactions,

suggesting that each benefit may be a function of tree canopy and

∗ Corresponding authorat: Yale Schoolof Forestry & Environmental Studies, 195

Prospect Street, NewHaven, CT 06511, United States. Tel.: +1 2036416570.

E-mailaddresses: [email protected], [email protected](B.Troxel).

leaf area (Scott et al., 1998; Dwyer and Miller, 1999; Xiao et al.,

2000a,b; Stoffberg et al., 2010).

Physiological understanding of trees reveals a close relationship

between plant stem growthand photosynthetic area (Berlyn, 1962;

Ashton, 1990). This relationship between bole size and other phys-

ical dimensions of growth is fundamental to the study of allometry

in forests. Traditionally associated with rural forests, allometric

models of growth and yield have been developed through rela-

tionships between tree dbh, tree height, and crown dimensions to

develop quantitative guidelines for spacing and thinning of man-

aged forests and timber plantations (Furnival, 1961; Curtis, 1967;

Stage, 1973).

The knowledge of size relationships and allometric equa-

tions has been recognized as a valuable tool that will enable

professionals to manipulate forest structure and composition to

meet desired economic, social, and ecological benefits (Nowak,

1994; Nowak and Dwyer, 2007). From these equations arborists,

researchers, and urban forest managers can develop appropri-

ate policy, analyze management scenarios, plan for spacing and

infrastructure constraints, and determine best management prac-

tices for the selection, sitting, planting, and maintenance of urban

trees (McPherson et al., 2000; Peper et al., 2001a,b; Larsen and

Kristoffersen, 2002; Stoffberg et al., 2008).

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B. Troxel et al. / Urban Forestry & Urban Greening 12 (2013) 144–153 147

Fig. 2. Measurements taken at each sample point, and crown volume calculations.

Y = 10(u+MSE/2) (10)

where Y is theestimated mean in arithmetic units;MSE isthe mean

squared error; yi is theobservedresponsefor the ith tree, i =1,2, . . .,n; n the number of observations; xi theageorthedbhofthe ith tree;

a and b the parameters to be estimated. Table 3 lists the predictedvalues (back transformed) for each species at 5 and 15 years after

transplantation (Baskerville, 1972; Peper et al., 2001a,b) (Fig. 3).

Results

Allthe allometricrelationshipsacrosseach of the growth dimen-

sions were highly significant at an alpha level of 0.05 (˛= 0.05).

For each of the parameters, shade trees (large trees with spreading

canopies) demonstrated stronger relationships than ornamental

trees (smaller trees with aesthetic features). The strongest fit for

all species, except for Tilia and Prunus cerasifera, was displayed by

the relationship between crown diameter and dbh. Eight of the

ten species had an R2 >0.700. Quercus species had the highest R2

(0.917), while Syringa reticulata and Cornus species had the lowest

R2 (0.642 and 0.495 respectively) (Table 2). The model for crown

volume exhibited a good fit for each of the shade tree species

(R2 > 0.850), however the coefficientsof determination for the orna-

mentals rangedfrom0.377to 0.730.Similarly,in themodel relating

height to dbh, the ornamentals displayed the lowest R2 (between

0.325 and 0.550) while the equations for shade trees represented amuch better fit (R2 > 0.663). When compared to the dbh vs. height

relationships, dbh vs. age exhibited lower R2 values overall with

much greater variation across the 10 species (0.212< R2 < 0.794).

Using these allometric relationships, dbh, tree height, crown

diameter, and crown volume were estimated at 5 and 15 years

after planting (Table 3). As expected, shade tree species had much

greater absolute dbh growth at the end of the first 15 years than

did ornamentals. Predictions for tree heightalso followed this same

pattern. Though Gleditsia triacanthos had the smallest dbh of the

shade tree species, its average crown volume was second only to

the Acer species. As P. calleryana and Tilia species are medium sized

trees and exhibit some aesthetic function, it is interesting to note

that dbh, crown diameter, and crown volume of P. serrulata may at

times exceed those of the two aforementioned species.



148 B. Troxel et al. / Urban Forestry & Urban Greening 12 (2013) 144–153

Table 2

Listed are the regression coefficients (a and b), adjusted coefficients of determination (R2 ), and the root mean squared error (RMSE). Regression equations were calculated

using: log( yi) = a+ b1 log( xi)+ b2 log x2

i

. Allequations were statisticallysignificant at an alpha level of 0.05.

