Forest Service Northern Research Station Research Paper NRS-32

Heartwood Taper in Northern 

Red Oak (Quercus rubra L.)

John P. Brown

United States Department of Agriculture

March 2019
Published by

U.S. FOREST SERVICE

11 CAMPUS BLVD SUITE 200

NEWTOWN SQUARE PA 19073

March 2019

Manuscript received for publication 26 June 2018

Abstract

To better understand how the practice of long–term tree retention affects value, northern red 

oak (Quercus rubra L.) trees from the Menominee Indian Reservation in Wisconsin were harvested 

and examined for patterns of heartwood development in relation to several tree characteristics. 

A total of 69 mature northern red oak trees from three dbh size classes, small (34-47 cm, 20 

trees), medium (48-60 cm, 20 trees), and large (≥ 61 cm, 29 trees), were logged and optimally 

bucked. Cross-sectional disks were then removed from the tops of the stumps and each log 

and were analyzed for patterns of change in heartwood radius. Four factors were found to 

have a statistically significant effect on heartwood radius: age of the tree, size class, height, and 

inside bark radius. The inside bark radius was the strongest predictor of heartwood radius. A 1 

cm increase in inside bark radius led to approximately a 0.95 cm increase in heartwood radius. 

Increasing height had a small negative effect, with heartwood radius decreasing approximately 

0.05 cm for each meter above ground. Age of the tree had a small positive effect of 0.0016 cm per 

year and was only significant in one expert model considered. These results provide consumers of 

oak logs and forest managers insight to the interior heartwood pattern and can lead to improved 

value assessments for northern red oak logs. 

The Author

JOHN P. BROWN is a research forester with the USDA Forest Service, Northern Research Station, 

Princeton, WV, jpbrown@fs.fed.us.

Cover Photo

Photo showing a cross-section of a red oak log. Photo by Janice Wiedenbeck, USDA Forest Service.

Quality Assurance

This publication conforms to the Northern Research Station’s Quality Assurance Implementation 

Plan which requires technical and policy review for all scientific publications produced or funded 

by the Station. The process included a blind technical review by at least two reviewers, who were 

selected by the Assistant Director for Research and unknown to the author. This review policy 

promotes the Forest Service guiding principles of using the best scientific knowledge, striving 

for quality and excellence, maintaining high ethical and professional standards, and being 

responsible and accountable for what we do.
1

INTRODUCTION

Northern red oak (Quercus rubra L.) is an important commercial species in the hardwood 

timber industry. Lower quality lumber is used for pallets and railroad ties, but with increasing 

quality, it is suitable for flooring, furniture and cabinets, molding, and veneer. Many factors 

are influential in determining the value of hardwood logs (Rast and others 1973), with defects 

being an important consideration in the assessment of log grade (Carpenter and others 1989). 

Size also plays a role in determining log grades (Hanks and others 1980).

Sapwood is found immediately inside the bark (phloem) and external to the heartwood 

portion of the xylem (wood) in a tree’s cross-section. Sapwood is the metabolically active 

portion of the wood in a living tree. In many, but not all species, the sapwood can be visually 

distinguished from the heartwood by a color change. In those species that show a color 

difference between heartwood and sapwood, the transition zone or boundary region may be 

less desirable for certain products than either 100 percent heartwood or sapwood portions. 

Sapwood is removed in the manufacture of veneer for several hardwood species (Wiedenbeck 

and others 2004) but typically is not for red oak.

In red oak, as in most species, the extractive chemicals contained in the heartwood are more 

resistant to decay organisms than those in the sapwood (Hawley et al. 1924). Thus, for certain 

end uses, the sapwood of red oak may be less desirable than the heartwood. An important 

difference between the heartwood and sapwood of red oak that is noteworthy is the risk of 

heartwood containing “wetwood,” a condition caused by anaerobic bacteria that leads to 

significant lumber drying defects (Ward and Pong 1980).

