DEPAR TMENT OF AGRICULT URE

True Fir Spacing and 

Yield Trials—20-Year 

Update

Robert O. Curtis

United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

Research Paper

PNW-RP-590

May 2013
Non-Discrimination Policy

The U.S. Department of Agriculture (USDA) prohibits discrimination against its customers, 

employees, and applicants for employment on the bases of race, color, national origin, 

age, disability, sex, gender identity, religion, reprisal, and where applicable, political beliefs, 

marital status, familial or parental status, sexual orientation, or all or part of an individual’s 

income is derived from any public assistance program, or protected genetic information in 

employment or in any program or activity conducted or funded by the Department. (Not all 

prohibited bases will apply to all programs and/or employment activities.) 

To File an Employment Complaint

If you wish to file an employment complaint, you must contact your agency’s EEO Counselor 

(PDF) within 45 days of the date of the alleged discriminatory act, event, or in the case of a 

personnel action. Additional information can be found online at http://www.ascr.usda.gov/

complaint_filing_file.html. 

To File a Program Complaint

If you wish to file a Civil Rights program complaint of discrimination, complete the USDA 

Program Discrimination Complaint Form (PDF), found online at http://www.ascr.usda.gov/

complaint_filing_cust.html, or at any USDA office, or call (866) 632-9992 to request the 

form. You may also write a letter containing all of the information requested in the form. 

Send your completed complaint form or letter to us by mail at U.S. Department of Agriculture, Director, Office of Adjudication, 1400 Independence Avenue, S.W., Washington, D.C. 

20250-9410, by fax (202) 690-7442 or email at program.intake@usda.gov. 

Persons with Disabilities

Individuals who are deaf, hard of hearing or have speech disabilities and you wish to file 

either an EEO or program complaint please contact USDA through the Federal Relay 

Service at (800) 877-8339 or (800) 845-6136 (in Spanish). 

Persons with disabilities, who wish to file a program complaint, please see information 

above on how to contact us by mail directly or by email. If you require alternative means 

of communication for program information (e.g., Braille, large print, audiotape, etc.) please 

contact USDA’s TARGET Center at (202) 720-2600 (voice and TDD). 

Supplemental Nutrition Assistance Program

For any other information dealing with Supplemental Nutrition Assistance Program (SNAP) 

issues, persons should either contact the USDA SNAP Hotline Number at (800) 221-5689, 

which is also in Spanish or call the State Information/Hotline Numbers. 

All Other Inquiries

For any other information not pertaining to civil rights, please refer to the listing of the USDA 

Agencies and Offices for specific agency information. 

Author

Robert O. Curtis is an emeritus scientist, Forestry Sciences Laboratory, 

3625 93rd Avenue, SW, Olympia, WA 98512-1101.
Abstract

Curtis, Robert O. 2013. True fir spacing and yield trials—20-year update. 

Res. Pap. PNW-RP-590. Portland, OR: U.S. Department of Agriculture, 

Forest Service, Pacific Northwest Research Station. 32 p.

This report updates data and comparisons from previous reports (Curtis and 

others 2000, Curtis 2008) on a series of precommercial thinning and yield trials 

in high-elevation true fir–hemlock stands, using data from the 12 replicates 

for which 20-year data are now available. The stands were varying mixtures 

of Pacific silver fir (Abies amabilis (Douglas ex Loudon) Douglas ex Forbes), 

western hemlock (Tsuga heterophylla (Raf.) Sarg.), and noble fir (Abies procera

Rehder). Trends noted in the 2008 report continue. Increment in top height was 

somewhat reduced at wide spacings. Volume increment and basal area increment 

increased as the residual number of trees increased. There was a small increase 

in diameter increment of the 80 largest trees per acre at wide spacing. Relative 

stand densities on the unthinned plots, as measured by stand density index (SDI) 

and relative density (RD), are still increasing; it appears that the maximum (not 

yet attained) is probably at least 20 to 25 percent greater than values observed in 

Douglas-fir.

Keywords: Precommercial thinning, increment, yield, Abies amabilis, Tsuga 

heterophylla, Abies procera, true firs, noble fir, Pacific silver fir.
ii

research paper PNW-rp-590

Summary

This report updates data and comparisons from previous reports (Curtis and others 

2000, Curtis 2008) on a series of precommercial thinning and yield trials in highelevation true fir–hemlock stands, using data from the 12 replicates for which 

20-year data are now available. The stands were varying mixtures of Pacific silver 

fir (Abies amabilis (Douglas ex Loudon) Douglas ex Forbes), western hemlock 

(Tsuga heterophylla (Raf.) Sarg.), and noble fir (Abies procera Rehder). Treatments 

included five levels of the residual number of trees plus an unthinned treatment. 

Trends noted in the 2008 report continue. Increment in top height was somewhat 

reduced at very wide spacings. Volume increment increased but at a decreasing 

rate as the residual number of trees increased, similar to trends observed in other 

thinning studies. Basal area increment increased with the residual number of trees 

at wide spacings, but was nearly constant for 430 and 700 trees per acre. There was 

an increase in diameter increment of the 80 largest trees per acre at wide spacing. 

Relative stand densities on the unthinned plots, as measured by stand density index 

(SDI) and relative density (RD), are still increasing. Maximum SDI and RD (not 

yet attained) will probably be at least 20 to 25 percent greater than corresponding 

values for Douglas-fir. Differences in height growth patterns between true firs and 

Douglas-fir, combined with the ability of true fir–hemlock stands to develop high 

basal areas, imply that true fir–hemlock stands of a given site index will be considerably more productive than Douglas-fir stands of the same numerical site index. 

Continuation of these trials for the next several decades should provide reliable 

information on development patterns and silvicultural responses that is needed as 

part of the process of developing models to guide management decisions.
iii

True Fir Spacing and Yield Trials—20-Year Update

Contents

1 Introduction

2 Previous Research

2 Past Management

3 The Study

4 Objectives

4 Study Area

4 Study Design

6 Plot Establishment and Measurement

9 Data Summarization

9 Height Estimates

9 Volume Estimates

10 Site Index Estimates

10 Species Composition

11 Analyses

12 20-Year Increment Analyses

18 Yield Analyses

23 Relative Stand Density Limits

25 Discussion

28 Acknowledgments

28 Metric Equivalents

29 References

32 Glossary of Symbols and Acronyms
iv

research paper PNW-rp-590
1

True Fir Spacing and Yield Trials—20-Year Update

Introduction

From 1987 to 1994, 18 precommercial thinning trials were established in true 

fir–hemlock stands along the west side of the Cascade Range in Washington and 

Oregon and in Washington’s Olympic Mountains. Establishment and 5-year results 

were reported by Curtis and others (2000), and 10-year results by Curtis (2008). 

The stands studied are within the Coastal True Fir–Hemlock type (Society of 

American Foresters type 226: Eyre 1980), primarily within the Abies amabilis zone

(Franklin and Dyrness 1973) but also with two in the Tsuga mertensiana zone. The 

principal tree species are Pacific silver fir (Abies amabilis (Douglas ex Loudon) 

Douglas ex Forbes), noble fir (Abies procera Rehder), and western hemlock (Tsuga 

heterophylla (Raf). Sarg.). Other minor associated species include western redcedar 

(Thuja plicata Donn ex D. Donn), yellow cedar (Chamaecyparis nootkatensis (D. 

Don) Spach), mountain hemlock (Tsuga mertensiana (Bong.) Carrière), subalpine 

fir (Abies lasiocarpa (Hook) Nutt.), western white pine (Pinus monticola Douglas 

ex D. Don) and Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco).

True fir–hemlock forests at higher elevations in the Cascade Range and Olympic Mountains play major roles as protective cover for watersheds and as scenic and 

recreational areas, and have in the past been important as timber-producing forests. 

Large areas of Abies amabilis–zone forest exist in the Mount Baker–Snoqualmie 

(MBS), Gifford Pinchot (GP), Olympic (OLY), Mount Hood (MH), and Willamette 

(WIL) National Forests. There are large additional areas in the national parks in 

the region, and limited areas on Washington Department of Natural Resources 

(WDNR) lands and on private ownerships. There are also large areas of similar 

forests that are important timber-producing areas on Vancouver Island and in the 

Coast Range of British Columbia.