Species log( yi) = a+ b1 log( xi)+ b2 log x2

i

Parameter a b1 b2 R2 (Adj) RMSE

Shade Quercus spp. DBH vs. age 0.269 1.165 −0.192 0.725 0.1023

Heightvs. DBH −0.149 1.082 −0.156 0.727 0.0872

Crown diameter vs.DBH −0.969 2.157 −0.584 0.917 0.0507

Crown volume vs.DBH −1.946 3.756 −0.480 0.852 0.2143

Acer spp. DBH vs. age 1.252 −1.148 1.083 0.790 0.0926

Height vs. DBH 0.686 −0.141 0.276 0.762 0.0595



Gleditsia

triacanthos

DBH vs. age −0.513 2.923 −1.211 0.794 0.1001

Height vs. DBH 0.177 0.674 −0.022 0.849 0.0588

Crown diameter vs. DBH 0.007 0.825 −0.077 0.880 0.0551

Crown volume vs.DBH −1.285 2.743 0.167 0.856 0.2691

Pyrus calleryana DBH vs. age 0.084 1.754 −0.589 0.562 0.1174

Heightvs. DBH −0.031 0.972 −0.155 0.694 0.0715



Tilia spp. DBH vs. age 0.837 0.069 0.272 0.396 0.0937

Height vs. DBH 0.183 0.268 0.224 0.663 0.0659

Crown diameter vs.DBH −0.275 0.600 0.161 0.777 0.0619Crown volume vs.DBH −2.441 4.193 −0.683 0.855 0.1356

Ornamental Prunus serrulata DBH vs. age 0.918 −0.196 0.526 0.479 0.1268

Height vs. DBH 0.267 0.300 0.046 0.381 0.0909



Malus spp. DBH vs. age 0.894 −0.359 0.493 0.481 0.1161

Heightvs. DBH −0.206 1.118 −0.271 0.550 0.0858


Crown volume vs. DBH 0.056 −0.262 1.343 0.377 0.3407

Prunus

cerasifera

DBH vs. age −0.126 2.411 −1.113 0.268 0.1140

Heightvs. DBH −0.246 1.155 −0.279 0.383 0.0887


Crown Volume vs.DBH −8.396 15.01 −5.484 0.730 0.2568

Syringa

reticulata

DBH vs. Age 0.351 1.117 −0.448 0.212 0.0976

Height vs. DBH 0.308 0.256 0.101 0.464 0.0523Crown Diameter vs.DBH −0.273 0.476 0.249 0.642 0.0781

Crown Volume vs.DBH −0.258 −1.105 2.260 0.619 0.2588

Cornus spp. DBH vs. Age 1.211 −1.208 0.953 0.277 0.1391

Heightvs. DBH −0.125 0.930 −0.212 0.325 0.1207

Crown Diameter vs.DBH −0.196 0.815 −0.059 0.495 0.1145

Crown Volume vs.DBH −2.753 5.551 −1.679 0.450 0.4209

Discussion

Across all tree species, significant allometric relationships were

found, although with variable R values. Adjusted coefficients of

variation (Table 2) were comparable to those cited in other recent

studies (Peper et al.,2001a,b; Quigley, 2004; Stoffberg et al., 2009;

Semenzato et al., 2011).

Allometric relations for size dimensions (height vs dbh, crown

diameter vs dbh, and crown volume vs dbh) demonstrate stronger

correlations than relationships that were a function of time (dbh vs

Table 3Predicted sizes for 10 genera at 5 and 15 years after planting are shown sorted by greatest crown volume growth in first 15 years after transplanting. Diameter at breast

height, tree height, crown diameter,and crown volumecan be predicted by Y = 10(a+b1 log( xi )+b2 log

x2i

+MSE/2)

.