While the heartwood formation process is not completely understood, it is the death of 

parenchyma cells and the deposition of extractives that lead to changes (Bamber and 

Fukazawa 1985). Nelson (1976) examined sapwood width in black walnut and black cherry, 

finding it was weakly correlated with tree age in walnut and uncorrelated in cherry. In 

addition, it was found in that study that sapwood thickness was narrower for both walnut and 

cherry at the top of the first butt log versus the ground level. Yang and Hazenberg (1991a) 

found that a positive linear relationship exists between tree age and heartwood width (radius) 

in quaking aspen (Populus tremuloides Michx.). The same relationship was found in jack pine 

(Pinus banksiana Lamb.) (Yang and Hazenberg 1991b). A curvilinear relationship between 

sapwood thickness and height was also shown for jack pine and tamarack (Larix laricina 

(Du Roi) K. Koch) (Yang and others 1985). Taylor and others (2002) note that in general, 

heartwood tapers from the ground up and increases with tree age with respect to certain 

species. In red oak, sapwood thickness is often observed as a thin ring surrounding the 

heartwood in mature trees. However, the proportion of heartwood has not been previously 

investigated. Quantifying the proportion of heartwood is important to determining potential 

yields of higher valued wood. The goal of this study is to determine if allometric relationships 

exist between heartwood, tree diameter, and height and also to determine whether tree age 

influences the proportion of heartwood in northern red oak trees, which may prove useful to 

loggers, log buyers, and inventory foresters.
2

METHODS

Site Description

The study area is located on the Menominee Indian Reservation, Menominee County, 

Wisconsin. The reservation has a mean annual temperature of 6.8 °C, with January the 

coldest month (-9.7 °C) and July the warmest (21.2 °C). Mean annual precipitation is 796 

mm, about 70 percent of which is evenly distributed throughout the spring and summer, with 

precipitation diminishing into the fall and through the winter. July is the wettest month (99 

mm) and February the driest (23 mm).

Experimental Design

The study was an opportunity to work concurrently with another study that investigated how 

the economic value of individual northern red oaks vary by tree characteristics (Dwyer and 

Dey 2007). A total of 69 trees were selected from three nominal dbh classes (DBHClass): small 

(34-47 cm, 20 trees), medium (48-60 cm, 20 trees) and large (≥ 61 cm, 29 trees), and dbh was 

recorded for each tree (DBH). All trees selected were in the dominant and codominant crown 

classes and were in vigor class 1 as defined by Menominee foresters (Dwyer and Dey 2007). 

Sample trees were selected from four sites among three habitat types: Acer-Fagus/Viburnum, 

Acer-Quercus/Viburnum, and Acer-Tsuga/Maianthemum (Kotar and Burger 1989). This 

forest habitat classification system is an assessment of forest site productivity that is based 

on associations of understory plants and is an indicator of the best forest cover types suited 

to that habitat. Northern red oak is a component species of the best forest cover types on the 

three habitat types selected. On the Menominee tribal forest, northern red oak is managed 

using both even-aged and uneven aged stands, with silvicultural systems selected based on the 

forest habitat classification system.

The trees were felled in February 2001 by Menominee logging crews with chainsaws leaving 

low stumps (< 30 cm). Optimally designed bucking guidelines were used by Menominee 

logging crews to buck the logs to length (Dwyer and Dey 2007). This resulted in a total of 

356 logs with a mean log length of 3.4 m. The shortest log was 2.5 m and the longest 5.1 m. 

Cross-sectional disks were cut from the stumps and from the top of every log from each tree. 

Log lengths and lengths of buckouts were recorded to the tenth of a foot and used to compute 

the height above stump in meters (HT) for the disks. Disks were numbered sequentially from 

the stump up to the highest disk. A total of 425 disks were cut and transported to the Forestry 

Sciences Laboratory at Princeton, West Virginia.

The amount and proportion of heartwood and sapwood were evaluated using the following 

procedures. Each disk was assigned a random angle ranging from 0-359 degrees in increments 

of 1 degree. A 20-cm-diameter circular protractor was placed with its center point at the pith 

of each disk. The random angle was then referenced on the protractor and a mark was made 

there and at angles 90, 180, and 270 degrees relative to it. Perpendicular lines were drawn 

across the disks through the two diameters defined by these marks. Linear measurements of 

each diameter in centimeters were taken at the bark-cambium boundary, sapwood-heartwood 

boundary, pith, heartwood-sapwood boundary, and cambium-bark boundary. The distance 

from the bark-cambium boundary to the pith is the radius inside bark (RIB) and the distance 

from the heartwood-sapwood boundary to the pith is the heartwood radius (HR). Ring counts 

were also recorded for each diameter at the same points.

