Factors influencing the accuracy of estimation of growth of Douglas fir trees

Factors influencing the accuracy of estimation of growth of Douglas fir trees

J. H. G. Smith

Faculty of Forestry, The University of British Columbia Vancouver (Kanada)

Abstract

lnfluences of 11 tree and stand characteristics on growth at breast heigth are described for 144 Douglas firs, Pseudotsuga menziesii (Mirb) Franco. Two incre- ment cores were extracted from each tree to estimate radial growth for each of the periods 1941-1950, 1951- 1955, and 1956- 1960. Basal area growth 1956- 1960 was also studied.

Site index and crown dass were best for estimation of radial growth, but dbh and height were best for determination of basal area growth per tree.

For 58 Douglas fir trees crown dass and dbh were the best indicators of average radial growth 1-10 years ago at all heights in the tree.

The extent to which growth at breast height can be used to estimate annual height growth and widths of earlywood, latewood and total ring throughout the whole tree was ilJustrated for 18 Douglas firs. Although highly variable, annual height incre- ment and widths of earlywood and total rings grown in any oalendar year are signifi- cantly corre1ated with the width of the ring grown at breast height in the same year.

lntroduction

Growth in diameter at breast height is emphasized here because it is commonly

and easily measured and usually is well correlated with growth of other variables of

interest. The influences of dimate and soil on growth of Douglas fir were studied

thoroughly by Griff i t h (1960a, b). Many factors determining growth in volume

and value were reviewed by Sm i t h, K er, and Cs i z m a z i a (1961). Douglas

fir height growth was analysed by Sm i t h, K er, and Heger (1960). Stern

analyses were used by Sm i t h and Walters (1964) to determine ratios of height

and diameter to age in order to facifüate growth predictions. Sm i t h (1964) report-

ed that root spread was highly sigrni:fücantly correJ.ated with crown spread which is

dosely associated with dbh in these stands.

In this paper some of the factors influencing dbh growth are illustrated with data on breast height growth of 144 Douglas fir trees and total tree growth of 18 rapidly grown Douglas fir trees from the U.B.C. Campus Forest. Data on 58 Douglas fir trees from the U.B.C. Research Forest also are reported, briefly. Simple correlation coefficients, r, are used to describe the degree of association among variables to facilitate comparisons of their relative utility from a statisitical point of view.

Need for data on individual trees

The individual tree is the basic unit for many fundamental scientific and general management studies (Sm i t h 1959, 1963, 1966). With data on individual trees iit is possible to simulate stand growth (N e w n h a m and S m i t h, 1964; S m i t h, New n h am and H e j j a s, 1965). Much remains to be learned, however, about how faithfully models of stand growth based upon studies of individual trees dupli- cate growth of stands in nature. The problem of predictions is complicated by the fact that natural stands seldom represent the genetic characteristics and the degree of management considered optimum. In order to make decisions on the kind of stands that can, and should, be grown it is necessary to have data from trees representing a great range in potential growth characteristics. We also must know to what extent growth can actually be controlled (Sm i t h, 1966).

Estimation of dbh growth

These data were obtained in the winter of 1961 from natural stands in the U.B.C.

Campus Forest. They were collected by 0. Horvath from representative trees to refine and extend studies made by K er (1953) concerning growth of immature Douglas fir by tree classes on the U.B.C. Research Forest north of Haney, B.C. Two increment cores were extracted at right angles to each other to reach the pith of each tree at breast height. Radia1 growth 1-5, 6-10 and 11-20 years ago was measured on each core. The two cores from each tree were measured by L. P a s z n e r to make two estimates of the specific gravity of each tree (W e l I w o o d and S m i t h, 1962). Multiple regression analyses of all data were made on an Alwac 111-E by J.Csizmazia.

The data were to provide a basis for estimation of growth in wood at breast height as a guide in studies of thinning, pruning, and general stand management. They are summarized by dbh in Table 1.

The averages given in Table 1 show that radial growth was decreasing from

1941-1960 except in the largest trees, most of which were re1atively open grown. The

slow growth of 10 inch trees is largely attributable to their intermediate crown class

and to strong competition from the top and sides.