This report is a partial update of the 2008 publication, with additional data and 

some differences in procedure. It repeats much of the background information given 

in the 2000 and 2008 reports and then presents some summaries and comparisons 

based on the 12 installations for which 20-year data are now available. Complete 

20-year measurements (at 0, 5, 10, and 20 years from establishment) from all 18 

installations will not be available for several years. It seemed desirable to carry out 

an interim analysis to (1) present currently available information, (2) provide guidance for later workers who may analyze the complete set, and (3) utilize the author’s 

acquaintance with the study from its inception. Any future analyst will not have 

this direct knowledge, and future capabilities may also be handicapped by prospective personnel and funding limitations. 

This report is an update 

of the 10-year results 

published in 2008.
2

research paper PNW-rp-590

Previous Research

Although there is a considerable body of information on stand development, yields, 

and site evaluation for low-elevation hemlock, little information is available on the 

true firs and high-elevation true fir–hemlock mixtures.

Herman and others (1978) and Hoyer and Herman (1989) developed height 

growth and site index estimates for noble fir and Pacific silver fir, based on stem 

analyses of trees from unmanaged old-growth stands. However, Murray and others 

(1991) found that early height growth of young Pacific silver fir and noble fir established on clearcuts was considerably more rapid than was predicted by the above 

curves. Thus, applicability of these curves to young stands appears problematic 

because of differences in stand establishment conditions and early competition, climatic changes, and possible biases associated with changes in competitive position 

over time of sample trees used in stem analyses.

Harrington and Murray (1982) compared height growth patterns in young 

Pacific silver fir, noble fir, and Douglas-fir. They point out that true firs characteristically have a period of slow juvenile growth, an extended period of almost linear 

rapid growth, and a final phase of appreciable growth extending to very advanced 

ages. Consequently, true firs often appear at an initial disadvantage in comparison 

with associated species, but may later equal or surpass their associates because of 

the longer period of sustained height growth.

Oliver and Kenady (1982) provided a summary of existing information for these 

species as of that date. Various U.S. Forest Service plant association guides have 

since presented several indicators of productivity by plant association (Brockway 

and others 1983; Hemstrom and others 1982; Henderson and Peter 1984; Henderson 

and others 1989, 1992; Logan and others 1987).

Past Management

Extensive harvesting in the true fir–hemlock forest type began in the early 1950s. 

Early operations commonly followed practices that generally had been successful in 

lower elevation Douglas-fir: namely, clearcut, burn the slash, and plant—often with 

Douglas-fir. A high proportion of these early plantations failed, and regeneration to 

true fir–hemlock took place by natural seeding over an extended period of years. 

The resulting stands are often patchy and contain considerable variability in tree 

sizes and ages. 

Over subsequent years, better species selection combined with improved nursery, site preparation, and planting practices greatly improved survival and produced 

many successful plantations. Favored species for planting have been noble fir or 

noble fir–Pacific silver fir mixtures, with other species such as Engelmann spruce 

A shift to planting true 

firs occurred after 

the frequent failures 

of earlier Douglas-fir 

plantations.
3

True Fir Spacing and Yield Trials—20-Year Update

(Picea engelmanni Parry ex Engelm.) or western white pine used on some frostprone sites. Reduced use of fire favored survival of natural advance regeneration of 

Pacific silver fir and hemlock. Numerous young true fir–hemlock stands now exist 

at higher elevations along the west side of the Cascade Range and in the Olympic 

Mountains.

Extensive precommercial thinning (PCT) began in the late 1970s. There has 

been some question about the feasibility or desirability of future commercial 

thinning, because some stands are on steep terrain and because these thin-barked 

species are highly susceptible to rot arising from logging injuries.

Common practice in the late 1970s through the 1990s was to thin at an early 

age to 350 to 400 stems per acre. Some foresters further reduced the number of 

leave trees, with the expectation that no further entry might be feasible until final 

harvest. This raised concerns about the effects of the number of residual trees on 

future stand development and the average tree size at which precommercial thinning should be done.

Today, much of the land under the Northwest Forest Plan (Thomas and others 

2006) is in late-successional old-growth forest reserves or wilderness currently 

managed for old-growth protection, restoration of old growth, or protection of 

old-growth-dependent species. The rest is mostly in matrix or adaptive management 

areas. A considerable portion of these areas is in the Abies amabilis zone. In some 

areas, the management goal is future timber production, whereas others are managed primarily for watershed, wildlife, or recreation values. Whatever the present or 

possible future management objectives, information about the dynamics of young 

true fir forests is very limited.

The Study

From 1987 to 1994, the Pacific Northwest Research Station (PNW) installed a 

series of 18 replicates of a spacing and yield trial in true fir–hemlock stands, with 

assistance from the Pacific Northwest Region of the U.S. Forest Service and the 

individual national forests concerned. These trials were established in stands considered ready for PCT under then-current operational practices. Seven were on the 

Mount Baker–Snoqualmie, one on the Olympic, five on the Gifford Pinchot, four 

on the Mount Hood, and one on the Willamette National Forests.

Extensive 

precommercial 

thinning began in 

the late 1970s.
4

research paper PNW-rp-590

Objectives 

Study objectives were to (1) determine the quantitative response of true fir–hemlock stands to a range of PCT stocking levels, and (2) obtain long-term growth data 

applicable to young managed stands as a basis for estimating development patterns 

and potential yields.

These trials should ultimately provide:

• Information on development of PCT stands needed for reliable estimates of 

productivity of young true fir–hemlock stands.

• Data useful, in combination with other data, for construction of simulators 

and stand projection systems for young-growth managed stands.

• A basis for choosing the optimum number of leave trees to meet different 

management goals.

• Information on successional and structural development over time for possible use in meeting landscape diversity, species habitat, and watershed 

management objectives.

Study Area 

The study area consists of the true fir–hemlock type as it occurs on the Mount 

Baker, Gifford Pinchot, Mount Hood, and Willamette National Forests. Emphasis 

was on stands located within the Pacific silver fir zone; however, several trials 

reach into the lower portions of the mountain hemlock zone.

For some years prior to the study, the national forests had been conducting 

extensive PCT in young true fir–hemlock. Choice of locations was therefore 

constrained by the fact that many otherwise suitable stands had already been 

operationally thinned.

Sites selected ranged from 3,000 to 4,500 ft in elevation. Most of the plant 

associations found on the study sites have widespread distribution within the 

respective national forests, according to plant association guides. Basic descriptive 

information for the installations is shown in table 1. 

Study Design

The study design is that of randomized blocks, with one unthinned and five 

thinning treatments per block. Where feasible, two plots of each treatment were 

established at a location for a total of 12 plots per installation. Few relatively 

homogeneous areas large enough to accommodate 12-plot installations were found. 

Of the 18 installations, 3 have 12 plots, 14 have 6 plots, and 1 has 5 plots (because 

initial stocking was insufficient to allow one of the thinning treatments).

Most of the stands in 

the study area were 

in the Abies amabilis

zone.
5

True Fir Spacing and Yield Trials—20-Year Update

Table 1—Basic descriptive information for the true fir spacing study installations

National Year Stand Breast Age at Total Dominant plant

Installation foresta Plots established origin height ageb stump age Elevation associationc

Number Year - - - - - - - Years - - - - - - - Feet

Alpine #4 MH 6 1990 Mixed 11 16 19 4,500 TSME/VAME/CLUN

Bonidu OLY 6 1990 Natural 16 21 24 3,000 ABAM/VAAL/CLUN

Cat Creek GP 6 1990 Natural 13 20 23 4,300 ABAM/RHAL

Crevice Creek MBS 6 1988 Mixed 22 26 29 3,000 ABAM/VAAL/CLUN

Cumberland MBS 6 1988 Natural 12 17 20 3,200 ABAM/VAAL/CLUN

Dog Creek MH 6 1991 Planted 13 17 20 3,600 ABAM/RNMA/XETE

Evans Creek MBS 6 1989 Natural 32 38 41 3,700 ABAM/VAAL/CLUN

Haller Pass MBS 5 1989 Planted 24 29 32 4,200 ABAM/VAME

Iron Mountain MBS 12 1987 Natural 19 25 28 3,500 ABAM/VAAL/CLUN

Pointer #3 GP 12 1991 Planted 10 14 17 4,100 TSME/VAME/XETE

Rattrap Pass MBS 6 1988 Mixed 14 20 23 3,200 ABAM/VAAL/CLUN

Tonga Ridge MBS 6 1989 Mixed 20 26 29 3,800 ABAM/VAAL/CLUN

The following installations were not used in this report because 20-year measurements were not yet available

Job #2 GP 6 1992 Planted 8 14 17 3,700 ABAM/ACTR/CLUN

Marys Creek WIL 6 1994 Planted 8 12 15 4,000 ABAM/RHMA/BENE

Memaloose MH 6 1992 Planted 13 21 24 4,000 ABAM/RHMA/XETE

North Mountain #2 MH 6 1993 Mixed 12 17 20 3,200 ABAM/VAAL/COCA

Cabin #2 GP 6 1994 Planted 7 11 14 3,000 ABAM/BENE

Twin #1 GP 12 1994 Planted 10 15 18 3,800 ABAM/VAME/CLUN

a

 National forest (NF) as follows: GP = Gifford Pinchot, MH = Mount Hood, MBS = Mount Baker–Snoqualmie, OLY = Olympic, WIL = Willamette.

b

 Years since attaining breast height.

c

 Plant associations are given in table 4.

