USDA Forest Service Research Paper PSW-RP-238. 1998. 27

Periodic Annual Diameter Increment After

Overstory Removal in Mixed Conifer Stands

Fabian C.C. Uzoh K. Leroy Dolph John R. Anstead

United States

Department

of Agriculture

Forest Service

Pacific Southwest

Research Station

http://www.psw.fs.fed.us/

Research Paper

PSW-RP-238
Abstract

Uzoh, Fabian C.C.; Dolph, K. Leroy; Anstead, John R. 1998. Periodic annual diameter

increment after overstory removal in mixed conifer stands. Res. Paper PSW-RP-238.

Albany, CA: Pacific Southwest Research Station, Forest Service, U.S. Department of

Agriculture; 22 p.

Diameter growth rates of understory trees were measured for periods both before and after

overstory removal on six study areas in northern California. All the species responded with

increased diameter growth after adjusting to their new environments. Linear regression

equations that predict periodic annual increment of the diameters of the residual trees after

treatment are presented for the six species in the study areas.

Retrieval Terms: California red fir, California white fir, Douglas-fir, incense-cedar, increment

(diameter), Jeffrey pine, northern California, ponderosa pine, sugar pine

The Authors

Fabian C.C. Uzoh is a Research Forester, K. Leroy Dolph was until his retirement in 1994

also a Research Forester, and John Anstead is a Forest Technician at Pacific Southwest

Research Station, USDA Forest Service, 2400 Washington Avenue, Redding, CA 96001.

Publisher:

Albany, California

Mailing address:

PO Box 245, Berkeley CA

94701-0245

510 559-6300

http://www.psw.fs.fed.us/

techpub.html

December 1998

Pacific Southwest Research Station

Forest Service

U.S. Department of Agriculture
Pacific Southwest

Research Station

USDA Forest Service

Research Paper

PSW-RP-238

December 1998

Periodic Annual Diameter Increment After Overstory

Removal in Mixed Conifer Stands

Fabian C.C. Uzoh K. Leroy Dolph John R. Anstead

Contents

In Brief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Study Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Plot Location and Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Tree Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Ashpan—Lassen National Forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Baker—Lassen National Forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Johnson’s Ravine—Plumas National Forest. . . . . . . . . . . . . . . . . . . . . . . . . . 5

Clear Creek—Plumas National Forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Algoma—Shasta-Trinity National Forest. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Nuisance—Swain Mountain Experimental Forest . . . . . . . . . . . . . . . . . . . . . 9

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
26 USDA Forest Service Research Paper PSW-RP-238. 1998.

In Brief...

Uzoh, Fabian C.C.; Dolph, K. Leroy; Anstead, John R. 1998. Periodic annual diameter increment

after overstory removal in mixed conifer stands. Res. Paper PSW-RP-238. Albany, CA: Pacific

Southwest Research Station, Forest Service, U.S. Department of Agriculture; 22 p.

Retrieval terms: California red fir, California white fir, Douglas-fir, incense-cedar, increment

(diameter), Jeffrey pine, northern California, ponderosa pine, sugar pine

Between 1978 and 1982, a total of 14 timber sale areas on the Plumas, Klamath,

Lassen, Modoc, and Shasta-Trinity National Forests and the Swain

Mountain Experimental Forest of the Pacific Southwest Research Station, all in northern

California, were designed and implemented as overstory removals. Sales were in the true fir

(TF), east-side pine (EP), or Sierra Nevada mixed-conifer (MC) timber type. Before cutting, the

Silvicultural Development Unit of Region 5 of the USDA Forest Service established two to seven

homogeneous units within each sale area for sampling before and after harvest conditions.

Overstory volume removed from the timber sale units ranged from 72 to 707 m3

/ha (753 to 9418

ft3

/acre). These units ranged from 0.73 to 3.0 hectares (1.2 to 7.4 acres), depending on stand size

and condition. From the 14 sale areas, 6 representative sale areas were selected for this study.

Two are in the Lassen National Forest, two in the Plumas National Forest, one in the ShastaTrinity National Forest, and one in the Swain Mountain Experimental Forest of the Pacific

Southwest Research Station (PSW), located in the Lassen National Forest. These six areas are

composed of Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco), California white fir (Abies concolor

[Gord. & Glend.] Lindl.), California red fir (Abies magnifica A. Murr.), incense-cedar (Libocedrus

decurrens Torr.), sugar pine (Pinus lambertiana Dougl.), ponderosa pine (Pinus ponderosa Laws.),

and Jeffrey pine (Pinus jeffreyi Grev. & Balf.). Between 1988 and 1989, residual trees 7.62 cm (3

inches) in diameter at breast height (d.b.h.) or larger were measured and cored. The increment

core samples were used to age sampled trees and to determine past diameter growth rate. The

trees were remeasured in 1994. To show the effect of overstory removal on residual trees, a 2-

dimensional bar chart was used to display combined data of periodic annual diameter increment

(cm) 8 and 10 years before treatment, periodic annual diameter increment (cm) 8 and 10 years

after treatment, and periodic annual diameter increment (cm) 9 to 16 years after treatment, by

species, for the entire study area. All the species responded with increased diameter growth after

adjusting to their new environments. With time, diameter growth response of sugar pine and

Douglas-fir on the average, was the greatest, independent of timber sale area, whereas that of

incense-cedar and ponderosa pine showed the least response. Within each timber sale area, units

with the most overstory removed showed the highest diameter response, after treatment,

whereas units with low amounts of overstory removal showed the least diameter response.

Regardless of unit or species, periodic annual diameter increments 8 or 10 years after treatment

were not different from their periodic annual diameter increments 8 or 10 years before treatment.

However, after the trees adjusted to their new environment, periodic annual diameter increment

9 to 16 years after treatment showed a substantial increase in growth compared to their

counterparts 8 or 10 years after treatment. Depending on species, periodic annual diameter

increment 8 or 10 years before treatment, the square of periodic annual diameter increment 8 or

10 years before treatment, initial diameter, the square of initial diameter, total basal area per plot

of residual trees larger in diameter than that of the subject tree, and total basal area per plot of

residual trees larger in diameter than that of the subject tree divided by the subject tree’s

diameter were good predictors of periodic annual diameter growth response of the residual trees

9 to 16 years after treatment. For developing the regression equations, as a result of analyses of

covariance, data on ponderosa pine and Jeffrey pine were combined.

ii
USDA Forest Service Research Paper PSW-RP-238. 1998. 1

Introduction

Today, in states like California, social, legislative, and economic considerations are

compelling public and private forest managers to look for alternatives to clearcutting that

will not dramatically change forest appearance. This paradigm shift is a result of one or

the combinations of the following factors: (1) our improved understanding of natural ecosystem

processes has increased greatly (O’Hara and others 1994, Oliver 1995); (2) management of

uneven-aged stands has become a popular alternative because it can achieve biological and

ecological diversity, ecosystem health and productivity, and sustainability of forest products and

amenities across the landscape (Guldin 1995, Hagle 1995, O’Hara and others 1994); (3) the general

public’s dislike for even-aged management practices in favor of multi-aged management

alternatives (Laacke and Fiddler 1986, Oliver 1995); and (4) the desire to practice ecologically

based and socially acceptable forest management—termed the “social phase” of forestry

development (Kimmins 1991).