Double bark thickness and average radial growth by dbh class and calendar year, 1941-60.

Av. dbh of class In.

6.05 8.00 10.2 11.8 14.1 16.2 18.2 20.2 21.7 23.5 25.9 27.9 29.9 31.7 34.0 35.6 39.6

No. trees sampled

4 27 36 18 11 10 4 4 5 1 5 4 11 2 1 1 1

Double hark Thickness

In.

0.58 0.76 1.30 1.58 1.60 1.62 1.70 1.80 2.08 2.00 2.18 2.28 2.42 2.40 2.40 2.80 2.60

56-60

0.45 0.54 0.29 0.41 0.51 0.53 0.52 0.61 0.65 0.53 0.55 0.42 0.58 0.66 0.88 0.88 1.05

Table 1 Average radial growth at BH, 1941-60

51-55 In.

0.59 0.62 0.35 0.48 0.64 0.74 0.52 0.69 0.53 0.53 0.73 0.64 0.62 0.68 0.88 1.15 1.20

41-50

1.96 1.65 0.83 1.07 1.20 1.42 1.30 1.25 1.55 1.55 1.60 1.26 1.45 1.98 1.53 2.18 1.75

1

51-60/41-50

0/o

53 70 77 83 96 89 80 104 76 68 80 84 86 68 115 93 128

Independent variables used included dbh (D), total age (A), estimated height at 100 years (SI), total height (H), average crown width at the 1argest complete branch whorl (CW), crown dass (CC) (coded as intermediate 1, codominant 2, dominant 3, and open 4), number of sides free of competition (NFS), and basal area per acre includ• ing each tree studied (BA) . The ratios of crown width in feet to dbh in inches (CW/D) and of total height to crown width were calculated (H/CW). Double hark thickness also was measured (DBT).

Dependent variables in Table 2 include radial growth estimates from core 1, core 2, and the average of cores 1 and 2 for the periods 1- 5, 6- 10 and 11- 20 years ago. In addition basal area growth was calculated in square feet from the average change in radius 1- 5 years ago. The simple correlation coefficients in Table 2 indicate the degree of association among independent variables and several measures of radial growth, 1941-1960. Live crown length and crown quality should also have been re- corded for these trees.

Average radial growth is hiighly correlated with its component values and with growth for va~ous perio~. The longer the period the more difficult the prediction becomes; e.g. R 1-5 and R 11- 20 have a simple correiation coefficient of only 0.754.

lnspection of the simple correlation coefficient by periods for each independent tree

variable shows changing importance of variables over time. Growth 1-5 years ago

Variation in the basic data and simple correlation coefficients among them and growth in radius

Table 2 and area at breast height.