Treatments—

The treatments consisted of five spacings, plus no treatment (NT). The corresponding target values in number of trees per unit area were as follows:

Spacing (ft) Trees per acre Area per tree (sq ft)

7.9 700 62.2

10.1 430 101.2

12.8 265 164.6

16.4 163 267.7

20.9 100 436.5

Seven hundred and 100 trees per acre were chosen as the limits of the range considered for thinning treatments, and intermediate values were calculated using a 

constant percentage change in area per tree.

Treatments were randomly allocated to plots within an installation.
6

research paper PNW-rp-590

Plot design—

Measurement plots were square within a larger treatment plot, of the dimensions 

given in table 2. In the first installation (Iron Mountain), the treatment plot was 200 

ft on a side. Thereafter, it was reduced to 180 ft (occasionally 160 ft) because of the 

difficulty in fitting plots into the available area. The plot sizes selected were thought 

sufficient to (1) give reasonably smooth diameter distributions, (2) give values reasonably stable in the presence of minor mortality, and (3) allow continuation of the 

plot to advanced ages, with or without one later thinning.

Measurement plot size was about 0.25 ac, with a slightly smaller plot (0.20 ac) 

for the unthinned plot and somewhat larger plots for the widest spacings, so that a 

reasonable number of leave trees would be included. To facilitate control of leavetree marking, the sides of the measurement plots were made multiples of the desired 

spacings, thus allowing subdivision of the plots into strips corresponding to the 

desired spacings.

Table 2—Standard dimensions of plots used in true fir spacing trials

Treatment plot Measurement plot

Treatment Spacing Area Side Area Side Buffer width

Number/acre Feet Acres Feet Acres Feet Feet

No thin ― 0.7438 180 0.200 93.3 43.4

700 7.9 .7438 180 .242 102.7 38.6

430 10.1 .7438 180 .234 101.0 39.5

265 12.8 .7438 180 .241 102.4 38.8

163 16.4 .7438 180 .302 114.8 32.6

100 20.9 .7438 180 .361 125.4 27.3

― = not applicable.

Plot Establishment and Measurement

Plot layout―

True fir–hemlock stands are characteristically patchy, and variation is unavoidable, but plot locations were selected to be as nearly comparable in site conditions 

and initial stand conditions as feasible. Plots were either contiguous or quite close 

to each other. Obvious site changes and root rot pockets were excluded. Treatments 

were assigned randomly after the treatment plots were located on the ground but 

before the measurement plots were established.

After initial plot location and treatment assignment, the corners of treatment 

plots and interior measurement plots were established with staff compass and tape. 

All distances were measured horizontally. Measurement plot boundary closure was 

within 2 ft.
7

True Fir Spacing and Yield Trials—20-Year Update

Initial tree measurements and marking―

Plots were subdivided with string at intervals equal to the desired spacing, and 

leave trees were selected as the best tree within each grid cell. To the extent possible, all treatment plots within an installation were adjusted to nearly comparable 

species composition. Tree vigor was given precedence over strict adherence to spacing or species criteria. Occasional exceptionally large (and presumably older) trees 

were excluded to make leave-tree diameter distributions and average diameters 

more comparable. All trees 0.6 in and larger in diameter at breast height (d.b.h.) 

were tallied by species and 1-in d.b.h. classes before thinning.

Because some cells within the grid lacked suitable leave trees, the specified 

numbers of leave trees were not met in all cases. Shifts in overall species composition caused by the thinning treatments were generally minor.

Leave-tree measurements―

Trees were measured after the growing season. Diameters at breast height were 

measured to the nearest 0.1 in (by diameter tape) on all leave trees on thinned 

plots, and on all trees 0.6 in d.b.h. and larger present on the unthinned plots. Initial 

number of trees 0.6 in and larger ranged from 395 per acre at Haller to 4,195 at 

Cumberland. 

Heights and heights to live crown were measured to the nearest 0.1 ft (with 

height poles or—in later remeasurements―with a laser instrument). Heights were 

measured on all leave trees at the two widest spacings, on the first two of every 

three trees at the 12.8-ft spacing, and on every other tree at the two closest spacings.

In unthinned plots, heights and heights to live crown were measured for at 

least 40 trees, more in mixed-species stands. Trees were selected across the entire 

plot and across the full range of diameter classes present, with about two-thirds of 

selected trees above the average diameter and one-third below. 

Stand age estimates―

Ring counts were made at breast height (b.h.) and stump height on a sample of trees 

cut in thinning, excluding trees showing a suppressed core. There was considerable variation because of differences in species growth rates, and because natural 

regeneration often occurred over several years. Regressions of ring count on d.b.h. 

were fit to all sample tree data from an individual installation. These equations 

were then used to estimate the average number of rings at breast and stump heights 

corresponding to mean diameter of leave trees on all thinned plots at an installation. Total age was taken as the estimated number of rings at stump +3, and was 

checked against date of planting in cases of known planting date and good survival. 

Seedlings established as advance regeneration (principally, Pacific silver fir) may 
8

research paper PNW-rp-590

Table 3—Species names in true fir spacing trials

Common name Scientific name Acronym

Trees:

Pacific silver fir Abies amabilis (Douglas ex Loudon) Douglas ex Forbes ABAM

Subalpine fir Abies lasiocarpa (Hook.) Nutt ABLA

Noble fir Abies procera Rehder ABPR

Yellow cedar Chamaecyparis nootkatensis (D. Don) Spach CHNO

Engelmann spruce Picea engelmanni Parry ex Engelm. PIEN

Western white pine Pinus monticola Douglas ex D. Don PIMO

Douglas-fir Pseudotsuga menziesii (Mirb.) Franco PSME

Western redcedar Thuja plicata Donn ex D. Don THPL

Western hemlock Tsuga heterophylla (Raf.) Sarg. TSHE

Mountain hemlock Tsuga mertensiana (Bong.) Carrière TSME

Shrubs and herbs:

Vanilla leaf Achlys triphylla (Sm.) DC. ACTR

Dwarf Oregon grape Berberis nervosa Pursh BENE

Queencup beadlily Clintonia uniflora (Menzies ex Schult. & Schult. f.) Kunth CLUN

Bunchberry Cornus canadensis L. COCA

Cascades azalea Rhododendron albiflorum Hook. RHAL

Rhododendron Rhododendron macrophyllum D. Don ex G. Don RHMA

Alaska huckleberry Vaccinium alaskaense Howell VAAL

Big huckleberry Vaccinium membranaceum D. Don ex G. Don VAME

Beargrass Xerophyllum tenax (Pursh) Nutt. XETE

have widely differing numbers of years in a suppressed condition and were not included in the above age estimates.

Estimated total stand ages at establishment ranged from 14 to 41 years. Elevations ranged from a low of 3,000 ft (Bonidu) to 4,500 ft (Alpine).

Description of ground vegetation―

All installations were classified by dominant plant association, in most cases by 

the area ecologist for the given national forest. More detailed descriptions were 

made for those installations located in the Mount Baker–Snoqualmie and Olympic 

National Forests (Curtis and others 2000), including ground vegetation species 

identification and inventory. Species acronyms and plant associations are shown in 

tables 3 and 4.

