MANAGEMENT NOTES Number 13

The Effects of Tree Spacing on Diameter, Height and Branch Size

in White Spruce

by Christoph Krieger1998

Introduction:

“To find the optimum number of trees per acre to plant or leave standing so as to achieve maximumgrowth per acre of superior form-class trees, having a good commercial value” had been the idea ofstarting Nelder spacing and controlled thinning experiments on Prince Edward Island in 1969 to1971. Nature seldom regenerates cut overs and abandoned farm land properly. Either too few ortoo many trees regenerate, leading to overly branchy, highly tapered (poor form) stems or shallowrooted, stagnating stems. Consequently an optimal spacing must exist between stems according tosite and tree species. “What is this spacing; and in thinning, when should this adjustment in standdensity take place?” (Anon.,1969-70).

To determine the best spacing for planting and thinning forest land several experimental plots wereestablished with white spruce (Picea glauca (Moench)Voss) and white cedar (Thuja occidentalis L.).The plots were planted or thinned out to the Nelder spacing design. Only four plots in two locationshave survived. A map showing the location of each surviving Nelder in P.E.I. is shown in Figure 2.

All four spacing trials were established as a modified Nelder 1a design (Figure 1, (Nelder,1962)) atfourteen densities, varying from 0.6 m to 5.4 m (Table1). This Nelder spacing design is a circular2 2

configuration of planted trees designed to provide a systematic increase in growing space along eachspoke (radius). Two arcs, one each at the inner and outer edges of the concentric circles wereestablished to act as guard rows. These circles of trees act as a buffer zone and separate the spacingtrial from the surrounding area. Excluding these guard rows from data analysis, all trees at each offourteen levels of growing space were replicated 48 times (14 x 48 = 672 trees) and were tested forgrowth responses.

The major advantage in this design over other spacing designs is the relatively small area (0.4 ha)required, which greatly reduces the influence that site variation has on the trial.

This is a publication of the P.E.I. Department of Agriculture and Forestry, Forestry Division

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Figure 1: Nelder Spacing designs.

(a) Design Ia; Shape fixed, area increases with radii.(b) Design Ib, Area fixed, shape changes with radii.(c) Design Ic, Equal area contours = vertical lines.

Equal shape contours = radii.(d) Design Id, Equal area contours = radii.

Equal shape contours = vertical lines.

Table: 1 Density of trees in the spacing trials.

Spacing

levels2 3 4 5 6 7 8 9 10 11 12 13 14

Growingspace (m )2 0.62 0.81 1.06 1.37 1.78 2.32 3.01 3.91 5.10 6.64 8.61 11.2 14.5

Stems/ha 16129 12345 9434 7299 5618 4310 3322 2558 1961 1506 1161 894 692

Stems/a 6532 5000 3821 2956 2275 1746 1345 1036 794 610 470 362 280

Spacing (m)

0.31 0.41 0.53 0.69 0.89 1.16 1.51 1.96 2.5 3.32 4.31 5.55 7.2

Spacing (ft.)

1.02 1.35 1.74 2.23 2.92 3.81 4.95 6.43 8.2 10.9 14.1 18.2 23.6

Kelly's Cross

Jacks Road

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Site Histories

C Jacks Road (Queens County) Two natural white spruce stands on old fields (former farmland) were thinned to the Nelderdesign and became Nelder plots in 1969. The trees were about 1.5 meters high in 1971.There was no record found regarding fill plantings. In the following years, only ingrowth hadbeen removed (Glen,1986). Diameter and height were measured in 1986, 1991 and 1997.

C Kelly`s Cross (Queens County)These two plots were also established on old fields in 1970 by planting to the Nelder spacingdesign with white spruce. Heavy grass and high mortality (...“less than 40 % survival”...)possibly due to the extremely late time of planting in 1970 and poor choice of planting stock(3-0) necessitated replanting in 1971 (2-1 stock was used) (Anon., 1969-70; Brewer, 1970).In the mid 80's ingrowth had been removed (Glen,1986). Diameter and height were measuredin 1986, 1991 and 1997.

Figure: 2 Location of the sites on Prince Edward Island.

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Methods

All trees on each fifth spoke of each of the Nelders were measured in November 1997. The treeposition (number), diameter (d.b.h.), height and branch diameters of the whorl closest to d.b.h. weremeasured. Tree diameter was measured with a diameter-tape to the nearest 0.1 cm at 1.3 m outsidebark (d.b.h.). The height of the trees was measured to the nearest 0.1 m with a digital hypsometer(‘Forestor Vertex’). All branch diameters were recorded (to the nearest 0.1 cm) for the closest whorlto breast height using a small caliper.