Simple correlation coefficients

Vuriablf's Units Min.1 M<'an SD 1 Max.¹

1 1 1

14 on 17 on 20 on 21 on 1-21 1-21 1-21 1-21

1 Dbh In. 5.6 15.0 7.9 39.6 .332 .264 .186 .853

2 Age Yr. 27 57.1 18.0 91 .100 .14,8 .306 .522

3 SI Ft. 75 129 33.2 200 .634 .606 .754 .167

4 H Ft. 50 90.9 21.3 135 .337 .298 .178 .747

5

cw

6 CW/D Ft./In. 0.75 1.62 0.42 2.90 .017 .031 .075 .444

7 CC - 1 2.42 1.03 3 .672 .599 .587 .679

8 NFS - 0 2.33 1.14, 4, .4-75 .421 .434 .554

9 BA Sq. Ft. 40 206 47.3 310 .276 .344 .325 .409

10 DBT In. - 1.54, 0.68 - .089 .019 .059

-

11 H/CW Ft./Ft. - 4.36 1.05 - -.239 - - -.326

12 Rl, 1-5 ² In. - 0.48 0.29 - .917 .752 .581

-

13 R2, 1-5 In. - 0.46 0.26 - .932 .763 .750

-

-

14 R, 1-5 In. - 0.47 0.26 - 1.00 .809 .711 .687

15 Rl, 6-10 In.

-

-

^-

16 R2, 6-10 In. - 0.57 0.30 - .776 .856 .798 -

17 -R, 6-10 In. - _0.56 0.31 - .809 1.00 .726

-

18 Rl, 11-20 In. - 1.32 0.66

-

-

19 R2, 11-20 In. ^- 1.28 0.66 - .711 .764 .958 -

20 R, 11-- 20 In. - 1.30 0.64 - .754 .726 1.00 -

-

21 BA, 1-5 Sq. Ft. - 0.166 0.156 - .687 - - 1.00

1 Minimum, standard deviation and maximum are shown for most variables.

2 Radial growth 1-5 years ago measured on core number one; R² refers to core 2, and R is the average of cores 1 and 2.

•

is most associated with current dbh, height, crown width, crown class, and number of sides free of competitors; but growth 11- 20 years ago can be estimated best by present age and site index.

A remarkable difference is shown in Table 2 by expressing :riadial growth jn terms of periodic increase in basal area per tree. lmportance of individual tree variables changes immensely, because growth in radius and growth in basal area are not corre- lated to a high degree (r is only 0.687). This problem iis defined more clearly in Table 3 which includes the squared corre1ation coefficients resulting from stepwise elimination of variables in multiple regression analysis. Variables are listed as

«· added» in order to illustrate ~heir changed order and relative importance resulting from use of different forms of the dependent variable. Using aJ.l independent tree variables to estimate radial growth raised the coeffücient of determination (r or R

from 0.451 to 0.589 and decreased the standard error of estimate from 0.19 to 0.17

inches. Estimation of basal area growth with all independent variables improved

similarly; r

increased from 0.728 to R

0.766, and standard error of estimate decreased from 0.081 to 0 .076 square feet. Although a much 1arger proportion of varriation in basal area growth was accounted for, its standard error of estimate expressed as a percentage of the mean was 46 in comparison with 36 for radial growth. This illustrates the necessity of choosing the appropriate dependent variables and of using coefficient of determination as well as standard error of estimate m evaluating multiple regression estimates of growth.

The limited influence of basal area per acre on growth of individual trees, as shown in Tables 2 and 3, may appear surprising. lt is much poorer than number of sides free of competitors, or position of crown in the stand. Crown class, as used here, represents much of the influence of stand density on indiviidual tree growth.

Accuracy of estimate has been improved slightly using the average of two cores, but the extra work involved does not seem to be justified for estimation of growth.

Tree growth in radius

Data from 58 Douglas fir trees whose variations m sapwood thickness were described by Smith, Walters and Wellwood (1966), also can be used to describe relative influences of several factors on growth.

Radial growth 1-10 years ago was measured on an average radius at stump height and at the top of each 16.3 foot log to the tip of each tree. Growth on 437 discs averaged 0.57 inches with a standard deviation of 0.31. Their coefficient of variation was 0.54. These measurements of radial growth were highly significantly correlated with dbh (r 0.376), crown class (r- .462; D = 1, CD = 2, I = 3, S = 4), diameter outside hark (dob) (r.277), years to base of live crown (r.129), hark thickness (r.234), and dob

(r.311). Radial growth decreased significantly with number of years from base of live crown (r-.092). Four variables which were expected to be important proved to be non significant. These were: section height (r.012), number of rings from pith (r-.060), section height as per cent of tree height (r- .054), and distance from base of 1ive crown (r.025).

Patterns of growth within trees

The difficulties of estimating growth at breast height are increased many times, if one is interested in describing sheaths of wood grown by the whole tree in any one year or period.

Duff and No l an (1953) drew attention to the fact that increments in the tree

diameter occur in three sequences, oblrique, horizontal and vertical. The oblique

sequence is composed of all sheaths of wood formed between branch whorls in any

one calendar year. The horizontal sequence of annual increments is formed by suc-

cessive annual rings at any one height in the tree. These were diagrammed by W a l -

t er s and So o s {1962). The

sequence of annual increments consists of wood formed at a common number of rings from the pith.