Species DBH (cm) Height (m) Crown diameter (m) Crown volume(m3)

5 years 15 years 5 years 15 years 5 years 15 years 5 years 15 years

Gleditsia triacanthos 9.7 19.9 7.1 11.1 5.9 9.5 53 498

Acer spp. 10.6 27.9 7.3 12.3 4.6 9.8 44 393

Quercus spp. 11.0 26.6 7.1 13.2 4.7 8.8 35 345

Pyrus calleryana 12.0 24.6 7.5 11.4 4.2 7.9 41 251

Prunus serrulata 12.6 30.1 5.0 7.2 4.4 8.9 23 150

Tilia spp. 11.6 21.9 5.7 9.5 3.8 7.1 21 105

Prunus cerasifera 11.8 16.9 5.2 6.2 4.3 6.0 33 78

Malus spp. 8.7 16.3 4.5 6.2 3.8 5.9 15 76

Cornus spp. 7.9 15.1 4.0 5.5 3.5 5.4 12 46

Syringa reticulata 9.1 12.4 4.7 5.4 2.8 3.8 8 23




17.515.012.510.07.55.0

45

40

35

30

25

20

15

10

5

AGE (yrs)

D B H

( c m )

RMSE 0.0926004

R-Sq(adj) 79.0%

Regression

95% CI

95% PI

DBH vs. Agelog10(DBH) = 1.252 - 1.148 log10(AGE) + 1.083 log10(AGE)**2

353025201510

17.5

15.0

12.5

10.0

7.5

5.0

DBH (cm)

H e i g h t (

m )

RMSE 0.0595101

R-Sq(adj) 76.2%

Regression

95% CI

95% PI

Height vs. DBH

log10(Tree_Height) = 0.6861 - 0.1409 log10(DBH) + 0.2758 log10(DBH)**2

353025201510

14

12

10

8

6

4

2

DBH (cm)

C r o w n D i a m e t e r ( m )

RMSE 0.0543580

R-Sq(adj) 89.8%

Regression

95% CI

95% PI

CrownDiameter vs. DBHlog10(Crown_Diameter) = - 0.5198 + 1.361 log10(DBH) - 0.2320 log10(DBH)**2

353025201510

700

600

500

400

300

200

100

0

DBH (cm)

C r o w n V o l u m e ( m ^ 3 )

RMSE 0.189698

R-Sq(adj) 85.2%

Regression

95%

CI

95% PI

Crown Volume vs.

DBHlog10(PAI_Volume) = - 2.494 + 5.147 log10(DBH) - 1.171 log10(DBH)**2

Fig. 3. Actual measurements (points), predicted responses (solid line), 95%

confidence interval (CI), 95% prediction intervals (PI), adjusted coefficient of deter-

mination, and RMSE areshownfor Acer spp. in New Haven,CT.

age). This suggests that while physical dimensions remain highly

correlated, thepatternof growthfor individuals of thesamespecies

(over time) is not always constant (Quigley, 2004). The nature of

site condition (biophysical – impervioussurface, shade, street type;

social – neighborhood, stewardship, demographics) may signifi-

cantly affect the growth of young trees.

Research has found inhibited growth rates to be correlated

with many urban site factors: constrained growing space (Rhoades

and Stipes, 1999), low soil moisture (Whitlow and Bassuck, 1987),

excessive soil moisture (Berrang et al., 1985), increased evapora-

tive demand (Kjelgren and Clark, 1992; Close et al., 1996), limited

nutrient availability (Ruark et al., 1983;Dyer andMader, 1986), dis-

ease andpathogens (Mallett and Volney, 1999), pests (Rhoades and

Stipes, 1999), competition with understory vegetation (Close et al.,

1996), and competition with neighboring trees (Nowak et al., 1990;

Rhoades and Stipes, 1999). At times, urban environmental condi-

tions such as higher temperature, greater CO2 concentrations, and

increased rates of nutrient deposition have been associated with

enhanced growth (Gregg et al., 2003). These inhibiting or enhanc-

ing environmental factors may be stunting some individuals while

releasing others and causing some of the variation in stem diame-

ter growth that has been observed within this population of urban

trees (Table 2).

When using age to predict dbh, shade trees (0.396 < R2 < 0.794)

demonstrate stronger correlations than ornamental trees

(0.212 < R2 < 0.481). It may be that ornamental trees are more

susceptible to urban conditions, while shade trees demonstrate

greater tolerance of environmental stressors. Accordingly, studies

have found small diameter trees, as well as younger trees, to be

more greatly impacted by urban site attributes (Quigley, 2004;

Nowak et al., 2004). Of the shade trees only T. species have a lower

R2 value than select ornamentals species. It is possible that the

impacts of urban biophysical factors have a greater effect on T.

species than other common shade tree species.