Remeasurement schedule―

All plots were remeasured at 5 and 10 years after establishment. Thereafter, they 

were placed on a 10-year remeasurement schedule, because of limitations in personnel and funding. Ingrowth trees 1.6 in in diameter or greater were tagged and 

recorded, on the entire plot at years 5 and 10 and thereafter on a subsampling basis 

(because of the large numbers present on some widely spaced plots).
9

True Fir Spacing and Yield Trials—20-Year Update

Table 4—Plant associations in true fir spacing trials

Plant associationsa

Pacific silver fir/Alaska huckleberry/queencup beadlily ABAM/VAAL/CLUN

Pacific silver fir/big huckleberry ABAM/VAME

Pacific silver fir/big huckleberry/queencup beadlily ABAM/VAME/CLUN

Pacific silver fir/Cascade azalea ABAM/RHAL

Pacific silver fir/rhododendron/queencup beadlily ABAM/RHMA/XETE

Pacific silver fir/vanilla leaf/queencup beadlily ABAM/ACTR/CLUN

Pacific silver fir/Alaska huckleberry/bunchberry ABAM/VAAL/COCA

Pacific silver fir/rhododendron/dwarf Oregon grape ABAM/RHMA/BENE

Pacific silver fir/dwarf Oregon grape ABAM/BENE

Mountain hemlock/big huckleberry/queencup beadlily TSME/VAME/CLUN

a

 Sources: Brockway and others 1983; Henderson and others 1989, 1992; Logan and others 1987.

Because of scheduling and access problems, not all intended 20-year measurements were made at exactly 20 years, although to date the maximum deviation has 

been 2 years.

Data Summarization

Height Estimates 

Height/diameter equations of the form

ln(H – 4.5) = a + b ∙ ln(D) + c ∙ ln2

(D)

were fit to data for each plot and each measurement, separately for each species for 

which reasonable samples were available. When samples were small, the squared 

term was omitted. These equations were then used to assign estimated heights to 

all trees for which actual measured heights were not available.

Volume Estimates

Cubic volumes of the entire stem (CVTS) were calculated using the following 

equations entered with measured d.b.h. and either measured or estimated height, 

as available.

• Pacific silver fir and noble fir: table 10 in Browne (1962).

• Redcedar and yellow cedar: table 4 in Browne (1962).

• Western hemlock and mountain hemlock: Wiley (1978).

• Douglas-fir: Bruce and DeMars (1974).

• Other miscellaneous species: Browne (1962).
10

research paper PNW-rp-590

Site Index Estimates

Site index estimates are based on mean height (measured or estimated) of silver 

fir included in the 80 largest diameter trees per acre. Silver fir was selected as the 

reference species because it is the most abundant. Eighty trees per acre rather than 

the more usual 40 per acre was chosen because, with these mixed-species stands 

and relatively small plots, 40 per acre often gives very small samples for a species. 

Previous work (Curtis 2008) had shown that top heights (H80) at the 10-year 

measurement in the widest spacings were often lower than the installation mean. 

For the 20-year data, graphs of H80 by treatment were plotted for each installation. 

In some installations, there was no apparent relation; in others, values for the widest 

spacings were markedly less. In the latter cases, site index estimates were based on 

treatments 1 through 4 only. A single mean site index was used for all plots within 

an installation.

The estimated site index for silver fir used here is a weighted mean of estimates 

from measured or estimated heights of silver fir included in the largest 80 trees per 

acre, and estimates based on conversion of corresponding values for noble fir and 

for hemlock to a silver fir site index. A site index based on silver fir measurements 

only is not feasible because not all plots have silver fir present.

Silver fir site indices were calculated using equations from Nigh (2009). Hemlock site indices were based on Wiley (1978) and converted to corresponding silver 

fir site indices using Nigh (1998).

Murray and others (1991) showed that the existing site index equations for noble 

fir (Herman and others 1978) are not satisfactory for young stands established on 

recent clearcuts. Limited comparisons suggested that height trends in the current 

data are more or less proportional to the silver fir trends, and Nigh (2009) was 

therefore used to assign noble fir site indices. Murray and others (1991) found that 

for silver fir and noble fir of comparable age established on clearcuts, the noble 

fir was about 10 percent taller than the associated silver fir at age 20. This value 

appeared consistent with the very limited comparisons possible with the current 

data, and was therefore used to convert noble fir estimates to corresponding silver 

fir estimates.

Species Composition 

Species composition was calculated as the percentage of total basal area represented 

by each species at the most recent (20 year) measurement on each plot. This was 

done on an individual plot basis because in some installations there are considerable 

differences among plots. It is evident both from other knowledge and from graphical comparisons that noble fir and western hemlock generally outgrow silver fir. 

Site index estimates 

are based on the 

heights of Pacific 

silver fir.
11

True Fir Spacing and Yield Trials—20-Year Update

Therefore, in the analyses discussed below, species composition is represented by 

a single variable, “%nfwh,” equal to the sum of the basal area percentages of noble 

fir and hemlock.

Analyses 

The regression analyses discussed below were preceded by fairly extensive graphical comparisons, most of which are omitted here. 

Stocking can be expressed as either target spacing (spac), target number of 

trees (TN), or actual number of tagged leave trees (TPA) present after thinning. 

In general, there is little difference between TN and TPA. Average area per tree 

= spacing2 = 43,560/TN, and therefore spacing = 208.7/sqrt(TN). Thus, TN and 

spacing are alternate transformations of the same basic variable. Below, I have 

generally used TN in preference to TPA; primarily because TN lends itself to 

simple graphical comparisons.

In the following work, regressions were fit using the stepwise option of 

PROC REG in SAS (Freund and Littell 1991). As is often the case with stepwise 

regressions, there were frequently several combinations of variables that gave 

similar values of the coefficient of determination (RSQ). Selection of equations 

here presented was a judgment call based on a combination of (1) RSQ values, 

(2) nominal significance of individual variables, (3) avoidance of equations with 

large numbers of predictor variables, and (4) consistency with trends shown in 

graphical comparisons. Because the equation forms were derived from the data 

rather than from any pre-specified hypotheses, nominal significance values 

(generally p < 0.01 for variables included) were interpreted only as guides to 

relative importance of variables. Goodness of fit was expressed as adjusted 

RSQ, which measures the reduction in the mean square due to regression and 

compensates for the effect of increase in the number of variables (Freund and 

Littell 1991, 23).

Two parallel analyses were done for each of the variables: CVTS, basal area 

(BA), and mean diameter of the largest 80 trees per acre (D80). The first analysis 

was a series of regressions of 20-year net change on stand variables. (In those cases 

where the measurement interval differed from 20 years, values were adjusted by 

proportion to a 20-year basis.) Twenty-year H80 increment was also regressed on 

stand variables. The number of 20-year observations available in each case was 59.

The second analysis was a series of yield regressions relating the logarithm of 

attained values of CVTS, BA, and D80 at years 0, 5, 10, and 20 to stand variables. 

Here, the number of observations was 59 × 4 measurements = 236.

Parallel analyses 

were done of 20-year 

increment and yield.
12

research paper PNW-rp-590

Figure 1—Means of 20-yr ∆H80 by treatment, thinned plots only, all species combined, with error 

bars for ± 1 standard error. TN = number of trees per acre left after thinning.

20-year Increment Analyses

20-year change in H80 (∆H80)—

Figure 1 shows mean values of 20-year increments in H80 by treatments, for 

thinned plots only with all species combined. Average increments were considerably less at the widest spacings (treatments 5 and 6), although this trend was not 

apparent in all individual installations.

 A simple regression of 20-year ∆H80 on spacing showed that 20-year ∆H80 

was significantly (p = 0.02) though very loosely correlated with spacing. Addition 

of the variables %nfwh and site index markedly improved the fit. The coefficient 

of spacing was negative and remained virtually unchanged as additional variables 

were added (table 5). There is on average a reduction in H80 growth associated with 

the wide spacings. This effect was considerably smaller than the effects of species 

composition and of site index. Also, as might be expected, height growth declines 

somewhat with increase in age at thinning—which is associated to some degree 

with site quality. Mean 20-year 

∆H80 increment (feet)

35

30

25

20

15

10

5

0

TN-700 TN-430 TN-265 TN-163 TN-100

Treatment

Top height increments 

were considerably less 

at the widest spacings.
13

True Fir Spacing and Yield Trials—20-Year Update

Table 5―Coefficients in regression: 20-year ∆H80 = a + Σb1∙X1 + ....... Thinned plots only; n = 59

Equation Initial age at

number Constant %nfwh Spacing Site index breast height Adj RSQ

1 35.2939 -0.43517 0.074

2 27.7941 0.14310 -0.42537 0.632

3 19.4926 0.12423 -0.43059 0.12287 0.671

4 22.5574 0.10179 -0.42438 0.16053 -0.28357 0.727

RSQ = coefficient of determination. 