By his analysis of 22.734 bands of earlywood and latewood from 18 Douglas fir trees grown in the U.B.C. Campus Forest Heger (1965) showed that distributions of earlywood and latewood layers are distinctly different. S m i t h, H e g e r, and I- I e j j a s (1966) used multiple regression techniques (K o z a k and Sm i t h, l 965) to describe the distribution of earlywood and latewood in these trees which were from 25 to 55 years old. Number of rings from pith and its reciprocal, square, or logarithm accounted for much of the variation in radial growth at breast height, and throughout the tree.

D u f f and N o l a n ' s { 1953) growth sequences are illustrated with further analyses of Heger' s (1965) tree No. 14, in Tab1e 4. A total of 1275 annual rings were measured in this tree which was 55 years oid, 24 inches in dbh and 122 feet tall with 45 per cent live crown. The number of rings measured is given as «No.- rings» or as «Disc.No.». No trends are evident in calendar year or discs from top but range in width of earlywood decreases strongly as number of rings increases.

lnfluence of form of dependent variable [radial growth (R) vs. basal area growth (BA)] on order Table 3 of elimination and portion of variation accounted for by independent variables.

R 1-5 years ago BA 1-5 years ago

Variable added

1 r² or R² Variable added

1 r² or R²

CC .4,355 D .7301

SI .5363 A .8044

D .5600 H .8052

H .5736 CW/D .8113

cw

A .6004 H/CW .8173

NFS .6025 SI .8231

H/CW .6026 NFS .8246

CW/D .6121

cw

BA .6121 BA .8247

The very low ranges in earlywood widths during 1947 and 1957 illustrate un- favourable climatic variations of some importance.

Sm i t h, Heger, and He j ja s {1966) showed that use of calendar year and

number of disc from top, with number of rings from pith in multiple regression

analyses, accounted for 5 % of variation in latewood, 45 % of variation in early-

wood and 34 % of variation in total ring widths. In this case ring width at breast

height during the same calendar year by itself accounted for 39.7 % of all variation

in ring widths in tree 14. The best three variables were calendar year, log

of number

of rings from pith, and number of discs from top. These accounted for 72 % of the

variation in ring width in this tree.

Minimum and maximum widths of earlywood and latewood for Heger's tree No.14 by: A. Calendar years, B. Number of discs from iop, and C. rings from pith. (By intervals of Jive.)

Table 4 A. Calendar year (oblique sequence)

Latewood

1 Earlywood

Year No. Width in thousandths ol Inches

rings

Min.

1 Max.

1 Min.

1 Max.

1917 5 005 088 035 232

1922 10 005 llO 025 269

1927 15 005 107 031 253

1932 20 005 127 035 273

1937 25 005 147 012 263

1942 30 005 126 015 275

1947 35 005 105 005 165

1952 40 005 100 023 245

1957 4

005 105 015 135

1962 50 005 097 035 180

B. Disc from top (horizontal sequence) Latewood

1

Earlywood

Disc Length

·wi<lth in thousandths of Inches

No. In.

Min. Max. Min.

1 Max.

5 12 005 030 025 24,0

10 35 005 087 025 125

15 30 005 llO 020 245

20 23 005 121 022 184

25 27 005 079 035 219

30 39 005 130 015 268

35

28 005 115 015 300

40 45 005 106 030 253

45 31 005 101 035 265

50 18 005 144 037 270

C. Rings from pith (vertical sequence) Latewood

1 Earlywood

Ring No. Width in thousandths of Inches

No. rings

Min. Max. Min. Max.

5 46 010 097 080 275

10 41 043 127 060 241

15 36 052 120 085 235

20 31 040 144 070 213

25 26 035 108 055 14,0

30 21 028 090 050 124

35 16 025 078 043 088

40 ll 035 063 037 090

45 6 026 071 047 070

50 1 - ^{054 - 056}

Correlations among ring width at breast height (RBH) and, at the same number of years Jrom pith, the corresponding widths of latewood (LT), earlywood (ET), "and total ring (RT) throughout the whole tree. Correlation coefficients are given also for latewood (LBH) and earlywood (EBH) with RBH at breast height only, for Heger' s 18 Douglas fir trees. Table 5

1 Tree

Simple correlation coefficicnts between RBH and values for same numbcr or rings from pith for:

No.