Consequently, this evolution in management philosophy makes silvicultural practices like

overstory removal attractive harvest alternatives to clearcutting and regeneration (Guldin 1995,

Laacke and Fiddler 1986) because removing overstory can create stands with structural diversity

that are well stocked with well-distributed crop trees that clearcutting may not provide (Guldin

1995, Helms and Standiford 1985, Laacke and Fiddler 1986, Oliver 1995). As a result, forest

managers are interested in understanding the advantages and disadvantages as well as stand

adequacy for overstory removal, because if properly implemented, the residual forest resulting

from overstory removal serves as immediate growing stock, reducing the time needed to grow

trees of merchantable size. In addition, from an esthetic perspective, the residual forest has an

appearance of a continuous forest canopy (Guldin 1995). The residual forest also provides soil

protection and cover for wildlife.

Nevertheless, overstory removal has three major disadvantages: (1) it may incorrectly be

applied on even-aged stands; (2) skilled loggers familiar with improved harvesting techniques

(which cost more) are necessary to protect advanced regeneration from damage and potential

disease problems; and (3) logging slash is difficult and costly to remove without harming the

advanced regeneration, and if left behind, the slash can be a fire hazard (Weatherspoon and

Skinner 1995). The above disadvantages notwithstanding, alternatives like overstory removal, if

implemented successfully, can result in uneven-aged mixed-species stands that are well stocked

with well-distributed crop trees.

Meanwhile, for a stand to be adequate for overstory removal, it has to exhibit the following

characteristics: (a) the stand has to be made up of at least two age classes, with the older class

merchantable and removable; and (b) the residual stand should be adequately stocked with welldistributed crop trees, whose value would equal or exceed that attainable should the stand

otherwise be regenerated (Laacke and Fiddler 1986).

The paper reports on the response of the diameter growth rate of residual trees (2.54 cm

d.b.h. or greater) to varying levels of overstory removal; documents the growth of these trees

over a long time in the true fir (TF), east-side pine (EP), and Sierra Nevada mixed-conifer (MC)

timber type on the Plumas, Klamath, Lassen, Modoc, and Shasta-Trinity National Forests and on

the Swain Mountain Experimental Forest of the Pacific Southwest Research Station, all in

northern California; and provides equations for predicting periodic annual diameter increment

of residual trees 14 to 16 years after treatment.

Methods

Between 1978 and 1982, a total of 14 timber sale areas on the Plumas, Klamath, Lassen, Modoc,

and Shasta-Trinity National Forests and on the Swain Mountain Experimental Forest were
2 USDA Forest Service Research Paper PSW-RP-238. 1998.

designed and implemented as overstory removals. Sales were in the true fir, east-side pine, or

Sierra Nevada mixed-conifer timber type. Before cutting, the Silvicultural Development Unit of

the USDA Forest service Region 5 established two to seven homogeneous units within each sale

area for sampling before and after harvest conditions.

Overstory volume removed from the timber sale units ranged from 72 to 707 m3/ha (753 to

9418 ft3/acre ). The sampling units established within each sale area ranged from 0.73 to 3.0

hectares (1.2 to 7.4 acres), depending on stand size and condition. From the 14 sale areas, six

representative sale areas were selected for this study—two on the Lassen National Forest, two on

the Plumas National Forest, one on the Shasta-Trinity National Forest, and one on the Swain

Mountain Experimental Forest, located in the Lassen National Forest. The six areas are composed

of Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco), California white fir (Abies concolor [Gord. &

Glend.] Lindl.), California red fir (Abies magnifica A. Murr.), incense-cedar (Libocedrus decurrens

Torr.), sugar pine (Pinus lambertiana Dougl.), ponderosa pine (Pinus ponderosa Laws.), and Jeffrey

pine (Pinus jeffreyi Grev. & Balf.). Between 1988 and 1989, residual trees 7.62 cm (3 inches)

diameter at breast height (d.b.h.) or larger were measured and cored. The increment cores were

used to age sampled trees and to determine past diameter growth rate. The trees were remeasured

in 1994.

Study Design

Plot Location and Installation

The characteristics of the six selected overstory removal sale areas are shown in table 1. Three

permanent plots were located in each sale area except for the Johnson’s Ravine sale in the Plumas

National Forest, which had only two suitable units available for plot installation. One plot was

installed in each of these units. The units were selected for plot installation on the basis of the

volume of overstory removed. These plots were installed in the units as follows: (1) the first plot

was installed in the unit from which the highest volume (m3/ha) had been removed, (2) the second

plot was installed in the unit from which the lowest volume had been removed, and (3) the third

Table 1—Overstory characteristics of timber stands on three National Forests in northern California.

Trees/

National Mean Unit Plot Volume hectare Forest

Forest Sale area d.b.h. no. Size removed removed type

cm ha M3/ha

Lassen Ashpan 66.04 1 3.2 148 37 MC

73.66 3 1.7 402 54 MC

93.98 5 1.4 302 27 MC

Lassen Baker 73.70 1 1.7 71 12 EP

76.20 2 1.9 112 30 EP

83.80 4 1.6 171 25 EP

Plumas Johnson 71.12 3 1.2 286 62 MC

Ravine 78.74 4 1.2 438 62 MC

Plumas Clear Creek 83.82 1 2.0 360 44 MC

106.70 2 1.1 416 30 MC

91.44 4 3.1 591 67 MC

Shasta-Trinity Algoma 94.00 2 1.5 177 20 MC

91.50 3 1.6 180 20 MC

124.50 4 1.5 117 07 MC

Lassen Swain Mtn. 101.60 1 1.3 467 52 TF

Nuisance 83.82 5 2.4 659 86 TF

88.90 6 2.2 618 74 TF

1

MC = mixed conifer; EP = east-side pine; TF = true fir.
USDA Forest Service Research Paper PSW-RP-238. 1998. 3

plot was installed in the unit from which the amount of volume removed was nearest the sale

area’s average. At the time of cutting, the mature stands in all the timber sale areas were all more

than 200 years old.

The first growth periods, 8 years or 10 years after treatment, were the length of time from

overstory removal to the time the plots were installed. The periods 14, 15 or 16 years after

treatment were the length of time from overstory removal to the time the plots were remeasured

in 1994.

The permanent plots were 0.1012 hectares (31.82 meters x 31.82 meters), each surrounded by

a 10.1-meter buffer strip. Plots were tentatively located on large-scale (1 cm ~ 30.48 m) maps of

each unit. Wherever possible, skid trails and other major disturbed areas were avoided. On units

with large undisturbed areas, the plot locations were selected randomly.

Tree Measurements

All trees 2.54 cm d.b.h. and larger were tagged and measured. The following characteristics and

measurements were recorded for each live tree:

• Tree number

• Species

• Damage and defects

• Age and radial increment

• Diameter at breast height (d.b.h.)

• Total tree height

• Height to base of live crown.

Trees 7.62 cm (3 inches) d.b.h. and larger were cored at breast height (1.4 m above ground

level on the uphill side of the tree). Radial growth was measured to the nearest 0.127 cm, ignoring

the current year’s growth, using a hand lens when necessary to determine diameter growth 8 or

10 years before treatment and 8 or 10 years after treatment. The increment core samples were also

used to age sampled trees. However, if it seemed likely that doing so would retard the tree’s

growth or survival, the tree was not bored.