Note: See “Glossary of Symbols and Acronyms” for definition of terms.

20-year net change in CVTS (∆CV)—

Means, maximums, and minimums of 20-year net change in CVTS by treatments 

are shown in figure 2. It is evident that volume growth declines with decreasing 

number of trees.

Figure 2—Means, maximums, and minimums of 20-year net ∆CVTS, with error bars for ± 1 

standard error. TN = number of trees per acre left after thinning.

In most, although not all, of these and later regressions, species composition as 

expressed by %nfwh appeared to be an important variable. This is consistent with 

general knowledge of species characteristics. In the regressions presented, %nfwh 

was forced into the regressions. 20-year net 

∆CVTS increment (ft3/acre)

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

No thin TN-700 TN-430 TN-265 TN-163 TN-100

Treatment

Mean

Maximum

Minimum Volume increments 

declined with a 

reduced number 

of leave trees.
14

research paper PNW-rp-590

Table 6―Coefficients in regressions: 20-year net ∆CV = a + Σb1 ∙ X1 + ... Thinned plots only; n = 59

Equation Constant %nfwh S S/TN S/sqrt(TN) S∙ln(TN) ln(elev) A1 S∙A1 S∙D1 B1 AdjRSQ

5 17088 100.98 -4385.1 -2424.56 0.761

6 30243 10.16 -627.4319 -3171.07 -404.12 6.55394 0.872

7 26167 10.723 48.381 -583.29 -3226.31 4.87 0.909

8 23454 7.73268 -1047.61 8.6863 -3024.49 28.5206 0.919

Note: See “Glossary of Symbols and Acronyms” for definition of terms.

Figure 3—Estimated 20-year net CVTS increment, based on equation 6 in table 6 using data means 

of %nfwh = 53, A1 = 17, D1 = 5.9, and elevation = 3,666. CVTS = cubic volume of entire stem.

Other variables that are obviously important are site index (S) and target 

number (TN) or transformations or combinations of these variables. In applications, 

A1 would generally be readily available, D1 and B1 (which are based on trees ≥1.6 

in d.b.h.) less so.

For regressions fit to thinned plots only, RSQs of those including B1 were 

greater than those with D1, which were greater than those with A1. A1 did not enter 

when D1 was included. Table 6 gives the equations of apparent best fit for each 

case.

Figure 3 shows the curves for sites 60, 75, and 90 based on equation 6 in table 6 

and the data mean values of %nfwh = 53, A1 = 17, and D1 = 5.9. 20-year net 

∆CVTS increment (ft3/acre)

6,000

5,000

4,000

3,000

2,000

1,000

0

0 100 200 300 400 500 600 700 800

Target number per acre

S60

S75

S90
15

True Fir Spacing and Yield Trials—20-Year Update

Figure 4—Means, maximums, and minimums of 20-year net ∆BA, with error bars for ± 1 standard 

error.

Table 7― Coefficients in regressions: 20-year net ∆BA – a + Σb1 ∙ X1 + ... Thinned plots only; n = 59

Equation Constant %nfwh S ∙ TN S ∙ TN2 S ∙ ln(TN) S/TN ln(elev) A1 D1 Adj RSQ

9 1211.72 0.16564 0.26945 -68.2816 -145.75 0.900

10 1224.86 0.08007 0.00468 -0.00000383 -145.16 -2.2986 7.2173 0.926

Note: See “Glossary of Symbols and Acronyms” for definition of terms.

20-year net change in basal area (∆BA)—

Means, maximums, and minimums of 20-year net change in BA by treatments 

(thinned plots only) are shown in figure 4. Clearly, BA increment decreases with 

decrease in the number of residual trees. 20-year net basal area increment (ft3/acre)

300

250

200

150

100

50

0

No thin TN-700 TN-430 TN-265 TN-163 TN-100

Treatment

Mean

Maximum

Minimum

Regressions were fit to data for thinned plots only. The two best equations 

obtained are given in table 7. Neither D1 nor A1 was effective individually, although 

the combination of A1 and D1 was. Interpretation of the combination of A1 and D1 

is unclear, as this is probably related to site quality.

Basal area increments 

declined with a 

reduced number 

of leave trees.
16

research paper PNW-rp-590

The relationships of 20-year net ∆BA to TN for sites 60, 75, and 90 are shown 

in figure 5. These curves are based on equation 10 in table 7, using the data mean 

values of %nfwh = 53, A1 = 17, D1 = 5.9, and elevation = 3,666. 20-year net basal area increment (ft2/acre)

180

160

140

120

100

80

60

40

20

0

0 100 200 300 400 500 600 700 800

Target number per acre

S60

S75

S90

Figure 5—Estimated 20-year net basal area increment, based on equation 10 in table 7, using data 

means of %nfwh = 53, A1 = 17, D1 = 5.9, and elevation = 3,666.

20-year change in mean diameter of the largest 80 trees per acre (∆D80)—

Means, maximums, and minimums of 20-year net change in D80 (thinned plots 

only) are shown in figure 6. ∆D80 decreased as the number of residual trees increased, although the differences are less striking than in the case of volume and 

of BA.

A series of regressions of 20-year ∆D80 on various independent variables, 

fit to thinned plots only, are shown in table 8. Fits were considerably poorer than 

those for CVTS and BA. Estimates were poor when either initial age or initial D80 

were omitted. Inclusion of either initial age or initial D80 markedly improved the 

fit, although RSQs were still much below those for the CVTS and BA regressions. 

Initial age and initial D80 did not enter together. The RSQ values were virtually 

the same for several variations of equations with five predictor variables. Initial 

age (b.h. age at time of thinning) is likely to be a more readily available value than 

initial D80, which also suggests that equation 13 is to be preferred.
17

True Fir Spacing and Yield Trials—20-Year Update

Table 8―Coefficients in regressions: 20-year ΔD80 = a +Σb1 ∙ X1 +... Thinned plots only; n = 59

Equation Constant %nfwh 1/sqrtTN S/sqrtTN S ∙ ln(TN) S2 ln(elev) A1 D1 Adj RSQ

11 35.11 0.01646 -0.00882 0.0005157 -3.49883 0.542

12 32.72 0.00994 -53.7625 0.92283 -3.1190 -0.36034 0.728

13 33.96 0.00562 -35.0461 0.71273 -3.2596 -0.12751 0.786

Note: See “Glossary of Symbols and Acronyms” for definition of terms.

Figure 6—Means, maximums, and minimums of 20-year net ∆D80, with error bars for ± 1 standard 

error.

Figure 7 shows estimates of 20-year ∆D80 given by equation 13 in table 8 for 

sites 60, 75, and 90, using the data means of %nfwh = 53, A1 = 17, and elevation = 

3,666.

The equations show response to TN increasing with site index, with little gain 

on the poorest sites. 20-year net 

∆D80 increment (inches)

12

10

8

6

4

2

0

No thin TN-700 TN-430 TN-265 TN-163 TN-100

Treatment

Mean

Maximum

Minimum
18

research paper PNW-rp-590

Yield Analyses

Cubic volume (CVTS)—

Regressions of the logarithm of net cubic volume yield on TN plus various stand 

variables gave the results shown in table 9. Inclusion of initial age (A1) made a 

small improvement in fit. Initial D80 (D1) had a negligible effect when considered 

alone. Including both A1 and D1 made a further slight improvement in RSQ, but at 

the cost of an excessively complicated equation; this is therefore not included in the 

table. Initial BA (B1) was an effective predictor but is inherently related to TN, and 

is therefore not included here.

Figure 7—Estimated 20-year D80 increment for site indexes 60, 75, and 90, from equation 13 in table 

8, entered with data means of %nfwh = 53, A1 = 17, and elevation = 3,666.