Fourteen butt disks did not receive ring counts due to missing pith caused by decay (10 trees), 

caused by damage, or having been lost in the field or in transport. The trees that these disks 
3

came from, however, had upper intact disks. Tree age was estimated for these trees using the 

northern red oak site index (SI) table for Michigan (Carmean and others 1989) according to 

the following method. Tree age (AgeTree) was obtained from intact butt disks. Tree ages were 

pooled according to the four sites the trees were collected from. For each upper disk of these 

trees, the disk ring count was subtracted from AgeTree. This value was the age of the tree 

for height up to that disk and together with the disk height formed a height age pair. Height 

age pairs from disks where trees were older than 20 years were pooled by site, with 338 disks 

having actual ages. The suitable parameter values of the SI equation (Eq. 1) for northern red 

oak (Carmean and others 1989: 63) were used to calculated SI for each available disk.

SI HT e Age HT0 1692 1 1 2648 0 0110 3 4334 0 3557. . . . .

(1)

Values for multiple disks were averaged by tree—there were one to six disks per tree—and 

then the SI for all trees on each site were averaged to determine SI for that site. Next, the 

height equation and the parameters for height (HT) from Carmean and others (1989) were 

used to determine estimated tree age (AgeEst). 

HT SI e Age SI6 1785 1 0 6619 0 0241 25 0185 0 7400. . . . .

(2)

Here, Age represents the age of the tree when it grew to the height of the removed disk, which is 

the difference of AgeEst and disk-ring count. Eq. 2 was applied to each disk from trees that were 

missing tree age. The reasoning here is that with a known SI for each site, the height age pairs 

of each disk should fall on the SI curve for that site. This nonlinear equation (Eq. 2) was solved 

for AgeEst (the unknown value) using the root function of Proc NLIN in SAS® software Version 

9.4 (SAS Institute Inc. 2012) with equations grouped by disks from the same tree. This allowed 

predicted ages to be imputed for trees missing age data. In two cases, inconsistent ages were 

obtained where AgeEst was smaller than the ring count of the first disk up from the stump. Here, 

the average height growth for the first disks of all aged trees within the same habitat type were 

used to estimate the number of years it took the non-aged trees to reach the height of their first 

disk. This number of years was added to the ring count of the first disk for that tree to determine 

AgeEst. Because all trees were in the dominant and codominant crown classes, and such trees are 

normally selected for SI, there is no reason to suspect bias in this method.

Data Analysis

The four radial measurements for all disks of each tree constitute repeated measures for that 

tree. Heartwood radius was therefore modeled as a linear mixed model, with each tree as the 

subject and radius nested within disks as the repeated effect. AgeTree, DBH, DBHClass, HT, 

and RIB were considered as fixed effect factors and SITE was considered as a random effect.

y = Xβ + Zγ + ε (3)

where

y is a vector where each element is the i

th HR from the jth disk from the kth tree, with i, j, and k 

indices.

X is a matrix consisting of values for AgeTree, DBH, DBHClass, HT, and RIB.

β is the vector of the unknown fixed effects parameters.

Z is the known design matrix based on the selected covariance structure.

γ is the vector of the unknown random effects parameters.

ε is the unobserved vector of random errors.
4

Initial analysis was conducted to determine a suitable covariance structure for the repeated 

effects. Consideration was given to possible covariance types that aligned with the relationship 

between the physical measurements. Disks were taken at irregularly spaced intervals of 

HT, while heart radius was measured four times on each disk (Fig. 1). The covariance types 

selected to test were compound symmetry (CS), compound symmetry grouped by disk for 

each tree, heterogeneous compound symmetry (CSH), Toeplitz (TOEP), banded Toeplitz 

(TOEP(q)), Toeplitz grouped by disk for each tree, unstructured (UN), and variance 

components (VC). The compound symmetry covariance structure in its general form has 

a constant covariance on the diagonal and a common correlation among any two differing 

observations. The Toeplitz covariance structure maintains a constant covariance on the 

diagonal of the covariance matrix. The off-diagonal correlations between measurements 

within a subject (here the tree) can vary for differing pairs of observations. The CSH structure 

lessens the overall correlation between observations by a power function of the correlation. 