Study Areas

Ashpan—Lassen National Forest

Unit 1—The unit is at 40° 38' 30" N. latitude and 121° 31' 00" N. longitude (T 32N, R 4E, S 9 NE1/

4) at an elevation of 1,646 m with an east exposure. The slope ranges from 0 to 35 percent. Soils are

of cinder/basalt origin, and commonly Typic Xerorthents-Yallane family association, generally

gravelly stony loam to very gravelly loamy coarse sand. Water runoff is slow. The permeability is

moderately rapid to rapid. Mean annual precipitation is 127 cm.

Unit 3—The unit is at 40° 36' 30" N. latitude and 121° 33' 00" N. longitude (T 32N, R 4E, S 20 SW1/

4) at an elevation of 1,707 m with a southwest exposure. The slope ranges from 0 to 35 percent.

Soils are of basalt origin, and commonly Yallane-Portola families association, gravelly fine sandy

loam to very gravelly sandy loam. Water runoff is slow. The permeability is moderately rapid.

Mean annual precipitation is 127 cm.

Unit 5—The unit is at 40° 36' 30" N. latitude and 121° 32' 15" N. longitude (T 32N, R 4E, S 29 NE1/

4) at an elevation of 1,707 m with a north-northwest exposure. The slope ranges from 0 to 35

percent. Soils are of basalt origin, and commonly Yallane-Portola families association, gravelly

fine sandy loam to very gravelly sandy loam. Water runoff is slow. The permeability is moderately

rapid. Mean annual precipitation is 127 cm.
4 USDA Forest Service Research Paper PSW-RP-238. 1998.

The characteristics of the residual forest after overstory removal at the Ashpan area in the

Lassen National Forest were:

SPECIES

True Fir Number of observations = 410

Average Range

Age (at breast height) (yr) 53 24 to 112

Initial d.b.h. (cm) 13.72 1.02 to 71.12

d.b.h. 8 years before treatment (cm) 14.99 1.52 to 76.20

d.b.h. 8 years after treatment (cm) 16.26 2.03 to 82.55

d.b.h. 15 years after treatment (cm) 17.70 2.54 to 83.82

Incense-cedar Number of observations = 25

Average Range

Age (at breast height) (yr) 37 29 to 49

Initial d.b.h. (cm) 5.59 1.78 to 11.68

d.b.h. 8 years before treatment (cm) 6.60 2.29 to 13.46

d.b.h. 8 years after treatment (cm) 7.47 3.05 to 15.24

d.b.h. 15 years after treatment (cm) 8.56 3.56 to 18.29

Sugar pine Number of observations = 26

Average Range

Age (at breast height) (yr) 33 21 to 65

Initial d.b.h. (cm) 8.51 2.03 to 28.19

d.b.h. 8 years before treatment (cm) 10.41 2.54 to 35.05

d.b.h. 8 years after treatment (cm) 12.37 3.05 to 43.18

d.b.h. 15 years after treatment (cm) 14.58 3.56 to 48.51

Ponderosa/Jeffrey pine

Number of observations = 33

Average Range

Age (at breast height) (yr) 50.5 21 to 89

Initial d.b.h. (cm) 12.45 1.52 to 42.67

d.b.h. 8 years before treatment (cm) 13.46 2.03 to 43.18

d.b.h. 8 years after treatment (cm) 14.48 2.54 to 43.94

d.b.h. 15 years after treatment (cm) 15.65 3.05 to 44.20

Baker—Lassen National Forest

Unit 1—The unit is at 40° 40' 30" N. latitude and 121° 23' 00" N. longitude (T 33N, R 5E, S 35 NE1/

4) at an elevation of 1,646 m with a southeast exposure. The slope ranges from 0 to 15 percent.

Soils are of andesite and basalt origin, are Bobbitt-Holland-Skalan family association, generally

gravelly loam to very gravelly sandy or clay loam, and water runoff is slow. The permeability is

moderately slow. Mean annual precipitation is 50.8 cm.

Unit 2—The unit is at 40° 39' 30" N. latitude and 121° 22' 00" N. longitude (T 32N, R 6E, S 6 SW1/

4) at an elevation of 1,640 m with a northwest exposure. The slope ranges from 0 to 15 percent.

Soils are of andesite and basalt origin, are Bobbitt-Holland-Skalan family association, generally
USDA Forest Service Research Paper PSW-RP-238. 1998. 5

gravelly loam to very gravelly sandy or clay loam, and water runoff is slow. Mean annual

precipitation is 76.2 cm.

Unit 4—The unit is at 40° 39' 30" N. latitude and 121° 19' 30" N. longitude (T 32N, R 6E, S 8 SE1/4)

at an elevation of 1,683 m with a northwest exposure. The slope ranges from 0 to 35 percent. Soils

are of basalt origin, are Trojan-Inville-Patio family association, generally gravelly sandy loam to

extremely gravelly clay loam, and water runoff is slow. Mean annual precipitation is 76.2 cm.

The characteristics of the residual forest after overstory removal at the Baker area in the

Lassen National Forest were:

SPECIES

True Fir Number of observations = 155

Average Range

Age (at breast height) (yr) 58 30 to 95

Initial d.b.h. (cm) 11.33 1.47 to 33.27

d.b.h. 8 years before treatment (cm) 12.60 1.98 to 35.84

d.b.h. 8 years after treatment (cm) 14.20 2.54 to 37.85

d.b.h. 15 years after treatment (cm) 15.82 2.95 to 41.25

Incense-cedar Number of observations = 119

Average Range

Age (at breast height) (yr) 59 32 to 102

Initial d.b.h. (cm) 7.44 1.42 to 27.89

d.b.h. 8 years before treatment (cm) 8.43 1.93 to 28.80

d.b.h. 8 years after treatment (cm) 9.65 2.54 to 29.72

d.b.h. 15 years after treatment (cm) 10.85 2.79 to 32.51

Ponderosa/Jeffrey pine Number of observations = 161

Average Range

Age (at breast height) (yr) 62 30 to 95

Initial d.b.h. (cm) 8.23 1.50 to 57.53

d.b.h. 8 years before treatment (cm) 9.53 1.98 to 58.95

d.b.h. 8 years after treatment (cm) 11.02 2.54 to 61.21

d.b.h. 15 years after treatment (cm) 12.12 2.95 to 63.50

Johnson’s Ravine—Plumas National Forest

Unit 2—The unit is at 40° 2' 30" N. latitude and 121° 4' 00" N. longitude (T 25N, R 8E, S 10 NE 1/4) at

an elevation of 1,402 m with a northeast exposure. The slope ranges from 50 to 70 percent. Soils are

of slightly fractured schist origin, are of Kistirn-Aiken-Deadwood families complex, generally very

gravelly loam to extremely gravely silty clay loam, and water runoff is slow. The permeability is

moderately slow. Soils are moderately well drained. Mean annual precipitation is 101.6 cm.

Unit 3—The unit is at 40° 3' 00" N. latitude and 121° 3' 30" N. longitude (T 25N, R 8E, S 2 SW 1/4) at

an elevation of 1,463 m with a northwest exposure. The slope ranges from 40 to 80 percent. Soils are

of slightly fractured schist origin, are of Kistirn-Aiken-Deadwood families complex, generally very

gravelly loam to extremely gravely silty clay loam, and water runoff is slow. The permeability is

moderately slow. Soils are moderately well drained. Mean annual precipitation is 101.6 cm.
6 USDA Forest Service Research Paper PSW-RP-238. 1998.