Table 9―Coefficients in regressions: ln(CVTS) = a + Σb1 ∙ X1 +... Thinned plots only, all measurements; 

n = 236

Equation Constant %nfwh 1/TN ln(S)∙ln(Agebh) ln(S)∙Agebh S∙ln(Agebh) ln(elev) ln(A1) ln(D1) Adj RSQ

14 -3.10416 0.00486 -116.92964 0.80576 -0.00706 0.948

15 -2.49088 0.00403 -116.57042 0.82540 -0.00622 -0.33732 0.952

16 5.55841 0.00361 -104.35798 0.78639 -0.00612 -0.72396 -1.49203 1.37866 0.971

Note: See “Glossary of Symbols and Acronyms” for definition of terms. 20-year 

∆D80 increment (inches)

10

8

6

4

2

0

0 100 200 300 400 500 600 700 800

Target number of trees

S60

S75

S90
19

True Fir Spacing and Yield Trials—20-Year Update

Figure 8—Estimated stand volume (CVTS) for site indexes 60, 75, and 90 (solid lines) by age at 

breast height, from equation 14 in table 9 for TN-100 (100 trees per acre) and overall data means 

of %nfwh and elevation. Dashed lines represent observed development of TN-100 (100 trees per 

acre) plots.

Figure 9—Estimated stand volume (CVTS) for site indexes 60, 75, and 90 (solid lines) by age at 

breast height, from equation 14 in table 9 for TN-265 (265 trees per acre) and overall data means 

of %nfwh and elevation. Dashed lines represent observed development of TN-265 (265 trees per 

acre) plots.

Curves of CVTS over breast-high age for sites 60, 75, and 90, based on equation 14 in table 9, using the data mean values of %nfwh, site index, and elevation, 

are shown in figure 8 for TN-100, figure 9 for TN-265, and figure 10 for TN-700, 

respectively. The curves are concave upward within the range of ages in the data; 

volumes are rising steeply on the better sites. There are marked differences among 

treatments (TN), within sites. The curves (solid) are overlaid on the curves (dotted) 

obtained by connecting the four data points available for each plot(s) in the specified treatment in each installation. CVTS (ft3/acre)

5,000

4,000

3,000

2,000

1,000

0

0 10 20 30 40 50 60

Breast-high age (years)

CVTS (ft3/acre)

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

0 10 20 30 40 50 60

Breast-high age (years)

S90

S75

S60

Volume increments 

were strongly related 

to site index, age, and 

number of trees.
20

research paper PNW-rp-590

Basal area (BA)—

Similar logarithmic regressions of net BA yield on TN plus various stand variables 

gave the results shown in table 10. Inclusion of age at thinning (A1) made an appreciable improvement in fit. Inclusion of initial D80 (D1) had little effect. Inclusion 

of both A1 and D1 made a marked improvement in RSQ, but does not have a clear 

interpretation; although the combination of A1 and B1 specifies an initial condition, 

it is also likely related to site quality, and would be usable only if both values are 

available for a stand.

Table 10―Coefficients in regressions: ln(BA) = a + Σb1 ∙ X1 +... Thinned plots only, all measurements; n = 236

Equation Constant %nfwh 1/TN ln(S) ∙ ln(Agebh) ln(S) ∙ Agebh In(elev) ln(A1) ln(D1) Adj RSQ

17 -3.01920 0.00332 -119.22599 0.60054 -0.00692 0.928

18 0.81964 0.00221 -118.39108 0.58769 -0.00434 -0.32371 -0.44852 0.943

19 2.58270 0.00132 -113.50706 0.47837 -0.36636 -0.96022 0.60549 0.953

Note: See “Glossary of Symbols and Acronyms” for definition of terms.

Figure 10—Estimated stand volume (CVTS) for site indexes 60, 75, and 90 (solid lines) by age at 

breast height, from equation 14 in table 9 for TN-700 (700 trees per acre) and overall data means of 

%nfwh and elevation. Dashed lines represent observed development of TN-700 plots.
21

True Fir Spacing and Yield Trials—20-Year Update

Figure 11—Estimated basal area (BA) for site indexes 60, 75, and 90 by age at breast height, from 

equation 17 in table 10 for TN-100 (100 trees per acre) and overall data means of %nfwh, elevation, 

and A1. Dashed lines represent observed development of TN-100 plots.

Figure 12—Estimated basal area (BA) for site indexes 60, 75, and 90 by age at breast height, from 

equation 17 in table 10 for TN-265 (265 trees per acre) and overall data means of %nfwh, elevation, 

and A1. Dashed lines represent observed development of TN-265 plots.

Curves of BA over b.h. age for sites 60, 75 and 90, based on equation 17 in 

table 10, using the overall means of %nfwh = 53, elevation = 3666, and A1 = 17,

are shown as figures 11 (TN-100), 12 (TN-265), and 13 (TN-700). 
22

research paper PNW-rp-590

Diameter of the largest 80 trees per acre (D80)—

A series of stepwise regressions were run, including TN and various stand 

variables. It became apparent that it was necessary to include D1 and A1. The 

probable explanation is that initial D80 (D1) comprises a large part of attained 

D80 (much more than in the case of CVTS and BA). The selected equation (of 

several with similar RSQs) was equation 20:

ln(D80) = -1.51013 + 0.00091316 • %nfwh + 0.00589 • S • (agebh-A1)/TN –

0.02127 • agebh + 0.03036 • (agebh – A1) + 0.24375 • ln(S) • ln(agebh) – 

0.00019812 • S • agebh + 0.51489 • ln(D1)

with adjusted RSQ = 0.953. 

The corresponding curves for TN-100, TN-256, TN-265, TN-430, and TN-700 

using overall means of %nfwh, S, A1, and D1, are shown in figure 14.

Figure 13—Estimated basal area (BA) for site indexes 60, 75, and 90 by age at breast height, 

from equation 17 in table 10 for TN-700 (700 trees per acre) and overall data means of %nfwh, 

elevation, and A1. Dashed lines represent observed development of TN-700 plots.

0 10 20 30 40 50 60

Breast-high age (years)

300

250

200

150

100

50

0

Basal area (ft2/acre)

S90

S75

S60
23

True Fir Spacing and Yield Trials—20-Year Update

Figure 14—Trends of D80 over time by treatments, from equation 20 using overall means of predictor variables %sfwh, S, A1 and D1. 

Relative Stand Density Limits

Two measures of relative stand density that are widely used in the region are Curtis 

relative density (RD) (Curtis 1982) and stand density index (SDI) (Reinecke 1933). 

These measures are nearly equivalent except for a scale factor. They are often used 

as guides to desirable stocking and position of stands relative to the maximum 

possible relative density. Although the usual forms of these measures are based 

on quadratic mean diameter, it has been shown that alternative summation forms 

(RDsum and SDIsum) are less influenced by the numerous small stems of shadetolerant species that are often present (Curtis 2010, Long and Daniel 1990) in stands 

with a skewed diameter distribution.

Trends of RDsum and SDIsum over time on the unthinned plots are shown in 

figures 15 and 16. As the highest stocking present, these unthinned plots are nearest 

to some maximum possible relative density. None of the thinned plots are as yet 

close to a maximum. D80 (inches)

14

13

12

11

10

9

8

7

6

15 20 25 30 35 40

Breast-high age (years)

TN-100

TN-163

TN-265

TN-430

TN-700

Unthinned plots have 

not reached a clearly 

defined maximum 

relative density.
24

research paper PNW-rp-590

Figure 15—Observed trends of RDsum over age for unthinned plots, for (1) mixed Pacific silver fir 

and hemlock, and (2) noble fir plantations. ABAM = Pacific silver fir; TSHE = western hemlock; 

ABPR = noble fir.

Figure 16—Observed trends of SDIsum over age for unthinned plots for (1) mixed Pacific silver fir 

and hemlock, and (2) noble fir plantations. ABAM = Pacific silver fir; TSHE = western hemlock; 

ABPR = noble fir.

160

140

120

100

80

60

40

20

0

RDsum

Breast-high age (years)

0 10 20 30 40 50 60

ABAM/TSHE

Planted ABPR

900

800

700

600

500

400

300

200

100

0

SDIsum

Breast-high age (years)

0 10 20 30 40 50 60

ABAM/TSHE

Planted ABPR
25

True Fir Spacing and Yield Trials—20-Year Update

Discussion

Overall, the trends shown in the 20-year data are similar in kind to those found in 

the 10-year analysis (Curtis 2008).

• Top height (H80) increment was reduced in the 100- and 163-trees-per-acre 

treatments.

• Volume increment on thinned plots increased as number of residual trees 

increased, but at a decreasing rate.

• Basal area increment in thinned plots increased as number of residual trees 

increased, up to the 430 trees per acre. However, there was little difference 

between the 430- and 700-trees-per-acre treatments.