Banding on the Toeplitz structure zeroes out the covariance between observations if they 

exceed the band selected. Here multiples of four for the band size were selected as there are 

four radii measured on each disk. Grouping covariance structures by disk limits calculation of 

the covariance to observations for that disk rather than by each tree.

Figure 1.—Example of the first two logs that demonstrates the arrangement of the repeated measures.
5

The model with the least Aikake information criterion (corrected) (AICc) value for the full 

model of HR=f(AgeTree, DBH, DBHclass, HT, RIB) was selected for further consideration 

(Littell and others 1996). Models were analyzed with these covariance structures using Proc 

Mixed in SAS® software Version 9.4 (SAS Institute Inc. 2012).

Preliminary modeling indicated that assumptions of normality and homoscedasticity were 

violated. Normal probability plots showed nonconformance to a normal distribution and 

residuals plotted against the predicted values and other independent variables exhibited 

heteroscedasticity (megaphone shaped residual patterns). This was remedied through the use 

of weighted least squares with the weight function determined to be a function of RIB.

Model selection proceeded using a set of three candidate models. A base model was formed 

that included RIB, HT, and the interaction term HT*RIB. Each of the three following terms 

was added as an additional term to the base to form the three candidates: AgeTree, DBH, and 

DBHclass. The three terms were considered in separate models to avoid multicollinearity as 

AgeTree and DBH were correlated (ρ = 0.76) and DBHclass is an ordinal variable categorized 

from DBH.

Model 1- HR = β0,1 + β1,1 AgeTree + β2,1 HT + β3,1 RIB + β4,1 HT*RIB (4)

Model 2- HR = β0,2 + β1,2 DBH + β2,2 HT + β3,2 RIB + β4,2 HT*RIB (5)

Model 3- HR = β0,3 + β1,3 DBHclass + β2,3 HT + β3,3 RIB + β4,3 HT*RIB (6)

Model selection proceeded using a backward selection process with statistical significance 

level α set to 0.05.

RESULTS

The Toeplitz covariance structure, grouped by disk, had the lowest AICc value and was used in 

subsequent model development (Table 1). The AICc value for compound symmetry, grouped 

by disk, was a close second at 1,898.

The interaction term HT*RIB was not significant for Model 1, p = 0.2691. For Model 2, both 

the interaction term HT*RIB and DBHclass were not significant, p = 0.1521 and p = 0.4413 

respectively. For Model 3, the interaction term HT*RIB was again not significant, p = 0.6965, 

as was DBHclass, p = 0.1948. This produced just two models with significant predictors 

(Table 2), as the final form of Models 2 and 3 (Model 2/3) were identical. Considering Model 

1, RIB has a positive effect on HR. A 1 cm increase in RIB increases HR by 0.9509 to 0.9621 

cm (95 percent confidence limits). AgeTree also has a positive effect on HT; an increase of 1 

year shows an increase of just 0.0016 to 0.0044 cm in HR or 0.016 to 0.044 cm every 10 years 

(95 percent confidence limits). HT has a negative effect on HR where a 1 m increase in HT 

decreases HR by 0.0464 to 0.0519 cm. The coefficients for Model 2/3 are nearly the same as for 

Model 1. A 1 cm increase in RIB increases HR by 0.9581 to 0.9628 cm (95 percent confidence 

limits) and a 1 m increase in HT decreases HR by 0.0435 to 0.0488 cm.
6

DISCUSSION

Both final models include RIB and HT, with coefficients that are effectively the same. 