The characteristics of the residual forest after overstory removal at the Johnson’s Ravine

area in the Plumas National Forest were:

SPECIES

True Fir Number of observations = 405

Average Range

Age (at breast height) (yr) 59 30 to 119

Initial d.b.h. (cm) 4.06 1.47 to 26.77

d.b.h. 8 years before treatment (cm) 4.72 1.98 to 28.78

d.b.h. 8 years after treatment (cm) 5.51 2.54 to 32.77

d.b.h. 15 years after treatment (cm) 6.38 2.79 to 35.5

Incense-cedar Number of observations = 17

Average Range

Age (at breast height) (yr) 97 45 to 245

Initial d.b.h. (cm) 8.26 1.63 to 35.15

d.b.h. 8 years before treatment (cm) 8.92 2.18 to 35.76

d.b.h. 8 years after treatment (cm) 9.70 2.79 to 36.07

d.b.h. 15 years after treatment (cm) 10.95 3.30 to 38.61

Sugar pine Number of observations = 10

Average Range

Age (at breast height) (yr) 79 71 to 88

Initial d.b.h. (cm) 5.11 1.70 to 8.81

d.b.h. 8 years before treatment (cm) 5.74 2.44 to 9.12

d.b.h. 8 years after treatment (cm) 6.45 3.05 to 9.91

d.b.h. 15 years after treatment (cm) 7.77 4.06 to 10.67

Douglas-fir Number of observations = 177

Average Range

Age (at breast height) (yr) 72 35 to 130

Initial d.b.h. (cm) 7.16 0.102 to 38.94

d.b.h. 8 years before treatment (cm) 7.90 1.98 to 40.67

d.b.h. 8 years after treatment (cm) 8.74 2.54 to 42.67

d.b.h. 15 years after treatment (cm) 10.01 2.79 to 45.21

Clear Creek—Plumas National Forest

Unit 1—The unit is at 40° 7' 00" N. latitude and 121° 8' 00" N. longitude (T 26N, R 8E, S 18 NW 1/

4) at an elevation of 1,402 m with a southeast exposure. The slope ranges from 50 to 70 percent.

Soils are of slightly fractured schist origin, are of Kistirn-Aiken-Deadwood families complex,

generally very gravelly loam to silty clay loam, and water runoff is slow. The permeability is

moderately slow. Soils are well-drained. Mean annual precipitation is 101.6 cm.

Unit 2—The unit is at 40° 8' 00" N. latitude and 121° 8' 00" N. longitude (T 26N, R 8E, S 6 SW 1/4)

at an elevation of 1,402 m with a northeast exposure. The slope ranges from 10 to 50 percent. Soils

are of slightly fractured schist origin, are of Kistirn-Aiken-Deadwood families complex, generally

very gravelly loam to silty clay loam, and water runoff is slow. The permeability is moderately

slow. Soils are well-drained. Mean annual precipitation is 101.6 cm.
USDA Forest Service Research Paper PSW-RP-238. 1998. 7

Unit 4—The unit is at 40° 7' 45" N. latitude and 121° 7' 15" N. longitude (T 26N, R 8E, S 7 SW 1/4)

at an elevation of 1,341 m with a northeast exposure. The slope ranges from 50 to 70 percent. Soils

are of slightly fractured schist origin, are of Kistirn-Aiken-Deadwood families complex, generally

very gravelly loam to silty clay loam, and water runoff is slow. The permeability is moderately

slow. Soils are well-drained. Mean annual precipitation is 101.6 cm.

The characteristics of the residual forest after overstory removal at the Clear Creek area in

the Plumas National Forest were:

SPECIES

True Fir Number of observations = 363

Average Range

Age (at breast height) (yr) 67 30 to 113

Initial d.b.h. (cm) 9.17 1.47 to 67.26

d.b.h. 10 years before treatment (cm) 10.21 1.98 to 72.11

d.b.h. 10 years after treatment (cm) 11.38 2.54 to 76.96

d.b.h. 16 years after treatment (cm) 12.83 2.54 to 80.01

Incense-cedar Number of observations = 60

Average Range

Age (at breast height) (yr) 69 37 to 123

Initial d.b.h. (cm) 10.59 2.08 to 64.54

d.b.h. 10 years before treatment (cm) 11.48 2.64 to 67.59

d.b.h. 10 years after treatment (cm) 12.42 3.30 to 70.61

d.b.h. 16 years after treatment (cm) 13.41 3.56 to 74.93

Sugar pine Number of observations = 8

Average Range

Age (at breast height) (yr) 80 26 to 114

Initial d.b.h. (cm) 20.70 1.70 to 43.38

d.b.h. 10 years before treatment (cm) 22.73 2.21 to 47.12

d.b.h. 10 years after treatment (cm) 25.32 2.79 to 50.55

d.b.h. 16 years after treatment (cm) 30.23 3.30 to 53.59

Douglas-fir Number of observations = 93

Average Range

Age (at breast height) (yr) 69 40 to 102

Initial d.b.h. (cm) 11.89 1.70 to 38.30

d.b.h. 10 years before treatment (cm) 12.95 2.21 to 41.20

d.b.h. 10 years after treatment (cm) 14.43 2.79 to 45.21

d.b.h. 16 years after treatment (cm) 16.84 3.30 to 49.02
8 USDA Forest Service Research Paper PSW-RP-238. 1998.

Algoma—Shasta-Trinity National Forest

Unit 2—The unit is at 41° 14' 30" N. latitude and 121° 53' 00" N. longitude (T 39N, R 1E, S 6 SW 1/

4) at an elevation of 1,312 m with a north-northeast exposure. The slope ranges from 0 to 20

percent. Soils are of weathered metavolcanic rock origin, are of Holland Family-Ashy

association, generally sandy clay loam, and water runoff is slow. The permeability is moderately

rapid to rapid. Mean annual precipitation is 127 cm.

Unit 3—The unit is at 41° 15' 00" N. latitude and 121° 54' 30" N. longitude (T 39N, R 1W, S 1 SE 1/

4) at an elevation of 1,158 m with a north-southwest exposure. The slope ranges from 0 to 20

percent. Soils are of basalt origin, are of Sadie family association, generally stony sandy loam, and

water runoff is slow. The permeability is moderately rapid. Mean annual precipitation is 127 cm.

Unit 4—The unit is at 41° 14' 30" N. latitude and 121° 53' 00" N. longitude (T 39N, R 1E, S 5 NW 1/

4) at an elevation of 1,158 m with a west exposure. The slope ranges from 0 to 35 percent. Soils are

of basalt origin, are of Sadie family association, generally stony sandy loam, and water runoff is

slow. The permeability is moderately rapid. Mean annual precipitation is 127 cm.

