Relationships between crown projected area and components of above-ground biomass in Norway spruce trees in even-aged stands: Empirical results and their interpretation

Forest Ecology and Management, 40 ( 1991 ) 243 -260 243 Elsevier Science Publ ishers B.V., Ams te rdam

Relationships between crown projected area and components of above-ground biomass in Norway spruce trees in even-aged stands: Empirical results

and their interpretation

Timo Kuuluvainen 1 University of Joensuu, Faculty of Forestry, P. O. Box I 11, SF-80101 Joensuu, Finland

(Accepted 29 November 1989 )

ABSTRACT

Kuuluvainen, T., 1991. Relationships between crown projected area and components of above-ground biomass in Norway spruce trees in even-aged stands: empirical results and their interpretation. For. Ecol. Manage., 40: 243-260.

Sample tree material was reanalyzed in order to study the relationships between horizontal crown projected area and components of above-ground biomass in Norway spruce (Picea abies (L.) Karst. ) trees growing in even-aged stands. The needle mass of dominant trees increased linearly with the increase in crown projected area, but in co-dominant and dominanted trees the increase in needle mass levelled off toward larger crown projected areas. The branch mass of dominant and co-dominant trees accumulated faster than linearly with increasing crown projected area, whereas in dominated trees an approximately linear relationship existed between these two variables. The increase in needle and branch mass per unit increase in crown projected area was highest in dominant trees and decreased to co-dominant and dominated trees, i.e. with tree position in the canopy. The stem mass accumulated obviously faster than linearly and similarly in all tree classes with the increase in crown projected area. The narrow crown shape indicated a high density of all components of above-ground biomass per unit of crown projected area.

INTRODUCTION

A main goal of intensive forestry is to increase the productivity of tree stands. Because stand growth is the sum of the growth of its constituent trees, special attention must be paid to how efficiently individual trees use the land area they occupy in growth (e.g. Cannell, 1976). To assess the efficiency of space utilization of forest trees, knowledge is required of two basic quantities, (i) the growth and biomass of a tree and (ii) the ground surface area it oc-

~Present address: Univers i ty of Helsinki, D e p a r t m e n t of Silviculture, U n i o n i n k a t u 40B, 00170 Helsinki, Finland.

0378 -1127 /91 /$03 .50 © 1991 - - Elsevier Science Publ ishers B.V.

244 TIMO KUULUVAINEN

cupies. Such knowledge is important when aiming to increase the efficiency of space utilization in tree stands, for example by breeding new crop-tree ideotypes.

Since space corresponds in a broad sense to resources, differences in tree architectures can be considered a way in which resources are captured. The architecture of most trees is developed by the serial repetition of organs by apical meristems. Following this thought, a tree can be regarded as an inte- grated complex of modules, usually shoots, linked together to constitute a hierarchy of these elementary structures (White, 1979; Hall6, 1986; Kello- m~iki and V/iis/inen, 1988). The aerial architecture of trees could thus be treated as a system of shoot-modules, where the living modules are supported by dead modules, and are connected to roots by a vascular system (Shinozaki et al., 1964a,b; Harper, 1977; Maillette, 1982a,b). Since the dry-matter production of a tree is a result of the dry-matter production of its shoots, the ways in which they are arranged and distributed in space largely determines the efficiency of resource utilization in growth by the individual tree (Harper, 1985).

Accordingly, when looking for possibilities to increase the productivity of plantation forests, special attention has to be paid to the effect of tree architecture and canopy design on the amount and disposition of growth (e.g. Farmer, 1976; Rook et al., 1985). In particular, the crown shape has often been considered to be related to the productivity of forest trees (e.g. Hoff- mann, 1968; Assmann, 1970; Oker-Blom and Kellom~iki, 1982; Kuuluvai- nen, 1988).

In this study I reanalyzed some of the morphological sample tree data published by Burger (1953 ) in order to examine the biomass-area relationships of individual Norway spruce (Picea abies (L.) Karst. ) trees growing in even- aged stands. Special attention was paid to the effect of crown shape on the amount ofbiomass per unit of crown projected area. The results are discussed in the context of the regulation of biomass-density relationships in individual trees and tree populations, as described by Yoda's self-thinning rule.