Consideration of the size of each significant effect demonstrates that the most influential 

factor for determining heartwood radius (HR) is radius inside bark (RIB). The tallest height 

measured for any disc was just over 25 m. For even this highest disk, 25 m in height decreases 

the HR by approximately 1 cm. The oldest disk was 182 years old and was the second disk 

of a tree missing its stump disk, with AgeEst = 193 years. Assuming 200 years for ease of 

calculation, the contribution to HR from that age is only 0.32 cm. With RIB ranging up to 78.3 

cm and RIB increasing 0.95-0.97 cm per cm of RIB, it is clear that RIB has the most influence 

on HR.

Cochard and Tyree (1990) reported that conductive sapwood in northern red oak is 

comprised predominantly by the two outermost growth layers. Taylor and others (2002) notes 

that heartwood volumes are cumulative. Once heartwood formation starts, sapwood cells 

die and become part of the heartwood, while new sapwood forms the outer growth rings. 

Consider also that each increase of 1 centimeter in radius inside bark leads to an increase of at 

least 0.95 cm in heartwood radius. In effect, heartwood radius nearly parallels the tree surface 

Table 1.—Values for the Aikake information criterion corrected 

(AICc) of the full model [HR=f(AgeTree, DBH, DBHclass, HT, RIB)] 

with differing covariance structures for the covariance of the 

repeated measures

Covariance structure AICc

Compound symmetry 2,516.8

Compound symmetry (grouped by disk) 1,898.0

Heterogenous Compound symmetry 2,433.5

Toeplitz *

Banded Toeplitz (4 bands) 2,490.2

Banded Toeplitz (8 bands) 2,425.4

Toeplitz (grouped by disk) 1,896.7

Unstructured * 

Variance components 2,794.6

*Final Hessian not positive definite

Table 2.—Solutions for the parameters of the final backward selected linear mixed models, 

Models 1-3, with 95 percent confidence intervals

Effect

Lower 95 

percent C.L. Estimate

Upper 95 

percent C.L. Std. error p

Intercept -0.3623 -0.2275 -0.0927 0.0685 0.001

Model 1 AgeTree 0.0016 0.0030 0.0044 0.0007 < 0.0001

RIB 0.9509 0.9565 0.9621 0.0028 < 0.0001

HT -0.0519 -0.0464 -0.0408 0.0028 < 0.0001

Intercept -0.3623 -0.0548 -0.0927 0.0564 0.3326

Model 2/3 RIB 0.9581 0.9628 0.9675 0.0024 < 0.0001

HT -0.0488 -0.0435 -0.0381 0.0027 < 0.0001
7

due to the strong influence radius inside bark has on heartwood radius, as the negative effect 

of HT is small. The standard error for the parameter on radius inside bark is small compared 

to the parameter. This indicates little variability in the estimate for radius inside bark, which 

translates to uniformity of shape for heartwood in cross-section. Wiedenbeck and others 

(2004) found that veneer log northern red oak commanded a premium when the heartwood 

was centered, so establishing that radius inside bark and its standard error is a good predictor 

of heartwood radius provides a useful tool for assessing log value, as the buyer will know that 

the heartwood is effectively running parallel to the RIB with little variation.

It is often the case that dbh and age are correlated measures for many tree species. For these 

sample trees, the correlation between tree age and dbh was 0.72. In addition, the full model 

also contained the class variable DBHClass, which is a categorization of the continuous 

variable DBH. Results of the three candidate models showed that there was a slight age effect 

as opposed to a size effect on heartwood. Therefore, there was a positive effect on heartwood 

formation resulting from trees being left to grow to older ages.

The Toeplitz grouped by disk covariance structure was identified as best. Because the 

disks were sampled from log ends, the distance between disks was much greater than the 

distance between radii on a disk. Both the best covariance structure and the second-best 

covariance structures were grouped by disk, the Toeplitz and compound symmetry structures 

respectively. This is evidence that there is close correlation between observations on a disk but 

that the observations between disks are less correlated. The better performance of the Toeplitz 

structure over compound symmetry may result from eccentricity of the bole from a circular 

form circumferentially.

CONCLUSIONS

The close alignment of heartwood radius to total wood radius inside bark provides buyers 

of northern red oak logs assurance that what is showing on the face of the log in respect to 

heartwood radius will be consistent relative to log radius throughout the length of the log. 