1 1 1 1 1

LT ET RT LBH EBII ^No.

1 -.4,22 .128¹ -.100 - .581 .841 294

2 -.075

-

3 -.309 .095 - -.012

-

4 -.257 .065 -.184 .244 .817 273

5 -.126 -.004 -- -.058 - .452 .935 273

6 -.227 .131 .022 .551 .922 273

7 .014 .092 .088 .409 .908 558

8 -.143 -.095 -.155 .693 .894, 1078

9 -.238 .167 .008 .821 .887 1137

11 -.065 -.007 -.030 - .805 .824 1170

13 -.250 -.181 -.232 .627 .954 1172

14 -.169 -.056 - -.113 .863 .966 1275

13M -.127 .161 .099 .225 .953 207

27M -.203 .270 .143 .666 .919 207

32M -.059 - .203 .131 - .697 .943 207

33M -.327 .016 - -.112 - .320 .938 207

1 Not significant correlation coefficients are underlined.

Heger's data were analysed further to illustrate the extent to which growth throughout each of his 18 trees can be described by measurements at breast height.

In Table 5 the small size of simp1e correlation coefficients shows that widths of late- wood, earlywood and total rings and percentage latewood, throughout the trees, are weakly associated with total widths at the same number of rings from breast height.

Although most are relatively small, because of the large numbers of measurements involved for each tree in Tables 5 and 6, many correlation coefficients are statisti- cally signifioant; non-signifioant values are underlined. Even the current year widths of rings at breast height are only moderately correlated with widths of latewood, earlywood, and total ring at all positions in the tree, or height increment, grown during the same calendar year (Table 6).

In multiple regression analyses, radial growth at breast height proved to be a moderately useful indicator of growth of wood throughout the tree (S m i t h, H e - g e r , and H e j j a s, 1966) .

Tables 5 and 6 illustrate the great differences which eX!ist from tree to tree. lt

also should be noted that total ring width depends much more upon width of early-

wood than on width of latewood, which is highly variable.

Correlations between ring width at breast height {RBH) and corresponding widths of latewood (LT), earlywood (ET), and total ring (RT) throughout whole trees in the same calendar year.

Correlation coefficients are given also for latewood (LBH) and earlywood (EBH) at breast height only, and for annual height increment (Hg) for Heger's 18 Douglas fir trees. Table 6

Tree

Simple correlation cocfficients between RBH and same calendar ycar values of:

No.

1 1 1 1 1

LT ET RT Hg LBH En:I

1 .298 .328 .440 .555 .677 .827

2 .264 .306 .347 -.271 .613 .804

3 .160 .431 .429 .257 .351 .967

4 .135 .327 .359 .311 .302 .810

5 .033¹ .352 .289 .245 .464 .938

6 .095 .4,04 .388 .567 .546 .924

7 .234 .347 .413 .382 .411 .907

8

- .o:rn

9 .216 .435 .4,58 .539

-

11 .066 .297 .285 .4,26 .807 .825

13 .266 .612 .599 .750 .624 .954,

14 .181 .667 .633 .583 - -

13M -.063 .475 .403 .339 .248 .954

27M -.004 .212 .185 .482 .693 .923

32M .189 .586 .556 .665 .729 .953

33M -.018 .181 .134 -.275 .833 .961

1 Not significant correlation coefficients are underlined.

Coefficients of variation

For the 18 trees described in Tables 5 and 6, all widths of latewood averaged 0.05 inches and had a standard deviation of 0.03. All widths of earlywood averaged 0.12 inches and had a standard deviation of 0.05 inches; all :riing widths averaged 0.176 inches and had a standard deviation of 0.06 inches. These means and absolute standard deviation or their coefficients of variation, 0.53, 0.43, and 0.36 for widths of latewood, earlywood, and total ring, respectively, may be of value in designing other studies of growth. The coefficients of variation are smaller than those for the data on average radial growfh 1-5 years ago shown in Table 2. Those had a coeffi- cient of variation of 0.55 that could be reduced by multiple regression analysis to give a standard error of • estimate of 36 per cent. Thris coefficient of variation was almost identical to that for the 437 discs from 58 trees discussed previously.