The characteristics of the residual forest after overstory removal at the Algoma area in the

Shasta-Trinity National Forest were:

SPECIES

True Fir Number of observations = 293

Average Range

Age (at breast height) (yr) 56 20 to 139

Initial d.b.h. (cm) 9.53 1.02 to 43.74

d.b.h. 10 years before treatment (cm) 10.80 1.88 to 46.86

d.b.h. 10 years after treatment (cm) 12.55 2.54 to 51.56

d.b.h. 16 years after treatment (cm) 13.79 2.54 to 59.44

Incense-cedar Number of observations = 281

Average Range

Age (at breast height) (yr) 51 23 to 115

Initial d.b.h. (cm) 8.36 1.42 to 72.59

d.b.h. 10 years before treatment (cm) 9.45 1.93 to 78.00

d.b.h. 10 years after treatment (cm) 10.59 2.54 to 82.55

d.b.h. 16 years after treatment (cm) 11.48 2.54 to 85.85

Sugar pine Number of observations = 5

Average Range

Age (at breast height) (yr) 63 43 to 74

Initial d.b.h. (cm) 22.83 1.93 to 59.16

d.b.h. 10 years before treatment (cm) 26.26 2.44 to 68.05

d.b.h. 10 years after treatment (cm) 30.58 3.05 to 79.50

d.b.h. 16 years after treatment (cm) 33.17 3.56 to 86.11
USDA Forest Service Research Paper PSW-RP-238. 1998. 9

Ponderosa/Jeffrey pineNumber of observations = 35

Average Range

Age (at breast height) (yr) 63 30 to 86

Initial d.b.h. (cm) 29.16 7.85 to 57.15

d.b.h. 10 years before treatment (cm) 31.45 9.83 to 59.56

d.b.h. 10 years after treatment (cm) 33.78 10.67 to 68.07

d.b.h. 16 years after treatment (cm) 36.75 10.67 to 73.66

Douglas-fir Number of observations = 42

Average Range

Age (at breast height) (yr) 59 35 to 86

Initial d.b.h. (cm) 10.90 1.93 to 38.56

d.b.h. 10 years before treatment (cm) 12.47 2.44 to 44.32

d.b.h. 10 years after treatment (cm) 14.96 3.05 to 52.07

d.b.h. 16 years after treatment (cm) 17.02 3.30 to 57.15

Nuisance—Swain Mountain Experimental Forest (Located in Lassen N.F.)

Unit 1—The unit is at 40° 25' 15" N. latitude and 121° 7' 00" N. longitude (T 30N, R 8E, S 32 NW1/4)

at an elevation of 2,073 m with a west exposure. The slope ranges from 0 to 35 percent. Soils are of

weathered basalt origin, are De Masters-Klicker family association, generally sandy loam to

extremely gravelly loam, and water runoff is slow. The permeability is moderate. Mean annual

precipitation is 127 cm.

Unit 5—The unit is at 40° 29' 30" N. latitude and 121° 5' 30" N. longitude (T 30N, R 8E, S 21 NW1/

4) at an elevation of 1,823 m with a north-northeast exposure. The slope ranges from 0 to 35

percent. Soils are of weathered basalt origin, are De Masters-Klicker family association, generally

sandy loam to extremely gravelly loam, and water runoff is slow. The permeability is moderate.

Mean annual precipitation is 127 cm.

Unit 6—The unit is at 40° 26' 30" N. latitude and 121° 5' 00" N. longitude (T 30N, R 8E, S 21 NW1/

4) at an elevation of 1,798 m with an east exposure. The slope ranges from 0 to 35 percent. Soils are

of weathered basalt origin, are De Masters-Klicker family association, generally sandy loam to

extremely gravelly loam, and water runoff is slow. The permeability is moderate. Mean annual

precipitation is 127 cm.

The characteristics of the residual forest after overstory removal at Nuisance area in the

Swain Mountain were:

SPECIES

White fir Number of observations = 151

Average Range

Age (at breast height) (yr) 83 37 to 139

Initial d.b.h. (cm) 16.23 0.33 to 56.57

d.b.h. 8 years before treatment (cm) 17.30 2.79 to 59.13

d.b.h. 8 years after treatment (cm) 19.03 3.30 to 62.99

d.b.h. 14 years after treatment (cm) 20.55 3.81 to 68.33
10 USDA Forest Service Research Paper PSW-RP-238. 1998.

SPECIES

Red fir Number of observations = 421

Average Range

Age (at breast height) (yr) 59 30 to 129

Initial d.b.h. (cm) 10.03 1.47 to 65.10

d.b.h. 8 years before treatment (cm) 4.35 1.98 to 68.81

d.b.h. 8 years after treatment (cm) 4.85 2.54 to 73.66

d.b.h. 14 years after treatment (cm) 5.38 2.79 to 76.96

Analysis

Past outside bark diameters at breast height, for each sample tree at the time of overstory removal

and 8 or 10 years before overstory removal, were calculated using bark growth adjustment

factors developed for each species (Dolph 1984). The following formula was used:

Dobp = Dobc - (k • r)

In which,

Dobp= past diameter at breast height, outside bark

Dobc

= current diameter at breast height, outside bark

r = average radial wood growth in inches for a specified number of years, as measured on

increment cores taken at breast height.

k = species-specific constant

Species k

Douglas-fir 2.2627

Ponderosa and Jeffrey pine 2.2304

Sugar pine 2.2566

White fir 2.2444

Incense-cedar 2.3883

To show the effects of overstory removal on residual trees, 2-dimensional bar charts were used

to depict periodic annual diameter increment (cm) 8 or 10 years before treatment, periodic annual

diameter increment (cm) 8 or 10 years after treatment, and periodic annual diameter increment

(cm) 9 to 16 years after treatment for the six species within the timber sale areas ( figs. 1—13).

Linear regression equations were used to select the model that provided the best fit for

periodic annual diameter increment of all the residual trees after treatment. The best linear

regression equation was defined as the model that minimized the residual mean square error,

was closest to meeting the assumptions of regression analysis, and contained predictor variables

with low multicollinearity.

Change in d.b.h. can be expressed either as a diameter growth rate or as basal area growth

rate (Hann and Larsen 1990). In this analysis, periodic annual diameter increment 14, 15, or 16

years after treatment was selected as the dependent variable for the species within the six timber

sale areas. The standard linear regression model used was:

where Y is the value of periodic annual diameter increment (cm) 14, 15, or 16 years after

treatment; X1

 is initial d.b.h. (cm) or periodic annual diameter increment (cm) 8 or 10 years

before treatment; X2 is the square of X1; and X3 is total basal area per plot of residual trees

larger in diameter than that of the subject tree or total basal area per plot of residual trees

Y X X Xe = +⋅+⋅ +⋅ + ββ β β 0 11 2 2 33
USDA Forest Service Research Paper PSW-RP-238. 1998. 11

larger in diameter than that of the subject tree divided by the subject tree’s diameter (m2); e is

the measurement’s error component, with an expected e value of zero and variance of σ2

; and

β0, β1, β2, β3 are regression coefficients to be estimated. For developing the regression

equations, as a result of analysis of covariance, ponderosa pine and Jeffrey pine data were

combined. Each of the study areas was composed of more than two species with the exception

of the Nuisance area, which had only red and white fir. White fir was the predominant

species at each of the study areas with the exception of the Nuisance units which were

composed of about 75 percent red fir and 25 percent white fir.

Results

Regardless of species, the residual trees responded by increasing their diameter growth after

adjusting to their new environment (figs. 1—13). However, on the basis of the observations we

can say that white fir, Douglas-fir, and sugar pine responded to release sooner than the other

species. The following periods were evaluated: 8 or 10 years before overstory removal, 8 or 10

years after overstory removal, and 9 to 16 years after overstory removal.