OUTLINES OF THE APPROACH

Let L denote the dimension of any structural component of the tree. Be- cause the growing area of the tree (s) is comparable to the second power, and mass (Y) to the third power of this dimension, one can write (Drew and Flewelling, 1977):

s~zL 2 (1)

Y ~ L 3 (2)

From eqns. ( 1 ) and (2) we get:

CROWN PROJECTED AREA AND ABOVE-GROUND BIOMASS IN NORWAY SPRUCE 245

s~_L2 ~ ( L 3 ) 2 / 3 ~ y2/3 (3)

Since, in a tree stand, the growing area of a tree is comparable to the inverse of stand density (N-1 ), one can get from eqn. (3):

Yocs3/2 ~ N - 3/2 (4)

According to eqn. (4), the mass of the tree is comparable to the power of 3/2 of the tree's growing area and to the power of - 3 / 2 of tree density in a closed, homogenous stand. The latter expression in equation (4) states the principle of the 3/2 power law of self-thinning, or the self-thinning rule (Yoda et al., 1963 ). This principle can also be applied to nonhomogenous stands, assuming that N = ~s;- ~, where s, is the growing area of tree i in the stand.

In a tree stand, each tree occupies an area determined by its crown projection. This means that on the area limited by the crown projection (A), the density of the tree i in s t and j is Aj7 ~. If the mass of this tree is Yj,, we get

Yji = C( 1/Aii ) -~= C(Aji) ~ ( 5 )

where C and k are parameters. Since equation (5) bears no implications on stand structure, it can be used

for trees from different stands. Furthermore, eqn. (5) indicates that the self- thinning rule is valid for a tree as a population of branches (leaves) whenever the tree is in the stage of self-thinning (Kellom~iki, 1986 ).

M A T E R I A L A N D M E T H O D S

Material

I utilized the sample tree material published by Burger ( 1953 ), consisting of measurements from 189 Norway spruce sample trees from even-aged stands in Switzerland. In order to homogenize the material, trees which had grown at a higher elevation than 1000 m above sea level were excluded, leaving 117 trees from the original sample. However, from this number both crown width and basic density of dry stemwood were documented for only 96 trees, which formed the sample tree population of this study. Burger ( 1953 ) had divided these 96 sample trees into four tree classes as follows: (a) dominants (first tree class), 40; (b) co-dominants (second tree class), 31; (c) dominated (third tree class ), 19; and (d) suppressed trees ( fourth tree class ), 6. Because there were so few suppressed trees, they were omit ted when the final results were presented.

The stand densities were known only in the case of 32 trees (P. Schmid- Haas, personal communicat ion, 1985 ). In these trees, which represented different tree classes, the crown shape did not correlate with stand density. For a detailed description of the original material see Burger ( 1953 ).

246

TABLE 1

Some statistical parameters of the variables of the sample tree population

TIMO KUULUVAINEN

Variable Mean Min. Max.

Tree age (years) 47.3 24.0 77.0 Diameter at 1.3 m (cm) 18.4 4.8 44.4 Tree height (m) 18.3 4.8 35.2 Stem dry-matter (kg) 134.8 2.3 886.9 Branch dry-matter (kg) 13.1 0.4 79.3 Needle dry-matter (kg) 10.4 0.6 46.4 Needle area (m 2) 137.8 8.5 678.3 Specific needle area (m 2 kg- ~ ) 5.9 4.4 7.2 Altitude of site (m) 585.7 400.0 960.0 Crown shape ratio 2.8 1.2 5.9 Harvest index 0.80 0.48 0.96

The characteristics of the sample trees selected for the study displayed a range of ages from 24 to 77 years, heights from 4.8 to 35.2 m, crown-shape ratios (crown-length/maximum-crown-width) from 1.2 to 5.9, total needle areas from 8.5 to 678.3 m 2, specific needle areas from 4.4 to 7.2 m 2 kg -1, altitudes of site from 400 to 960 m a.s.l., and harvest indices from 0.48 to 0.96, determined as the ratio between stem dry-matter and the total above- ground dry-matter (Table I ).