While in most species, crown volume vs. stem size maintained

a strong relationship, Malus species and C. species displayed sig-

nificantly weakened crown volume correlations (R2 =0.377 and

R2 = 0.450 respectively). Given that crown volume is an expres-sion of multiple crown dimensions (height, width, and density)

it may be that the volume value is more sensitive to defects in

crown development. It is likely that these small diameter species

are particularly sensitive to urban conditions, as demonstrated

by the low dbh vs. age correlation. As a result of this stunted

growth and reduced vigor, these trees are more susceptible to

pathogens and other inhibiting environmental factors that neg-

atively effect stem growth and crown development (Semenzato

et al., 2011).

Conclusion

Regionally, this work will improve the management of youngtrees, allowing urban forest managers to more accurately project

the growth of urban landscapes into the near future. Locally, with

specific allometric equations for New Haven, organizations such as

the Urban Resources Initiative will be better equipped to meet the

community forestry goals and objectives of their organization as

well as those of the city.

It should be noted that while the methods used to develop the

allometricrelationships are transferable, the limited study of urban

allometry in the northeast United States makes direct comparisons

of the data difficult. The use of these models for trees growing in

different climate zones or trees outside of the intended age range is

tenuous. Furthermore, because this study was a census of a defined

population of trees, the species composition and sample number

was constrained. With a greater number of sample points and a




greater range of ages, the observed variation in dbh vs. age may

have been reduced.

This study begins to establish species-specific allometric rela-

tions for the northeast region and should be considered a

foundation for further research. Specifically, future efforts should

be directed towards the inclusion of biophysical and social

attributes that impact the growth of trees. This data could then

be used to develop site-specific allometric models. In doing so, it

is theorized that the observed variation between age and size will

be reduced and that there will be greater predictive strength at a

species-specific and site-specific level.

Acknowledgments

This work was initiated and supported by the Urban Resources

Initiative (URI) and the Hixon Center for Urban Ecology at the Yale

School of Forestry and Environmental Studies. Deep gratitude and

appreciation is also given to Elaine Hooper, Chris Ozyck and the

colleagues and classmates who helped to guide the entire process.

Appendix A

Summary of equations for 10 common species predicting DBH,

height, crown diameter and crown volume: estimated parameters

(a, bi), adjusted coefficient of determination (R2) and root mean

squared error (RMSE). Allmodels aresignificant with an alpha level

of 0.05(˛ =0.05).

Species Model a b1 b2 b3 R2 (Adj) RMSE

Acer spp. DBHvs. age

y = a [log( x +1)]b 1.564 0.906 0.736 0.1045

y = a + bx 0.377 0.852 0.755 0.0999

y = a + b1 x + b2 x2 1.252 −1.148 1.083 0.790 0.0926

y = a + b1 x + b2 x2 + b3 x3 1.146 −0.774 0.658 0.156 0.785 0.0935

Heightvs. DBH

y = a [log( x +1)]b 1.247 0.685 0.755 0.0609

y = a + bx 0.291 0.529 0.760 0.0598

y = a + b1 x + b2 x2 0.686 −0.141 0.276 0.762 0.0595

y = a + b1 x + b2 x2 + b3 x3−2.537 8.122 −6.666 1.912 0.768 0.0587

Crown diameter vs. DBH

y = a [log( x +1)]b 0.739 1.041 0.873 0.0538

y = a + bx −0.187 0.798 0.897 0.0545

y = a + b1 x + b2 x2−0.520 1.361 0.232 0.898 0.0544

y = a + b1 x + b2 x2 + b3 x3−0.826 2.145 −0.891 0.182 0.896 0.0549

Crown volumevs. DBH

y = a [log( x +1)]b 0.317 3.011 0.859 0.1876

y = a + bx −0.082 2.293 0.848 0.1919

y = a + b1 x + b2 x2−2.494 5.147 −1.171 0.852 0.1897

y = a + b1 x + b2 x2 + b3 x3−11.15 27.31 −19.78 5.121 0.852 0.1897

Cornus spp. DBH vs. Age

y = a [log( x +1)]b 1.546 0.617 0.263 0.1414

y = a + bx 0.396 0.576 0.263 0.1404

y = a + b1 x + b2 x2 1.211 −1.208 0.953 0.277 0.1391 y = a + b1 x + b2 x2 + b3 x3