For predicting periodic annual diameter increment 9 to 16 years after treatment, all the

independent variables strengthened the regression model. However, initial diameter (cm), the

square of initial diameter, and total basal area per plot of residual trees larger in diameter than that

of the subject tree provided the best fit for fitting ponderosa pine and sugar pine, (tables 2 and 3),

whereas periodic annual diameter increment (cm) 8 or 10 years before treatment, the square of

periodic annual diameter increment (cm) 8 or 10 years before treatment, and total basal area per

plot of residual trees larger in diameter than that of the subject tree divided by the subject tree’s

diameter (m2) provided the best fit for fitting white fir, red fir, incense-cedar, and Douglas-fir

(tables 4, 5, 6, and 7).
12 USDA Forest Service Research Paper PSW-RP-238. 1998.

Figure 1—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

units after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 8 years before treatment, 0 to 8 years after treatment, and 9 to 15 years after

treatment for Ashpan units on the Lassen National Forest.

Figure 2—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

species after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 8 years before treatment, 0 to 8 years after treatment, and 9 to 15 years after

treatment for Ashpan units on the Lassen National Forest.

0.5

0.4

0.3

0.2

0.1

0

True fir I. cedar S. pine P. pine

Dbh P.A.I. (cm)

Response by species

8 years before treatment (cm)

0-8 years after treatment (cm)

9-15 years after treatment (cm)

Ashpan units on the Lassen National Forests

Response by units

0.4

0.3

0.2

0.1

0

148 402 303

Dbh P.A.I. (cm)

m /ha removed per unit 3

8 years before treatment (cm)

0-8 years after treatment (cm)

9-15 years after treatment (cm)
USDA Forest Service Research Paper PSW-RP-238. 1998. 13

Response by units

0.4

0.3

0.2

0.1

0

112 172

Dbh P.A.I. (cm)

m /ha removed per unit 3

8 years before treatment (cm)

0-8 years after treatment (cm)

9-15 years after treatment (cm)

72

Figure 3—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees

by units after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 8 years before treatment, 0 to 8 years after treatment, and 9 to 15 years after

treatment for Baker units on the Lassen National Forest.

Response by species

True fir I. cedar P. pine

Dbh P.A.I. (cm)

0.3

0.2

0.1

0

8 years before treatment (cm)

0-8 years after treatment (cm)

9-15 years after treatment (cm)

Figure 4—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees

by species after varying levels of overstory removal in mixed conifer stands (diameter

classes combined) 8 years before treatment, 0 to 8 years after treatment, and 9 to 15 years

after treatment for Baker units on the Lassen National Forest.

Baker units on the Lassen National Forest
14 USDA Forest Service Research Paper PSW-RP-238. 1998.

Figure 5—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

units after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 8 years before treatment, 0 to 8 years after treatment, and 9 to 15 years after

treatment for Johnson’s Ravine units on the Plumas National Forest.

Figure 6—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

species after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 8 years before treatment, 0 to 8 years after treatment, and 9 to 15 years after

treatment for Johnson’s Ravine units on the Plumas National Forest.

Response by units

Dbh P.A.I. (cm)

0.3

0.2

0.1

0

286 438

m /ha removed per unit 3

8 years before treatment (cm)

0-8 years after treatment (cm)

9-15 years after treatment (cm)

True fir I. cedar S. pine D. fir

0.3

0.2

0.1

0

Dbh P.A.I. (cm)

Response by species

8 years before treatment (cm)

0-8 years after treatment (cm)

9-15 years after treatment (cm)

Johnson’s Ravine units on the Plumas National Forest
USDA Forest Service Research Paper PSW-RP-238. 1998. 15

Figure 8—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

species after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 10 years before treatment, 0 to 10 years after treatment, and 11 to 16 years after

treatment for Clear Creek units on the Plumas National Forest.

Figure 7—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

units after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 10 years before treatment, 0 to 10 years after treatment, and 11 to 16 years after

treatment for Clear Creek units on the Plumas National Forest.

Response by units

0.3

0.2

0.1

0

Dbh P.A.I. (cm)

360 416 591

m /ha removed per unit 3

10 years before treatment (cm)

0-10 years after treatment (cm)

11-16 years after treatment (cm)

0.5

0.4

0.3

0.2

0.1

0

True fir I. cedar S. pine D. fir

Dbh P.A.I. (cm)

Response by species

10 years before treatment (cm)

0-10 years after treatment (cm)

11-16 years after treatment (cm)

Clear Creek units on the Plumas National Forest
16 USDA Forest Service Research Paper PSW-RP-238. 1998.

Response by units

0.4

0.3

0.2

0.1

0

177 180 117

Dbh P.A.I. (cm)

m /ha removed per unit 3

10 years before treatment (cm)

0-10 years after treatment (cm)

11-16 years after treatment (cm)

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

True fir I. cedar S. pine P. pine D. fir

Dbh P.A.I. (cm)

Response by species

10 years before treatment (cm)

0-10 years after treatment (cm)

11-16 years after treatment (cm)

Figure 9—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

units after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 10 years before treatment, 0 to 10 years after treatment, and 11 to 16 years after

treatment for Algoma units on the Shasta-Trinity National Forest.

Figure 10—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

species after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 10 years before treatment, 0 to 10 years after treatment, and 11 to 16 years after

treatment for Algoma units on the Shasta-Trinity National Forest.

Algoma units on the Shasta-Trinity National Forest
USDA Forest Service Research Paper PSW-RP-238. 1998. 17

Response by units

0.4

0.3

0.2

0.1

0

467 659 618

Dbh P.A.I. (cm)

m /ha removed per unit 3

8 years before treatment (cm)

0-8 years after treatment (cm)

9-14 years after treatment (cm)

Response by species

Dbh P.A.I. (cm)

0.3

0.2

0.1

0

white fir red fir

8 years before treatment (cm)

0-8 years after treatment (cm)

9-14 years after treatment (cm)

Figure 11—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

units after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 8 years before treatment, 0 to 8 years after treatment, and 9 to 14 years after

treatment for Nuisance units on the Swain Mountain Experimental Forest.

Figure 12—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees by

species after varying levels of overstory removal in mixed conifer stands (diameter classes

combined) 8 years before treatment, 0 to 8 years after treatment, and 9 to 14 years after

treatment for Nuisance units on the Swain Mountain Experimental Forest.

Nuisance units on the Swain Mountain Experimental Forest
18 USDA Forest Service Research Paper PSW-RP-238. 1998.

Discussion

The amount of overstory removed was arbitrarily chosen and was not replicated. As a result, it is

not possible to directly test the effects of levels of overstory removed. Additionally, removal

intensity (e.g., volume removed/initial volume), a likely independent variable, was not used in

the regression equations because there was little variation among units.

Nevertheless, as shown in figs. 1—13, regardless of timber sale area and species, residual

trees responded to overstory removal by increasing their diameter growth after adjusting to their

new environment (the 9- to 16-year period). Within each timber sale area, units with the most

overstory removed showed the highest increase in diameter after treatment, whereas units with

low amounts of overstory removal showed the smallest increase in diameter (figs. 1, 3, 5, 7, 9,

and 11). This result corresponds to the findings of Gordon (1973) for northern California.

However, we cannot determine how many years it took the residual trees to adjust to their new

environment, because measurements were not done on an annual basis. But on the basis of

observations, we can say that it took the residual trees between 3 and 7 years to adjust to their

new environment, depending on the best combinations of amount of overstory removed, stand

condition, and tree potential (Oliver and Larson 1996, p. 95). This result corresponds to the

findings of McCaughey and Schmidt (1982).