This provides certainty for estimating yields of heartwood where it is important to product 

outputs. Some of the uncertainty for loggers bidding on standing trees may be alleviated as 

well. These results also demonstrate that there is a positive effect for heartwood radius due to 

age and increased inside bark radius for northern red oak trees. This provides forest managers 

support for retaining trees for longer periods of time, such as in deferment cutting and 

variable retention systems. Further study is necessary, however, to determine whether these 

relationships hold for lower grade trees and other regions.

ACKNOWLEDGMENTS

Thanks go to Menominee Tribal Enterprises forestry staff for permitting tree sampling and 

conducting logging of tree samples and to John Dwyer and Daniel Dey for coordinating 

study plans. Special thanks to Michael Wiemann for initial study implementation and to Neal 

Bennett and Deborah Butler for help with data measurements.
8

LITERATURE CITED

Bamber, R.K.; Fukazawa, K. 1985. Sapwood and heartwood: a review. Forestry Abstracts. 

46(9): 567-580.

Carmean, W.H.; Hahn, J.T.; Jacobs, R.D. 1989. Site index curves for forest tree species in 

the eastern United States. Gen. Tech. Rep. NC-128. St. Paul, MN: U.S. Department of 

Agriculture, Forest Service, North Central Forest Experiment Station. 142 p.

Carpenter, R.D.; Sonderman, D.L.; Rast, E.D.; Jones, M.J. 1989. Defects in hardwood timber.

Agricultural Handbook 678. Washington, DE: U.S. Department of Agriculture, Forest 

Service, Northeastern Forest Experiment Station. 88 p.

Cochard, H.; Tyree, M.T. 1990. Xylem dysfunction in Quercus: vessel sizes, tyloses, 

cavitation, and seasonal changes in embolism. Tree Physiology. 6(4):393-407. https://doi.

org/10.1093/treephys/6.4.393.

Dwyer, J.P.; Dey, D.C. 2007. Product recovery from tree grade 1 northern red oak on 

Menominee tribal lands. In: Buckly, D.S.; Clatterbuck, W.K., eds. Proceedings, 15th 

central hardwood forest. e-Gen. Tech. Rep. SRS-101. Asheville, NC: U.S. Department of 

Agriculture, Forest Service, Southern Research Station: 478-484.

Hanks, L.F.; Gammon, G.L.; Brisbin, R.L.; Rast, E.D. 1980. Hardwood log grades and 

lumber grade yields for factory lumber logs. Res. Pap. NE-468. Upper Darby, PA: U.S. 

Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. 92 p.

Hawley, L.F.; Fleck, L.C.; Richards, C.A. 1924. The relation between durability and chemical 

composition in wood. Ind. Eng. Chem. 16(7): 699-700.

Kotar, J.; Burger, T.L. 1989. Forest habitat type classification for the Menominee Indian 

Reservation. Madison, WI: University of Wisconsin, Department of Forestry. 90.

Littell, R.C.; Milliken, G.A.; Stroup, W.W.; Wolfinger, R.D. 1996. SAS System for mixed 

models. Cary, NC: SAS Institute Inc. 633.

Nelson, N.D. 1976. Gross influences of heartwood formation in black walnut and black 

cherry. FPL-268. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest 

Products Laboratory. 11 p.

Rast, E.D.; Sonderman, D.L.; Gammon, G.L. 1973. A guide to hardwood log grading.

Gen. Tech. Rep. NE-1. Broomall, PA: U.S. Department of Agriculture, Forest Service, 

Northeastern Forest Experiment Station. 31 p.

SAS Institute Inc. 2012. SAS Version 9.4. Cary, NC.

Taylor, A.M.; Gartner, B.L.; Morrell, J.J. 2002. Heartwood formation and natural durability-

-a review. Wood and Fiber Science. 34(4):587-611.

Ward, J.C.; Pong, W.Y. 1980. Wetwood in trees: a timber resource problem. Gen. Tech. Rep. 