−3.019 13.35 −15.35 5.952 0.288 0.1381

Heightvs. DBH

y = a [log( x +1)]b 1.088 0.579 0.343 0.1120

y = a + bx 0.064 0.523 0.330 0.1203

y = a + b1 x + b2 x2−0.125 0.930 −0.212 0.325 0.1207

y = a + b1 x + b2 x2 + b3 x3 0.277 −0.368 1.136 −0.451 0.317 0.1215


y = a [log( x +1)]b 0.089 0.772 0.506 0.1140

y = a + bx −0.144 0.702 0.502 0.1138

y = a + b1 x + b2 x2−0.196 0.815 −0.059 0.495 0.1145

y = a + b1 x + b2 x2 + b3 x3 1.121 −3.435 4.355 −1.478 0.496 0.1144

Crown volumevs. DBH

y = a [log( x +1)]b 0.314 2.579 0.462 0.4196

y = a + bx −1.224 2.299 0.441 0.4242

y = a + b1 x + b2 x2−2.753 5.551 −1.679 0.450 0.4209

y = a + b1 x + b2 x2 + b3 x3−1.778 2.400 1.600 −1.095 0.441 0.4244

Gleditsia triacanthos DBHvs. Age

y = a [log( x +1)]b 1.469 0.888 0.799 0.1013

y = a + bx 0.289 0.863 0.786 0.1027

y = a + b1 x + b2 x2−0.513 2.923 −1.211 0.794 0.1001

y = a + b1 x + b2 x2 + b3 x3−1.925 7.940 −6.910 2.088 0.787 0.1025

Height vs.DBH

y = a [log( x +1)]b 1.243 0.708 0.856 0.0583

y = a + bx 0.197 0.631 0.854 0.0578

y = a + b1 x + b2 x2 0.177 0.674 −0.022 0.849 0.0588

y = a + b1 x + b2 x2 + b3 x3 0.064 1.046 −0.418 0.136 0.843 0.0598


y = a [log( x +1)]b 1.105 0.757 0.886 0.0544

y = a + bx 0.078 0.673 0.883 0.0543

y = a + b1 x + b2 x2 0.007 0.825 −0.077 0.880 0.0551

y = a + b1 x + b2 x2 + b3 x3−1.39 5.42 −4.963 1.681 0.885 0.0539

Crown volumevs. DBH





y = a [log( x +1)]b 0.263 3.447 0.865 0.2670

y = a + bx −1.440 3.074 0.863 0.2624

y = a + b1 x + b2 x2−1.285 2.743 0.167 0.856 0.2691

y = a + b1 x + b2 x2 + b3 x3−4.525 13.47 −11.30 3.961 0.851 0.2739

Malus spp. DBHvs. Age

y = a [log( x +1)]b 1.786 0.538 0.486 0.1169

y = a + bx 0.530 0.515 0.483 0.1159

y = a + b1 x + b2 x2 0.894 −0.359 0.493 0.481 0.1161

y = a + b1 x + b2 x2 + b3 x3−0.324 4.108 −4.798 2.023 0.472 0.1171

Height vs. DBH

y = a [log( x +1)]b 1.063 0.661 0.570 0.0848

y = a + bx 0.039 0.594 0.551 0.0856

y = a + b1 x + b2 x2−0.206 1.118 −0.271 0.550 0.0858

y = a + b1 x + b2 x2 + b3 x3−0.389 1.780 −1.026 0.274 0.540 0.0868


y = a [log( x +1)]b 0.767 0.964 0.746 0.0831

y = a + bx −0.288 0.858 0.714 0.0872

y = a + b1 x + b2 x2−0.924 2.212 −0.701 0.745 0.0823

y = a + b1 x + b2 x2 + b3 x3−2.167 6.693 −5.810 1.858 0.758 0.0802

Crown volumevs. DBH

y = a [log( x +1)]b 0.327 2.609 0.405 0.3375

y = a + bx −1.188 2.343 0.392 0.3365

y = a + b1 x + b2 x2 0.056 −0.262 1.343 0.377 0.3407

y = a + b1 x + b2 x2 + b3 x3−11.22 35.11 −35.21 12.45 0.361 0.3449

Prunus cerasifera DBHvs. Age yva [log( x +1)]b 2.086 0.488 0.270 0.1153

yva + bx 0.703 0.457 0.246 0.1161

y = a + b1 x + b2 x2−0.126 2.411 −1.113 0.2680 0.1140