Furthermore, on average, diameter growth response of sugar pine was the greatest (regardless

of timber sale area), followed by that of Douglas-fir and white fir. Incense-cedar and ponderosa

pine showed the least response. This result corresponds well to the findings of Oliver and Dolph

(1992) for northern California.

On average, periodic annual diameter increments 8 or 10 years after treatment were not

different from those 8 or 10 years before treatment (fig. 13). However, after the residual trees had

adjusted to their new environment, periodic annual diameter increment 9 to 16 years after

treatment showed a substantial increase in growth response compared to their counterparts 8 or

10 years after treatment. Although how long this acceleration in growth will continue is uncertain,

studies have shown that it can continue 21 to 30 years after treatment (Herring and McMinn 1980,

Roe and DeJarnette 1965).

Figure 13—Periodic annual diameter increment (P.A.I.), at breast height, of residual trees

by species after varying levels of overstory removal in mixed conifer stands (diameter

classes combined) 8 to 10 years before treatment, 0 to 8 years or 10 years after

treatment, and 9 to 16 years after treatment.

0.5

0.4

0.3

0.2

0.1

0

True fir I. cedar S. pine P. pine D. fir

Dbh P.A.I. (cm)

Overall summary or response

by species

8 or 10 years before treatment (cm)

0-8 or 10 years after treatment (cm)

9-16 years after treatment (cm)
USDA Forest Service Research Paper PSW-RP-238. 1998. 19

Table 3—Equation parameter estimates and summary statistics of periodic annual diameter increment for sugar

pine after overstory removal in mixed conifer stands.

95 pct Confidence interval _____________________________________________________________________________________________________________________________________________________________________________

Parameters Estimate S. E. Tolerance T-statistic P(2-tail)

β0 0.09657 0.04254 . 2.27022 0.02826

β1 0.01733 0.00526 0.08611 3.29563 0.00197

β2 -0.00004 0.00010 0.08573 -0.36602 0.71614

β3 -0.15214 0.14024 0.95708 -1.08484 0.28404

Y X X Xe = +⋅+⋅ +⋅ + ββ β β 0 11 2 2 33 ; R2 = 0.440; = 0.704 ; Standard error of estimate (e) = 0.12847; N = 47

Variables Observations Minimum Maximum Mean Standard Dev.

Y (cm) 47 0.05249 1.12871 0.26292 0.22814

X1 (cm) 47 1.70000 59.16000 11.26735 12.14813

X2 (cm2) 47 2.89000 3499.90560 271.51830 630.66983

X3 (m2) 47 0.00000 0.49000 0.16490 0.13775

E (Y) (cm) is the expected value of periodic annual diameter increment 14 to 16 years after treatment.

X1 (cm) initial diameter.

X2 (cm) is the square of X1.

X3 (m2) is the sum of the residual trees’ basal area in trees with dbh larger than the subject tree’s dbh1.

N is the number of observations.

Table 2—Equation parameter estimates and summary statistics of periodic annual diameter increment for

ponderosa pine after overstory removal in mixed conifer stands.

95 pct Confidence interval _____________________________________________________________________________________________________________________________________________________________________________

Parameters Estimate S. E. Tolerance T-statistic P(2-tail)

β0 0.11500 0.01581 . 7.27220 0.00000

β1 0.01164 0.00175 0.11148 6.65058 0.00000

β2 -0.00011 0.00004 0.11167 -3.19883 0.00158

β3 -0.25098 0.04439 0.98643 -5.65404 0.00000

EY X X X ( ) = +⋅+⋅ +⋅ ββ β β 0 11 2 2 33; R2 = 0.440 ; Standard error of estimate = 0.10418; N = 237

Variables Observations Minimum Maximum Mean Standard Dev.

Y (cm) 237 0.02371 0.91916 0.17875 0.13827

X1 (cm) 234 1.50000 57.53000 11.97363 11.73668

X2 (cm) 234 2.25000 3309.70090 280.53613 567.86875

X3 (m2) 234 0.00000 0.84000 0.16912 0.16332

E (Y) (cm) is the expected value of periodic annual diameter increment 14 to 16 years after treatment.

X1 (cm) initial diameter.

X2 (cm2) is the square of X1.

X3 (m2

) is the sum of the residual trees’ basal area in trees with dbh larger than the subject tree’s dbh1.

N is the number of observations.

Linear regression equations were developed to predict periodic annual diameter increment

14 to 16 years after treatment. The equations were developed for each species for the entire timber

sale area. For developing the regression equations, data on ponderosa pine and Jeffrey pine were

combined as a result of analysis of covariance. The independent variables were X1, initial

diameter (cm) or periodic annual diameter increment (cm) 8 or 10 years before treatment; X2, the

square of X1; and X3, the total basal area per plot of residual trees larger in diameter than that of

the subject tree or total basal area per plot of residual trees larger in diameter than that of the

subject tree divided by the subject tree’s diameter (m2). X1, periodic annual diameter increment

(cm) 8 or 10 years before treatment; X2, the square of X1; and X3, the total basal area per plot of

residual trees larger in diameter than that of the subject tree divided by the subject tree’s

diameter (m2), provided the best fit for white fir, red fir, incense-cedar, and Douglas-fir, whereas

X1, initial diameter (cm); X2, the square of X1; and X3, the total basal area per plot of residual trees

larger in diameter than that of the subject tree’s diameter (m2), provided the best fit for ponderosa
20 USDA Forest Service Research Paper PSW-RP-238. 1998.

Table 5—Equation parameter estimates and summary statistics of periodic annual diameter increment for red fir

after overstory removal in mixed conifer stands.

95 pct Confidence interval _____________________________________________________________________________________________________________________________________________________________________________

Parameters Estimate S. E. Tolerance T-statistic P(2-tail)

β0 0.00937 0.01307 . 0.71698 0.47389

β1 2.25729 0.18499 0.09287 12.06021 0.00000

β2 -2.07631 0.50329 0.10026 -4.12546 0.00005

β3 -0.19411 0.08047 0.78756 -2.41236 0.01639

EY X X X ( ) = +⋅+⋅ +⋅ ββ β β 0 11 2 2 33; R2 = 0.720 ; Standard error of estimate = 0.07634; N = 421

Variables Observations Minimum Maximum Mean Standard Dev.

Y (cm) 421 0.03556 0.75692 0.16628 0.14358

X1 (cm) 421 0.02149 0.46111 0.07847 0.06816

X2 (cm2) 421 0.00046 0.21262 0.01079 0.02374

X3 (m2) 421 0.00000 0.39378 0.06083 0.06134

E (Y) (cm) is the expected value of periodic annual diameter increment 14 to 16 years after treatment.

X1 (cm) initial diameter.

X2 (cm2) is the square of X1.

X3 (m2

) is the sum of the residual trees’ basal area in trees with dbhs larger than the subject tree’s dbh1

divided by the subject tree’s diameter.

N is the number of observations.

Table 4—Equation parameter estimates and summary statistics of periodic annual diameter increment for

white fir after overstory removal in mixed conifer stands.

95 pct Confidence interval _____________________________________________________________________________________________________________________________________________________________________________

Parameters Estimate S. E. Tolerance T-statistic P(2-tail)

β0 0.03227 0.00503 . 6.41563 0.00000

β1 2.14009 0.08277 0.11550 26.00021 0.00000

β2 -1.33025 0.24385 0.11909 -5.45520 0.00000

β3 -0.28469 0.03667 0.91434 -7.76285 0.00000

EY X X X ( ) = +⋅+⋅ +⋅ ββ β β 0 11 2 2 33; R2= 0.712 ; Standard error of estimate = 0.07591; N = 1774

Variables Observations Minimum Maximum Mean Standard Dev.