• There was a modest increase in diameter growth of the 80 largest trees per 

acre as number of residual trees decreased.

Thus, the decrease in top height increment at the widest spacings was at least 

partially offset by increased diameter increment. There was a re-allocation of 

growth from height increment to diameter increment.

The yield regressions (equations 14 to 20) were fit to all data combined, without 

regard to the fact that there were four measurements on each plot. The expected 

effect of such serial correlation is that estimates of regression coefficients will 

be unbiased, but that measures of fit and significance such as RSQ and F will 

be biased upward. Because a primary point of interest is the shape of the growth 

curves, it was necessary to include the intermediate measurements. The number 

of repeated measurements per plot (4) is small compared to the total number of 

measurements (265), and it was assumed that the coefficients in prediction equations would be unaffected and that RSQ values could be used for ranking different 

equations. Variables of borderline nominal significance were generally omitted.

In figures 8 through 13, the calculated volume and BA yield curves are overlaid 

on the observed growth trends of the same treatment in individual installations. 

This format (1) provides a visual impression of the concordance of the fitted yield 

curves with the actual data, and (2) shows the actual range of the basic data. The 

empirical equations presented here summarize actual observed development, but 

should not be extrapolated outside this range. One would expect yield curves to follow one of the commonly used sigmoid growth functions, but as yet the age range 

of the data is insufficient to allow fitting of these.

Residuals from even the best fitting regressions (both for 20-year increment 

and for yield) show differences associated with individual installations. These 

differences are attributable in part to imprecise site index estimates, and probably to 

incomplete expression of effects of species differences. The frequent occurrence of 
26

research paper PNW-rp-590

elevation as an effective predictor may also be substituting for these deficiencies.

Inclusion of initial age (A1) or initial D80 (D1) frequently improved fits. It is 

reasonable of expect that stage of development at time of thinning would have an 

effect on response. Ther combination of A1 and D1 is probably also related to site 

productivity, and may in part offset the deficiencies in the site index estimates. But 

with only 12 locations represented in the sample, one can have little confidence in 

the generality of the numerical coefficients for A1 and D1.

The volume yield curves show a wide difference in yield between the minimum 

(S60) and maximum (S90) site indexes present. The curves are concave upward and 

growth is accelerating on the better sites. This is in accord with the characteristic 

growth patterns of noble fir and Pacific silver fir; these typically have a prolonged 

period of slow juvenile growth followed by a long sustained period of much more 

rapid and nearly linear growth. This pattern, combined with the ability of true firs 

to develop high BAs, implies that a given 50-year site index for true firs indicates 

considerably greater potential productivity than the same site index for Douglas-fir 

although the biological rotation would likely be longer. (Also, because the site index 

used here was based on trees included in the largest 80 per acre, site index values 

based on the more usual 40 per acre would be slightly greater.)

This analysis has not summarized ingrowth as a separate component. The 

wider spacings frequently have abundant ingrowth, which because of its small size 

has as yet had little influence on volume and BA. But this is changing. It seems 

likely that the widest spacings will develop into two-storied stands, a characteristic 

that may be of importance from the wildlife and visual effects standpoints. There 

are also major differences—visually apparent but not addressed here—in shrub 

understory composition and vigor that may be important to both wildlife and 

recreational uses (such as huckleberry production).

Mortality on thinned plots has not been summarized, but has been very minor 

to date.

The original motivation for this study was a perceived need for guidelines 

for precommercial thinning. From this standpoint, it is clear that there is no gain 

in production by retaining more than about 400 trees per acre. This would be an 

appropriate choice for short rotations or if early commercial thinning were considered feasible. However, the true firs are susceptible to rot entering through logging 

injuries. Also, these lands involve high recreational and scenic values. These 

considerations, the growth patterns of the species, and the fact that the majority of 

these lands are in public ownership, all suggest that any future management for timber production will likely involve relatively long rotations and infrequent entries, in 

contrast to typical management of low-elevation Douglas-fir.

Growth is accelerating 

on the better sites.
27

True Fir Spacing and Yield Trials—20-Year Update

Considerably lower residual stocking—perhaps 200 well-distributed stems per 

acre—is probably appropriate.

At this time, it seems that evaluation of the long-term development patterns and 

yield potential of these stands are likely to become the most important aspect of 

the study. This will require that the study be continued for a considerable period of 

years. 

There are still six installations that have not reached the 20-year measurement, 

and these were therefore not included in these comparisons. The analysis should be 

reworked when the additional data become available. 

A particular point of interest is the development patterns of noble fir plantations, which make up substantial areas in the region. When all 18 installations 

become available, the data will include 8 such plantations. The noble fir plantations 

included were generally comparable to other successful plantations of the species, 

whereas those plots in naturally regenerated stands were highly selected for better 

initial stocking and greater relative uniformity than the average of existing naturally regenerated stands, which tend to be patchy and somewhat irregular.

Both early observations in noble fir plantations and observation of older, 

naturally established stands indicate that noble fir is a highly desirable species. A 

separate analysis of the eight noble fir installations would be desirable. Analysis 

of these single-species even-aged stands would be considerably neater, and would 

allow addressing a number of questions. In particular, is the assumption made 

above, that height growth curves of young noble fir are proportional to the existing 

Pacific silver fir curves (Nigh 2009), valid? If not, we should be able to develop new 

curves for young noble fir that—with only limited extrapolation—would provide 

improved site estimates for stands under age 50 at b.h.

The relative density trends for the unthinned plots (figs. 15 and 16) do not 

clearly define a maximum relative density. The denser plots have lost considerable 

numbers of trees, although many mortality trees were below the 1.6 -in diameter 

limit used in the summaries. The trends do suggest that for Pacific silver fir and 

Pacific silver fir/hemlock mixtures, the upper limit is at least 20 to 25 percent 

greater than values typical of Douglas-fir. This result is consistent with Long 

(1985), with estimates by Poage and others (2007) for western hemlock–Sitka 

spruce in southeast Alaska, and with the expectation that the limit will be higher 

for shade-tolerant species. The low position of the three noble fir stands included in 

figures 15 and 16 probably reflects some combination of the lesser shade tolerance 

of the species and the fact that—being plantations—the initial number of trees was 

much lower than in unthinned silver fir and hemlock, and tree distribution was 

more uniform.

Noble fir development 

is of particular interest.
28

research paper PNW-rp-590

Aside from immediate limitations in personnel and funding, the recent deemphasis of timber production as an objective on the national forests has meant a 

loss of the strong support that originally made this study possible. Yet, all history 

indicates that policies and needs will change over time. Although some people 

tend to dismiss the importance of these high-elevation forests for timber production, these forests include a wide range of topography and potential productivity, 

and there are very considerable areas that are highly productive and well-suited 

to timber production. Their potential productivity and response to treatment are 

also pertinent to estimates of carbon storage. Although this study was originally 

established with a timber production objective in mind, many nontimber values can 

be enhanced through silviculture, and traditional practices can be modified to be 

compatible with multiple objectives. There is no substitute for reliable information 

on development patterns and silvicultural responses as a basis for future decisions 

on management options. Basic data provided by this study will be valuable in 

developing models for this purpose. 

We cannot anticipate all future information needs, but all past experience indicates that long-term studies such as this have great value for a variety of purposes, 

including some not envisioned at the time of study establishment. It is therefore 

important that measurement of this study be continued for the next several decades.

Acknowledgments

Helpful reviews were provided by Peter Gould, David Marshall, Aaron Weiskittel, 

and Ashley Steel. Dave Thornton maintained and edited the data. Leslie Brodie 

assisted in preparation of figures.

Metric Equivalents

When you have: Multiply by: To find:

Inches (in) 2.54 Centimeters

Feet (ft) 0.3048 Meters

Square feet (ft2

) 0.929 Square meters

Acres (ac) 0.405 Hectares

Trees per acre 2.471 Trees per hectare

Square feet per acre (ft2/ac) 0.229 Square meters per hectare

Cubic feet per acre (ft3

/ac) 0.07 Cubic meters per hectare
29

True Fir Spacing and Yield Trials—20-Year Update

References

Brockway, D.G.; Topik, C.; Hemstrom, M.A.; Emmingham, W.H. 1983. 

Plant association and management guide for the Pacific silver fir zone: Gifford 

Pinchot National Forest. R6-Ecol-1301-1983. Portland, OR: U.S. Department of 

Agriculture, Forest Service, Pacific Northwest Region. 122 p.