y = a + b1 x + b2 x2 + b3 x3−2.138 9.457 −9.134 2.981 0.263 0.1147

Height vs. DBH

y = a [log( x +1)]b 1.055 0.658 0.406 0.0879

y = a + bx 0.091 0.536 0.391 0.0881

y = a + b1 x + b2 x2−0.246 1.155 −0.279 0.383 0.0887

y = a + b1 x + b2 x2 + b3 x3 1.921 −4.870 5.210 −1.649 0.373 0.0894


y = a [log( x +1)]b 0.731 0.994 0.698 0.0722

y = a + bx −0.251 0.806 0.679 0.0737

y = a + b1 x + b2 x2−1.340 2.803 −0.901 0.701 0.0711

y = a + b1 x + b2 x2 + b3 x3 1.654 −5.515 6.690 −2.278 0.699 0.0714

Crown volumevs. DBH

y = a [log( x +1)]b 0.122 3.638 0.690 0.2786

y = a + bx −1.862 2.942 0.657 0.2891 y = a + b1 x + b2 x2

−8.396 15.01 −5.484 0.730 0.2568

y = a + b1 x + b2 x2 + b3 x3 14.03 −47.34 51.42 −17.06 0.743 0.2502

Prunus serrulata DBHvs. Age

y = a [log( x +1)]b 1.845 0.736 0.472 0.1280

y = a + bx 0.541 0.713 0.476 0.1272

y = a + b1 x + b2 x2 0.918 −0.196 0.526 0.479 0.1268

y = a + b1 x + b2 x2 + b3 x3 1.532 −2.417 3.134 −0.998 0.476 0.1271

Height vs. DBH

y = a [log( x +1)]b 1.168 0.524 0.385 0.0909

y = a + bx 0.204 0.410 0.384 0.0907

y = a + b1 x + b2 x2 0.267 0.300 0.046 0.381 0.0909

y = a + b1 x + b2 x2 + b3 x3−0.153 1.400 −0.900 0.2667 0.378 0.0912


yva [log( x +1)]b 0.612 1.135 0.767 0.0859

y = a + bx −0.381 0.884 0.763 0.0864

y = a + b1 x + b2 x2−0.792 1.591 −0.298 0.765 0.0861

y = a + b1 x + b2 x2 + b3 x3 0.338 −1.371 2.249 −0.718 0.764 0.0862

Crown volumevs. DBH

yva [log( x +1)]b 0.219 2.865 0.662 0.2808

y = a + bx −1.237 2.228 0.656 0.2814

y = a + b1 x + b2 x2−1.731 3.076 −0.357 0.655 0.2821

y = a + b1 x + b2 x2 + b3 x3−4.205 9.570 −5.950 1.578 0.653 0.2828

Pyrus calleryana DBHvs. Age

y = a [log( x +1)]b 1.788 0.758 0.614 0.1085

y = a + bx 0.533 0.699 0.556 0.1182

y = a + b1 x + b2 x2 0.084 1.754 −0.589 0.562 0.1174

y = a + b1 x + b2 x2 + b3 x3 3.421 −10.09 12.99 −5.044 0.576 0.1155

Height vs. DBH

y = a [log( x +1)]b 1.136 0.758 0.683 0.0708

y = a + bx 0.177 0.609 0.696 0.0713

y = a + b1 x + b2 x2−0.031 0.972 −0.155 0.694 0.0715

y = a + b1 x + b2 x2 + b3 x3−0.723 2.738 −1.708 0.437 0.691 0.0718





Crown diameter vs.DBH

y = a [log( x +1)]b 0.609 1.158 0.874 0.0603

y = a + bx −0.391 0.908 0.874 0.0600

y = a + b1 x + b2 x2−0.519 1.130 −0.094 0.872 0.0603

y = a + b1 x + b2 x2 + b3 x3−0.089 0.016 0.854 −0.265 0.871 0.0606

Crown volume vs.DBH

y = a [log( x +1)]b 0.190 3.376 0.829 0.1823

y = a + bx −1.373 2.662 0.859 0.1839

y = a + b1 x + b2 x2−2.601 4.819 −0.927 0.860 0.1833

y = a + b1 x + b2 x2 + b3 x3 1.837 −6.980 9.390 −2.964 0.859 0.1838

Quercus spp. DBH vs. Age

y = a [log( x +1)]b 1.626 0.867 0.734 0.1015

y = a + bx 0.411 0.827 0.728 0.1016

y = a + b1 x + b2 x2 0.269 1.165 −0.192 0.725 0.1023