E (Y) (cm) 1774 0.01863 1.13030 0.17229 0.14126

X1 (cm) 1774 0.01368 0.63500 0.07622 0.06687

X2 (cm2) 1774 0.00019 0.40323 0.01028 0.02391

X3 (m2) 1774 0.00000 1.03030 0.04083 0.06011

Y (cm) is the expected value of periodic annual diameter increment 14 to 16 years after treatment.

X1 (cm) is periodic annual diameter increment 8 to 10 years before treatment.

X2 (cm2

) is the square of X1.

X3 (m2) is the sum of the residual trees’ basal area in trees with dbh larger than the subject tree’s dbh1

divided by the subject tree’s diameter.

N is the number of observations.

pine and sugar pine. Total basal area per plot of residual trees larger in diameter than that of the

subject tree divided by the subject tree’s diameter was an effective predictor because trees across

the plots may have identical X3i values but not identical dbhi values. Although all the independent

variables strengthened the regression model, initial diameter and periodic annual diameter

increment 8 or 10 years before treatment were the best predictors of periodic annual diameter

increment 9 to 16 years after treatments.

Residual trees compete for the growing space previously occupied by the removed overstory

trees, and the growing space is influenced by species composition and crown position (Oliver and

Larson 1996, p. 95). X3 was included in the equations to estimate the competitive position that a

residual tree holds within a plot after overstory removal. X3 has been used as a tree-position variable

in equations for predicting basal area growth because it defines a tree’s position in relation to all trees
USDA Forest Service Research Paper PSW-RP-238. 1998. 21

Table 7—Equation parameter estimates and summary statistics of periodic annual diameter increment for

Douglas-fir after overstory removal in mixed conifer stands.

95 pct Confidence interval _____________________________________________________________________________________________________________________________________________________________________________

Parameters Estimate S. E. Tolerance T-statistic P(2-tail)

β0 0.03459 0.01337 . 2.58642 0.01018

β1 2.44742 0.22947 0.13376 11.00170 0.00000

β2 -1.30855 0.65383 0.13913 -2.00136 0.04627

β3 -0.33468 0.12834 0.90131 -2.60769 0.00958

EY X X X ( ) = +⋅+⋅ +⋅ ββ β β 0 11 2 2 33; R2= 0.683 ; Standard error of estimate = 0.08090; N = 312

Variables Observations Minimum Maximum Mean Standard Dev.

Y (cm) 312 0.03556 0.83661 0.18091 0.14288

X1 (cm) 312 0.00339 0.48651 0.06841 0.05982

X2 (cm2) 312 0.00001 0.23669 0.00825 0.02291

X3 (m2) 312 0.00000 0.80000 0.03075 0.05844

E (Y) (cm) is the expected value of periodic annual diameter increment 14 to 16 years after treatment.

X1 (cm) initial diameter.

X2 (cm2) is the square of X1.

X3 (m2) is the sum of the residual trees’ basal area in trees with dbh larger than the subject tree’s dbh1

divided by the subject tree's diameter.

N is the number of observations.

Table 6—Equation parameter estimates and summary statistics of periodic annual diameter increment for incensecedar after overstory removal in mixed conifer stands.

95 pct Confidence interval _____________________________________________________________________________________________________________________________________________________________________________

Parameters Estimate S. E. Tolerance T-statistic P(2-tail)

β0 0.02593 0.01051 . 2.46779 0.01399

β1 1.73447 0.18182 0.10236 9.53970 0.00000

β2 -1.11102 0.65484 0.10809 -1.69662 0.09051

β3 -0.13430 0.05806 0.84698 -2.31314 0.02120

EY X X X ( ) = +⋅+⋅ +⋅ ββ β β 0 11 2 2 33; R2= 0.618 ; Standard error of estimate = 0.06043; N = 428

Variables Observations Minimum Maximum Mean Standard Dev.

E (Y) (cm) 428 0.03493 0.55721 0.14371 0.09692

X1 (cm) 428 0.02032 0.36407 0.07133 0.04807

X2 (cm2) 428 0.00041 0.13254 0.00739 0.01276

X3 (m2) 428 0.00000 0.41104 0.05514 0.07037

Y (cm) is the expected value of periodic annual diameter increment 14 to 16 years after treatment.

X1 (cm) initial diameter.

X2 (cm2) is the square of X1.

X3 (m2) is the sum of the residual trees’ basal area in trees with dbh larger than the subject tree’s dbh1

divided by the subject tree's diameter.

N is the number of observations.

measured in a plot or stand (Dolph 1988, Ritchie and Hann 1985, Wykoff 1986). Because X3 is the sum

of basal area of the residual trees in trees with diameter larger than the subject tree’s diameter, the

largest-diameter tree in the plot would have an X3 value of zero, whereas the smallest-diameter tree in

the plot would have an X3 value near but somewhat less than the plots’s total basal area.

Additionally, the increment attained by an individual tree is also dependent on its competitive

status relative to neighboring trees—a tree’s relative size. As a result, relative size is tied to stand

density. Therefore, in sparsely stocked plots or stands, dominance would be less of a factor,

because the more open-grown the tree, the less it is influenced by competitors (Wykoff 1990). The

effect of competitive stress due to neighboring trees is represented by X3 , because for a given tree,

diameter increment should decrease as X3 increases and vice versa. Consequently, the coefficient

of X3 is negative, indicating a competition modifier that would reduce diameter growth rates
22 USDA Forest Service Research Paper PSW-RP-238. 1998.

relative to a tree’s competitive status. Also, the size of the coefficient of X3 for the various species

indicates their competitive status relative to other species in the plot.

Conclusion

Regardless of timber sale area and species, residual trees responded to overstory removal by

increasing their diameter growth after adjusting to their new environment (the 9- to 16-year

period) (fig. 13). Although not statistically tested, units with the most overstory removed showed

the highest diameter response after treatment, whereas units with low amounts of overstory

removal showed the least diameter response regardless of timber sale area (Figs. 1—13).

Finally, examination of the linear regression equations developed to predict periodic annual

diameter increment 14 to 16 years after treatment shows that the equations are consistent with our

current biological and silvicultural knowledge. Although the coefficients for some of the species were

not statistically significant, all the independent variables strengthened the regression equations.

References

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the Sierra Nevada. Res. Note PSW-368. Berkeley, CA: Pacific Southwest Forest and Range Experiment Station, Forest

Service; U.S. Department of Agriculture; 4 p.

Dolph, K. Leroy. 1988. Prediction of periodic basal area increment for young-growth mixed conifers in the Sierra

Nevada. Res. Paper RP-190. Berkeley, CA: Pacific Southwest Forest and Range Experiment Station, Forest Service,

U.S. Department of Agriculture; 20 p.

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Oliver, C.D.; Larson B.C. 1996. Forest stand dynamics, updated edition. New York: Wiley; 502 p.

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USDA Forest Service Research Paper PSW-RP-238. 1998. 23
24 USDA Forest Service Research Paper PSW-RP-238. 1998.
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PSW-RP-238

Research PaperResearch StationPacific SouthwestForest Serviceof AgricultureDepartmentUnited States

Overstory Removal in Mixed Conifer StandsPeriodic Annual Diameter Increment After