To achieve meaningful results, high tree mortality was avoided, especially close to the center, bychoosing only “optimal” trees. If one of the closest eight/next neighbors was dead, the candidatetree was rejected. A replacement tree with the same spacing (i.e. within the same arc of the Nelder)which had eight living neighbors was chosen as an ‘optimal’ tree.

The treatment of data consisted of regression analysis and t-test procedures (SYSTAT). The resultsof the analyses are summarized in the following Table and Figures.

Discussion

1. DiameterThe development of stem diameter is, to a far greater extent than height development, dependenton stem numbers and therefore dependent on the growing space available to the trees (Assmann,1970).As spacing and thinning experiments have consistently shown stands with wider spacings or standspreviously thinned have larger average diameters than similar stands with closer spacings orcomparable unthinned stands over time. (Clutter et al., 1983).

All though there were different establishment methods used for both Nelders the diameter range issimilar. Generally speaking minimum, maximum and average diameter of the Jacks Road siteexceeded those at Kelly`s Cross (Table 2). Through all the diameter points a regression using theWEIBULL-function ( diameter = a*(1-Exp(-( tree spacing/b )^c )) ) was calculated (Figure 3) andstrong correlations are shown for Kelly`s Cross R = 0.97 and for Jacks Road R = 0.89 2 2

Table: 2 Minimum, maximum and average stem diameter (cm.) of Jacks Road and Kelly`sCross in 1997.

minimum maximum average standard deviation numberdiameter cm. diameter cm. diameter cm. of trees

Jacks Road 5.3 30.5 15.1 5.2 256

Kelly`s Cross 3.6 27.3 14.4 4.5 254

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Table: 3 Average diameter (cm) for various spacing densities (stems/ha) of Jacks Road andKelly`s Cross for the years 1986, 1995 and 1997.

Jacks Road Kelly`s Cross

stems/ha 1986 1995 1997 1986 1995 1997

16,129 8.7 10.4 11.3 6.4 8.5 9.1

12,345 7.4 11.0 12.2 6.8 8.5 8.9

9,434 7.8 11.5 14.8 7.5 10.3 9.9

7,299 8.0 9.6 11.0 8.1 10.3 10.3

5,618 9.7 11.7 14.0 8.3 12.1 13.1

4,310 9.4 11.6 15.7 8.3 13.6 13.6

3,323 10.0 11.9 15.4 9.5 13.6 15.2

2,558 11.4 14.0 16.8 10.1 15.1 16.1

1,961 11.4 14.0 16.2 10.2 16.2 16.9

1,506 11.6 14.9 17.6 10.0 17.2 17.3

1,161 11.9 15.6 18.7 9.7 18.0 18.8

893 12.8 17.5 20.2 9.2 19.2 19.4

692 12.5 17.5 24.6 8.9 17.1 19.4

In Table 3 the average diameter for various spacing densities (stems\ha) of Jacks Road and Kelly`sCross are compared. The density of each circle\arc is shown for the years of 1986, 1995 and 1997.Both sites increased in breast height diameter growth with decreasing stand density.

2. HeightEmpirical evidence from thinning experiments indicates that height growth is not greatly affected bythe manipulation of stand density. The average height of the stand may be changed by thinning,depending on the thinning method, but within wide limits of stand density height growth seems to beunaffected, especially when the comparison is restricted to dominant and codominant trees or evenaged stands (Clutter et al., 1983).

Minimum, maximum and average height of Jacks Road (plantation) exceeded again those of Kelly`sCross (Table 4).

8

10

12

14

16

18

20

22

diam

(cm

)

0 4000 8000 12000 16000 stems/ha

KC

JR

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Figure: 3 Diameter at breast height (cm) vs stems\ha of Kelly`s Cross (KC) and Jacks Road(JR) in 1997.

Table: 4 Minimum, maximum, average height and standard deviation of Jacks Road andKelly`s Cross.

minimum maximum average standard number ofheight m. height m. height m. deviation trees

Jacks Road 8.2 15.5 12.1 1.7 100

Kelly`s Cross 5.4 12.2 8.8 1.4 109

As expected there was no relationship found between height and spacing. Correlations of bothNelders were below R = 0.1. 2

Figure 4 compares the height growth vs diameter of the Kelly’s Cross site. It clearly shows thatwithin the years - 1986, 1995 and 1997 - height and diameters are increasing. The same trend occursfor Jacks Road. Both Nelder sites show very high correlations between height and diameter growthwith r-square between 0.98 and 0.99.