Browne, J.E. 1962. Standard cubic foot volume tables for the commercial species 

of British Columbia. Victoria, BC: British Columbia Forest Service. 107 p.

Bruce, D.; DeMars, D.J. 1974. Volume equations for second-growth Douglasfir. Res. Note PNW-239. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Forest and Range Experiment Station. 5 p.

Curtis, R.O. 2008. True-fir spacing trials—10-year results. Gen. Tech. Rep. 

PNW-GTR-749. Portland, OR: U.S. Department of Agriculture, Forest Service, 

Pacific Northwest Research Station. 36 p.

Curtis, R.O. 2010. Effect of diameter limits and stand structure on relative density 

indices: a case study. Western Journal of Applied Forestry. 25(4): 169–175.

Curtis, R.O.; Clendenen, G.W.; Henderson, J.A. 2000. True fir-hemlock spacing 

trials: design and first results. Gen. Tech. Rep. PNW-GTR-492. Portland, OR: 

U.S. Department of Agriculture, Forest Service, Pacific Northwest Research 

Station. 35 p.

Eyre, F.H. 1980. Forest cover types of the United States and Canada. Washington, 

DC: Society of American Foresters. 148 p.

Franklin, J.F.; Dyrness, C.T. 1973. Natural vegetation of Oregon and Washington. 

Gen. Tech. Rep. PNW-8. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Forest and Range Experiment Station. 417 p.

Freund, R.J.; Littell, R.C. 1991. SAS system for regression, 2nd ed. Cary, NC: 

SAS Institute, Inc. 210 p. 

Harrington, C.A.; Murray, M.D. 1982. Patterns of height growth in western 

true firs. In: Oliver, C.D.; Kenady, R.M., eds. Proceedings of the biology and 

management of true fir in the Pacific Northwest symposium. Institute of Forest 

Resources. Contrib. 45. Seattle, WA: University of Washington, College of 

Forest Resources: 209–214.
30

research paper PNW-rp-590

Hemstrom, M.A.; Emmingham, W.H.; Halverson, N.M.; Logan, S.E.; Topik, 

C. 1982. Plant association and management guide for the Pacific silver fir zone. 

Mt. Hood and Willamette National Forests. R6-Ecol-199-1982A. Portland, OR: 

U.S. Department of Agriculture, Forest Service, Pacific Northwest Region. 104 p. 

Henderson, J.A.; Lesher, R.D.; Peter, D.H.; Shaw, D.C. 1992. Field guide to the 

forested plant associations of the Mount Baker–Snoqualmie National Forest. 

Tech. Pap. R6 ECOL TP 028-91. Portland, OR: U.S. Department of Agriculture, 

Forest Service, Pacific Northwest Region. 196 p.

Henderson, J.A.; Peter, D.H. 1984. Preliminary plant associations and habitat 

types of the Mt. Baker Ranger District, Mount Baker–Snoqualmie National 

Forest. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific 

Northwest Region. 60 p.

Henderson, J.A.; Peter, D.H.; Lesher, R.D.; Shaw, D.C. 1989. Forested plant 

associations of the Olympic National Forest. Tech. Pap. R6 Ecol. 001-88. 

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

Region. 502 p.

Herman, F.R.; Curtis, R.O.; DeMars, D.J. 1978. Height growth and site index 

estimates for noble fir in high-elevation forests of the Oregon-Washington 

Cascades. Res. Pap. PNW-243. Portland, OR: U.S. Department of Agriculture, 

Forest Service, Pacific Northwest Forest and Range Experiment Station. 15 p.

Hoyer, G.E.; Herman, F.R. 1989. Height-age and site index curves for Pacific 

silver fir in the Pacific Northwest. Res. Pap. PNW-RP-418. Portland, OR: U.S. 

Department of Agriculture, Forest Service, Pacific Northwest Research Station. 

33 p.

Logan, S.E.; Hemstrom, M.A.; Paviat, W. 1987. Plant association and 

management guide—Willamette National Forest. R6-Ecol-257-A-86. Portland, 

OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Region. 

223 p.

Long, J.N. 1985. A practical approach to density management. Forestry Chronicle. 

19(1): 23–27.

Long, J.N.; Daniel, T.W. 1990. Assessment of growing stock in uneven-aged 

stands. Western Journal of Applied Forestry. 5(3): 93–96.

Murray, M.D.; Coble, D.; Curtis, R.O. 1991. Height growth of young Pacific 

silver fir and noble fir established on clearcuts in the Pacific silver fir zone of 

western Washington. Canadian Journal of Forest Research. 21: 1213–1221. 
31

True Fir Spacing and Yield Trials—20-Year Update

Nigh, G.D. 1998. Site index conversion equations for mixed western hemlockamabilis fir stands. Extension note 26. Victoria, BC: Research Branch, British 

Columbia Ministry of Forests. 4 p.

Nigh, G.D. 2009. Amabilis fir height-age and growth intercept models for British 

Columbia. Res. Rpt. 30. Victoria, BC: British Columbia Ministry of Forests and 

Range. 13 p.

Oliver, C.D.; Kenady, R.M. eds. 1982. Proceedings of the biology and 

management of true firs in the Pacific Northwest symposium. Institute of Forest 

Resources, Contrib. 45. Seattle, WA: University of Washington, College of Forest 

Resources. 344 p.

Poage, N.J.; Marshall, D.D.; McClellan, M.H. 2007. Maximum stand-density 

index of 40 western hemlock–Sitka spruce stands in southeast Alaska. Western 

Journal of Applied Forestry. 22(2): 99–104.

Reinecke, L.H. 1933. Perfecting a stand-density index for even-aged forests. 

Journal of Agricultural Research. 46: 627–638.

Thomas, J.W.; Franklin, J.F.; Gordon, J.; Johnson, K.N. 2006. The Northwest 

Forest Plan: origins, compnents, implementation experience, and suggestions for 

change. Conservation Biology 20(2): 277–287.

Wiley, K.N. 1978. Site index tables for western hemlock in the Pacific Northwest. 

Weyerhaeuser Forestry Paper No. 17. Centralia, WA: Western Forestry Research 

Center, Weyerhaeuser Company. 28 p.

Wiley, K.N.; Bower, D.R.; Shaw, D.L.; Kovich, D.G. 1978. Standard cubic-foot 

tables for total- and merchantable-stem volumes and tariff access for western 

hemlock in Washington and Oregon. Weyerhaeuser Forestry Paper No. 18. 

Centralia, WA: Western Forestry Research Center, Weyerhaeuser Company.

157 p.
32

research paper PNW-rp-590

Glossary of Symbols and Acronyms

%nfwh = Sum of percentage basal area in noble fir and hemlock at measurement 4.

S = Site index = Estimated mean height of largest 80 silver fir per acre at breast 

high age 50.

S60 , etc. = Site index 60, feet.

TN = Target number of leave trees per acre.

spac = Spacing of leave trees after thinning, feet.

elev = Elevation, feet.

age b.h. = agebh = Breast-high age, years.

A1 = Breast-high age at time of thinning.

D1 = D80 at time of thinning, inches.

CVTS = Volume of entire stem, cubic feet per acre.

BA = Basal area, square feet per acre.

D80 = Mean diameter of the largest 80 trees per acre, inches.

ΔCV = Periodic net change in CVTS, cubic feet per acre

ΔBA = Periodic net change in basal area, square feet per acre.

ΔD80 = Periodic net change in D80, inches.

ln(X) = Natural logarithm (base e) of X.

X • Y = Product of X and Y.

sqrtX = Square root of X.

RSQ = (Multiple correlation coefficient)2

 = coefficient of determination.

adjRSQ = RSQ adjusted for number of variables = 1 - (1 - RSQ) • (n - 1)/

(N - m - 1) (Freund and Littell 1991, 23).
Pacific Northwest Research Station

Web site http://www.fs.fed.us/pnw

Telephone (503) 808-2592

Publication requests (503) 808-2138

FAX (503) 808-2130

E-mail pnw_pnwpubs@fs.fed.us

Mailing address Publications Distribution

	 	 Pacific Northwest Research Station

 P.O. Box 3890

	 	 Portland, OR 97208-3890
U.S. Department of Agriculture

Pacific Northwest Research Station

333 SW First Avenue

P.O. Box 3890

Portland, OR 97208-3890

Official Business

Penalty for Private Use, $300