Coefficients of variation for all ring widths measured throughout each of Heger's 18 trees ranged from 0.279 for No. 11 to 0.426 for tree No. 2.

Average ring widths and coefficients of variation at breast height are similar to

those for ring widths throughout the whole tree.

Sampling required

If we can assume that all instruments are correctly adjusted, and that systematic errors in their use have been reduced by training of staff to give acceptable precision, we still have to define an acceptable level of sampling error. To date in British Colum- bia the problem of accuracy required has seemed minor in relation to the uncertain- ties associated witb description of immense ranges in tree size, log quality, hiddr.n defect, and waste from incomplete utilization, and felling breakage.

The difficulty of stating accuracy required is increased by willingness to accept

degrees of confidence for each component in estimates of growth. Widely fluctuating levels of market values for stumpage and manufactured products also complicate estimates of value growth. These problems may be simplified if growth is lo be estimated in terms of pulp yield per acre.

A commonly accepted goal is to set the acceptable limit of error at 10 per cent 19 times out of 20. To achieve this for estimation of breast height radial growth 1-5 years ago would require a minimum of !~

^{= 52} trees. Roughly the same number of measurement would be needed to defüne annual ring width for a sample tree. These would have to be representatively distributed to sample the growth sequences shown in Table 4. More samples would be required to describe variation in earlywood or latewood and their differences in distribution within growth sequences must be remembered.

Estimation of mortality

Almost all trees slarl growth in a relalively open level of stocking, and gradually increase competilion with their neighbours. Stand density increases, therefore, until some trees become crowded and overtopped or suppressed and sooner or later die.

There is much need to study the timing, amount and distribution of mortality in reLa- tion to many tree and

characteristics. Estimates of growth should be combined with studies of response to release and of probability of survival of individual trees.

Cyclic variations in weather and climatic extremes

Cyclic variations in weather and climatic extremes

The effects of short term climatic changes on periodic growth must be known in relation to long term cyclic variations. The extent to which climatic extremes reduce growth and increase mortality in any one period should be studied more completely.

For example, the growth data given in Tables 1-3 for 1956-1960 may reflect some

damage caused by a sudden severe frost on November 11, 1955 and an extremely

dry summer in 1958.

Limiting characteristics of multiple regression analysis

With multiple regression techniques we can easily be overwhelmed by the mass of analyses generated but still find it diffücult, if not impossible, to explore all combina- tions of interest (K o z a k and S m i t h, 1965) . The importance of using the ap- propriate measure of growth has already been illustrated. The methods of combining and eliminating variables and the opportunities for transformation and combination of variables also can have important influences on the results. Logical considerations and practical importance ~f variables must always be kept in mind.

The equations finally chosen should be based upon simple, easily measured, and statistically efficient variables fully representative of a large portion of the data to which they are to be applied. No equations have been given here for growth estima- tion because description of variation and relative importance of factors were of most interest. There is considerable need for analyses of multiple regression techniques in comparison with other multivariate methods such as that of W a 11 i s (1965).

Conclusions

The variation in and nature of, independent variables used in prediction, the form of the dependent variable, and the methods used for statistioal analysis have much influence on the accuracy of growth estimation. These can be much more important than techniques of measurements.

Growth in radius at breast height , and throughout whole trees is highly variable.

Although statistical significance can be obtained with many estimating equations and by various combinations of variables, emphasis always should be p1aced on use of those which are most logical, simple, consistent, and statistically efficient.

Crown class, dbh, and site index were the most , important variables in this study.

Growth throughout the tree can be estimated significantly, but with much variation, by use of measurements at breast height. In planning sampling, the existence of growth sequences should be considered carefully. lt has been shown here that varia- tion in growth within a single annual increment throughout a tree is often as 1 arge as that within a stand measured at breast height.

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