0

2

4

6

8

10 he

ight

(m)

0 5 10 15 20 25 30 diam (cm)

1986

1995

1997

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Figure: 4 Height (m) vs tree diameter (cm) of Kelly`s Cross for the years 1986, 1995 and1997.

3. Knot diameterThe maximum branch diameter is that of the largest branch in the whorl of branches closest to breastheight (1.3 meter). These maximum branch diameters were averaged and the standard deviation ofthe average was calculated for each tree spacing (arc of the Nelder).

As expected, the average maximum branch diameter increases with increased growing space. Thisis clearly shown in Table 5 for the average maximum knot diameter of the Kelly`s Cross plantation.The Jacks Road site (natural stand) doesn’t fit perfectly into the Nelder design, hence the trend is notshown as clearly. Prior to the thinning which created the Jacks Road Nelder the high density of theoriginal stand would have resulted in small branch diameters which have compromised the resultsof the Jacks Road site.

The average and maximum knot diameter are shown in Figure 5 and Figure 6. Nelders at both sitesshow a typical development; the Kelly`s Cross site exceeded the Jacks Road site by about 1 cm(Table 6).

In Figure 5 an average knot diameter of 1 inch\2.5 cm is reached at Kelly`s Cross site at a growingspace of 6 m . The Jacks Road site did not obtain 2.5 cm. A maximum knot diameter of 1 inch\2.52

cm is reached at the Kelly`s Cross site at a growing space of 3.5 m and at the Jacks Road site at 42

m . 2

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Table: 5 Average maximum branch diameter (cm) and standard deviation of Jacks Road andKelly`s Cross.

Kelly`s Cross Jacks Road

stems/ha average maximum standard average standard(cm) deviation maximum. deviation

(cm)

16,129 1.4 0.3 1.4 0.3

12,345 1.5 0.3 1.4 0.2

9,434 1.6 0.3 1.5 0.4

7,299 1.7 0.3 1.3 0.3

5,618 1.8 0.3 1.4 0.3

4,310 1.8 0.3 1.4 0.3

3,323 2.1 0.3 1.7 0.4

2,558 2.3 0.3 1.8 0.3

1,961 2.7 0.4 1.9 0.3

1,506 2.8 0.5 2.2 0.5

1,161 3.3 0.5 2.4 0.7

893 3.5 0.5 2.6 0.6

692 3.8 0.7 2.7 0.6

Table: 6 Minimum and maximum values of the average and maximum knot diameter (cm) atKelly`s Cross and Jacks Road.

average knot diameter maximum knot diameter

(cm) (cm)

minimum maximum minimum maximum

Kelly`s Cross 1 & 2 1.1 1.1 3.1 3.1 1.6 2.6 5.0 4.1

Jacks Road 1 & 2 1.1 1.0 2.4 2.3 2.4 1.9 3.2 3.3

1

1.5

2

2.5

3

3.5

diam

(cm

)

0 2 4 6 8 10 12 14 16 area (m2)

KC1

KC2

JR1

JR2

1

1.5

2

2.5

3

3.5

4

4.5

5

diam

(cm

)

0 2 4 6 8 10 12 14 16 area (m2)

KC1

KC2

JR1

JR2

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Figure: 5 Average knot diameter (cm) vs growing space (m ) of Jacks Road and Kelly`s2

Cross in 1997.

Figure: 6 Maximum knot diameter (cm) vs growing space (m ) of Jacks Road and Kelly`s2

Cross in 1997.

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Conclusions

Generally speaking one inch (2.5 cm) or less maximum knot diameter is the acceptable limit for fourinch lumber as shown in Table 7.

The Kelly`s Cross site reaches the acceptable knot/branch diameter of one inch with a planted densityaround 2,200 stems per hectare. However, plantations should be established so that the bestgrade of lumber (select) is produced. Therefore the number of stems per hectare at time of crownclosure should be around 3000 stems per hectare to produce a maximum average knot diameter of3/4 inch or 1.9 cm.

The British Forestry Commission recommends that for quality timber of Sitka Spruce (Piceasitchensis (Bong.) Carrière) a minimum of 2500 stems per hectare (2 m x 2 m) be fully established(Lee, 1996). The Bavarian Forest Service suggests the same density for Norway Spruce (Picea abies(L.) Karst.) (Kennel, 1996).

Table: 7 Grade & Corresponding maximum edge knot diameter (MLB, 1997).