y = a + b1 x + b2 x2 + b3 x3 1.231 −2.263 3.731 −1.450 0.721 0.1029

Heightvs. DBH

y = a [log( x +1)]b 0.995 0.897 0.735 0.0865

y = a + bx 0.039 0.733 0.730 0.0866

y = a + b1 x + b2 x2−0.149 1.082 −0.156 0.727 0.0872

y = a + b1 x + b2 x2 + b3 x3 0.480 −0.685 1.456 −0.480 0.722 0.0879


y = a [log( x +1)]b 0.723 1.053 0.915 0.0517

y = a + bx −2.660 0.855 0.899 0.0557

y = a + b1 x + b2 x2−0.969 2.157 −0.584 0.917 0.0507

y = a + b1 x + b2 x2 + b3 x3−2.145 5.460 −3.598 0.897 0.917 0.0505

Crown volume vs.DBH y = a [log( x +1)]b 0.219 3.269 0.858 0.2121

y = a + bx −1.388 2.704 0.854 0.2129

y = a + b1 x + b2 x2−1.946 3.756 −0.480 0.852 0.2143

y = a + b1 x + b2 x2 + b3 x3−9.734 25.95 −21.06 6.229 0.858 0.2103

Syringa reticulata DBH vs. Age

y = a [log( x +1)]b 2.045 0.341 0.239 0.0970

y = a + bx 0.692 0.319 0.218 0.0973

y = a + b1 x + b2 x2 0.351 1.117 −0.448 0.212 0.0976

y = a + b1 x + b2 x2 + b3 x3 3.272 −9.414 11.85 −4.669 0.217 0.0974

Heightvs. DBH

y = a [log( x +1)]b 1.255 0.504 0.482 0.0519

y = a + bx 0.213 0.453 0.475 0.0517

y = a + b1 x + b2 x2 0.308 0.256 0.101 0.464 0.0523

y = a + b1 x + b2 x2 + b3 x3 0.141 0.796 −0.471 0.199 0.452 0.0528


y = a [log( x +1)]b

0.623 1.067 0.649 0.0782 y = a + bx −0.505 0.960 0.648 0.0774

y = a + b1 x + b2 x2−0.273 0.476 0.249 0.642 0.0781

y = a + b1 x + b2 x2 + b3 x3 3.227 −11.03 12.45 −4.236 0.650 0.0772

Crown volume vs.DBH

y = a [log( x +1)]b 0.124 3.448 0.618 0.2626

y = a + bx −2.25 3.168 0.620 0.2586

y = a + b1 x + b2 x2−0.258 −1.105 2.260 0.619 0.2588

y = a + b1 x + b2 x2 + b3 x3 17.12 −58.79 64.96 −22.36 0.641 0.2514

Tilia spp. DBH vs. Age

y = a [log( x +1)]b 2.003 0.552 0.417 0.0932

y = a + bx 0.642 0.536 0.408 0.0928

y = a + b1 x + b2 x2 0.837 0.069 0.272 0.396 0.0937

y = a + b1 x + b2 x2 + b3 x3−0.635 5.470 −6.190 2.518 0.384 0.0946

Heightvs. DBH

y = a [log( x +1)]b 0.844 0.965 0.675 0.0655

y = a + bx −0.102 0.776 0.671 0.0652

y = a + b1 x + b2 x2 0.183 0.268 0.224 0.663 0.0659

y = a + b1 x + b2 x2 + b3 x3 1.817 −4.120 4.130 −1.147 0.655 0.0667


y = a [log( x +1)]b 0.569 1.199 0.785 0.0615

y = a + bx −0.479 0.964 0.782 0.0612

y = a + b1 x + b2 x2−0.275 0.600 0.161 0.777 0.0619

y = a + b1 x + b2 x2 + b3 x3−11.08 29.65 −25.66 7.586 0.785 0.0607

Crown volume vs.DBH

y = a [log( x +1)]b 0.163 3.300 0.864 0.1333

y = a + bx −1.556 2.629 0.859 0.1337

y = a + b1 x + b2 x2−2.441 4.193 −0.683 0.855 0.1356

y = a + b1 x + b2 x2 + b3 x3−15.14 37.81 −30.11 8.530 0.851 0.1373

relationships between bole and crown size for young urban trees in northeastern usa(4).pdf

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