PNW-112. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest 

Experiment Station. 56 p.
9

Wiedenbeck, J.K.; Wiemann, M.; Alderman, D.; et al. 2004. Defining hardwood veneer log 

quality attributes. Gen. Tech. Rep. NE-313. Newtown Square, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Research Station. 9 p.

Yang, K.C.; Hazenberg, G. 1991a. Relationship between tree age and sapwood/hardwood 

width in Populus tremuloides Michx. Wood and Fiber Science. 23(2): 247-252.

Yang, K.C.; Hazenberg, G. 1991b. Sapwood and heartwood width relationship to tree age 

in Pinus banksiana. Canadian Journal of Forest Research. 21(4): 521-525. https://doi.

org/10.1139/x91-071.

Yang, K.C.; Hazenberg, G.; Bradfield, G.E.; Maze, J.R. 1985. Vertical variation of sapwood 

thickness in Pinus banksiana Lamb. and Larix laricina (Du Roi) K. Koch. Canadian 

Journal of Forest Research. 15(5): 822-828. https://doi.org/10.1139/x85-133.
Brown, John P. 2019. Heartwood taper in northern red oak (Quercus rubra L.). Res. Pap. NRS32. Newtown Square, PA: U.S. Department of Agriculture, Forest Service, Northern Research 

Station. 9 p. https://doi.org/10.2737/NRS-RP-32.

To better understand how the practice of long–term tree retention affects value, northern red 

oak (Quercus rubra L.) trees from the Menominee Indian Reservation in Wisconsin were 

harvested and examined for patterns of heartwood development in relation to several tree 

characteristics. A total of 69 mature northern red oak trees from three dbh size classes, small 

(34-47 cm, 20 trees), medium (48-60 cm, 20 trees), and large (≥ 61 cm, 29 trees), were logged 

and optimally bucked. Cross-sectional disks were then removed from the tops of the stumps 

and each log and were analyzed for patterns of change in heartwood radius. Four factors were 

found to have a statistically significant effect on heartwood radius: age of the tree, size class, 

height, and inside bark radius. The inside bark radius was the strongest predictor of heartwood 

radius. A 1 cm increase in inside bark radius led to approximately a 0.95 cm increase in 

heartwood radius. Increasing height had a small negative effect, with heartwood radius 

decreasing approximately 0.05 cm for each meter above ground. Age of the tree had a small 

positive effect of 0.0016 cm per year and was only significant in one expert model considered. 

These results provide consumers of oak logs and forest managers insight to the interior 

heartwood pattern and can lead to improved value assessments for northern red oak logs.

KEY WORDS: heartwood, taper, northern red oak, linear mixed models

In accordance with Federal civil rights law and U.S. Department of Agriculture (USDA) civil rights regulations 

and policies, the USDA, its Agencies, offices, and employees, and institutions participating in or administering 

USDA programs are prohibited from discriminating based on race, color, national origin, religion, sex, gender 

identity (including gender expression), sexual orientation, disability, age, marital status, family/parental status, 

income derived from a public assistance program, political beliefs, or reprisal or retaliation for prior civil rights 

activity, in any program or activity conducted or funded by USDA (not all bases apply to all programs). Remedies 

and complaint filing deadlines vary by program or incident.

Persons with disabilities who require alternative means of communication for program information (e.g., Braille, 

large print, audiotape, American Sign Language, etc.) should contact the responsible Agency or USDA’s TARGET 

Center at (202) 720-2600 (voice and TTY) or contact USDA through the Federal Relay Service at (800) 877-8339. 

Additionally, program information may be made available in languages other than English. 

To file a program discrimination complaint, complete the USDA Program Discrimination Complaint Form, AD3027, found online at http://www.ascr.usda.gov/complaint_filing_cust.html and at any USDA office or write 

a letter addressed to USDA and provide in the letter all of the information requested in the form. To request 

a copy of the complaint form, call (866) 632-9992. Submit your completed form or letter to USDA by: (1) mail: 

U.S. Department of Agriculture, Office of the Assistant Secretary for Civil Rights, 1400 Independence Avenue, 

SW, Washington, D.C. 20250-9410; (2) fax: (202) 690-7442; or (3) email: program.intake@usda.gov.