Nominal # 2 # 1 SelectWidth grade grade grade

(inches) (inches) (cm) (inches) (cm) (inches) (cm)

3 7/8 0.9 3/4 0.8 ½ 0.5

4 1 1/4 3.1 1 2.5 3/4 1.9

6 1 7/8 4.7 1 ½ 3.8 1 1/8 2.8

8 2 ½ 6.3 2 5.0 1 ½ 3.8

10 3 1/4 8.1 2 ½ 6.3 1 7/8 4.7

A planting density of 3000 stems/ha effectively eliminates the risk of lumber being reduced from theselect grade to # 1 grade for any dimension lumber. Planting at 2200 stems/ha would ensure that alllumber would meet the edge knot size for #2 and better, the predominant grade for lumber from thisregion.

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Table: 8 Regression equations predicting mean values for Kelly`s Cross and Jacks Road.

Site Variables and regression equations Number of trees R2

Height

Kelly`s Cross (1997) y = 15.225*(1-Exp (- (x/34.0)^0.176)) 109 0.976

Kelly`s Cross (1991) y = 12.925*(1-Exp (- (x/44.04)^0.33)) 476 0.980

Kelly`s Cross (1986) y = 12.448*(1-Exp (- (x/38.19)^0.47)) 1032 0.983

Jacks Road (1997) y = 13.21*(1-Exp (- (x/7.255)^1.437)) 100 0.989

Jacks Road (1991) y = 18.627*(1-Exp (- (x/32.28)^0.47)) 238 0.979

Jacks Road (1986) y = 12.998*(1-Exp (- (x/17.12)^0.52)) 209 0.978

variables: y = height, x = diameter breast height

Stem Diameter

Kelly`s Cross (1997) y = 21.827*(1-Exp (- (x/2.457)^0.533)) 254 0.974

Jacks Road (1997) y = 113.59*(1-Exp (-(x/434.45)^-0.48)) 256 0.893

variables: y = diameter breast height, x = tree spacing expressed in square meters

Maximum Branch Diameter at BreastHeight

Kelly`s Cross y = 7.546*(1-Exp (- (x/32.856)^0.439)) 258 0.972

Jacks Road y = 7.559*(1-Exp (- (x/198.32)^0.314)) 256 0.946

variables: y = maximum branch diameter x = tree spacing expressed in square meters

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ReferencesAnon., 1969-70; file notes on the Nelder spacing and controlled thinning experiment, 1969 - 1970Anon., 1984; Information Report status of Nelder spacing trials in New Brunswick, Department of

Natural Resources, Forest Management Branch, December 1984, 10ppAssmann, E., 1970; The Principles of Forest Yield Study, Pergamon Press, CCNo. 74-114851, 506 ppBrewer, J.T., 1970; notes to Nelder file, September 1970Clutter, J.L. et al., 1983; Timber Management, A Quantitative Approach, John Wiley & Sons Inc., July 1982, 333ppGlen, W.M., 1986; notes to Nelder fileKennel, E., 1996; personal communication, Faculty of Forestry, Ludwig-Maximilian-University,

MunichKrinard, R.M., 1985; Cottonwood development through 19 years in a Nelder`s design, USDA

Research Note SO-322, December 1985, 4ppLee, S.J., 1996; Aspects of wood quality, Scottish forestry, number 4, October 1996, 234ppMatheson, E.T. and Stewart, P.R., 1986; Canadian Forestry Service - Maritimes Technical Note NO.

149, March 1986, 7ppMLB, 1997; Maritime Lumber Bureau, P.O.Box 459, Amherst, N.S. B4H 4A1, fax noteNelder, J.A., 1962; New kinds of systematic designs for spacing experiments, Journal of the

American statistical Association, number 298, June 1962, 238-307ppVan Slyke, A.L., ca. 1963; Study spacing and thinning with Nelder`s new systematic designs,

University of New Brunswick, Fredericton, 11ppVan Slyke, A.L., ca. 1963; Analysis of Nelder systematic spacing designs, Forestry 466, Term

Project, University of New Brunswick, Fredericton, 12pp

Project Staff measurement 1986 Lane Campbell & Joe Ryanmeasurement 1991 Mike Bradley & Chris Higginsmeasurement 1995 Martin Rosemeasurement 1997 Christoph Krieger, Charles Campbell, Jon Hutchinsondata analysis Christoph Krieger, Jon Hutchinsonreport preparation Christoph Krieger

Acknowledgments

The author thanks the Prince Edward Island Department of Agriculture and Forestry for allowing himto work as a volunteer between October 1997 and February 1998 and for permission to measure thetrees on their Nelder spacing trials.

My specific thanks to Mr W. Glen and Mr P. McKnight and all members of the Silviculture Sectionfor their support and congeniality .

Charlottetown, April 1 , 1998 Christoph Kriegerst