Computations

The crown projected area was calculated from the maximum crown diameter by assuming a circular crown projection. The needle dry-matter of the trees is given directly by Burger ( 1953, table 11 ). The dry-matter of branches was calculated using the treewise information given by Burger (1953, table 11 ) as:

Y b : [FYnb-- {FYnb 'MRnb/ ( 1 0 0 q ' M R n b ) } ] - - Yn ( 6 )

where Yb is dry-matter of branches (kg), FYnb is fresh-matter of needles and branches combined (kg), MRnb is moisture ratio (% of water from dry-matter) of needles and branches combined, and Yn is dry-matter of needles (kg).

In order to derive the stem dry-matter, the fresh volume of the stem was first calculated with Laasasenaho's ( 1982 ) equation, using Dbh and tree height as predictors (see Burger 1953, table 1 ). The stem dry volume of the trees was then calculated using the information given by Burger (1953, Tables 2 and 9) as:

Ys = Vs" [ ( 1 0 0 - - S H s ) / 1 0 0 ] "BDs ( 7 )

where Ys is stem dry mass (kg), Vs is stem fresh volume (m3), SHs is shrink-

CROWN PROJECTED AREA AND ABOVE-GROUND BIOMASS IN NORWAY SPRI JCE

TABLE 2

The transformations for the variables in the analysis of covariance

247

Variable Symbol Transformation

Stem mass/crown projected area Needle mass/crown projected area Branch mass/crown projected area Total above-ground mass/crown projected area

L/.4 , / '(Y/.4 ) )',/.4 In (Y.,/A) Y j A In ( YJA ) Y /A In( Y/A )

age percent of stem volume from fresh to dry wood and BD s is the basic density of dry stemwood (kg m-3) .

Techniques of analysis

In order to examine at tree level the relationship between the horizontal crown projected area and the different components of above-ground biomass (needles, branches and bole), the linear form of model ( 5 ) was utilized:

In (~ i ) = k-In (Aj,) + In (C) ( 8 )

where Yj, is the mass of the biomass component and Ai, is the horizontal crown projected area of the tree i in stand j; C and k are parameters.

The factors affecting the accumulation of biomass on crown projection were studied using one-way analysis of variance with covariates. Because different tree classes obviously receive different amounts of radiation, tree class was taken as the classification variable and crown-shape ratio, tree age, altitude of site and harvest index were used as covariates. Since the variance of ex- amined variables proved unequal (Bartlett-Box, P< 0.05), transformations were necessary (see Table 2 ). The direction of the effect of the studied variables on the biomass values per unit of crown projected area was assessed by regression analysis.

RESULTS

Components of biomass in relation to crown projected area

In dominant and co-dominant trees, the branch biomass accumulated faster than linearly with the increase in horizontal crown projected area, whereas in dominated trees an approximately linear relationship existed between these two variables (Fig. la). The rate of biomass increase per unit increase in crown projected area was highest in dominant trees and decreased to co-dominant and dominated trees, i.e. with tree position in the canopy. These pat- terns of branch biomass accumulation were accordingly reflected in the ex-

248

50 Branch mass, kg

40

30

20

10

0

/:

10 20

Croon pro]ec led area, m 2

40

30

20

10

0

T I M O K U U L U V A I N E N

N e e d l e m a s s , kg

b

lO 20

Croun p r o j e c t e d area, m 2

600 Stem mass, kg

500

400

300

200

100

0

~ ~ c .~,,..,:, 750 Tota l mass, kg

500

250

d / ,~"'" ;

lO 20 lO 20

Croun pro]ec ted area, m 2 Croun projec ted area, m 2

.... B l l tree

classes

.... 1. t ree c lass

........ 2. t ree c lass

- - 3 . t ree c lass

Fig. 1. (a ) Branch mass, (b) needle mass, (c) stem mass and (d) total above-ground biomass of the trees as a function of crown projected area in tree classes 1-3 and all tree classes taken into account; according to the models in Table 3.

ponent values of the allometric equation (eqn. 5, Table 3), i.e. the exponent was greater than unity in dominant and co-dominant trees and close to unity in dominated trees.

The increase in needle biomass per unit increase in crown projected area was highest in dominant trees, and decreased to co-dominant and dominated trees (Fig. I b ). The exponent of the allometric equation was, in the dominant trees, approximately equal to one, but in the co-dominant and dominated trees less than one (Table 3 ). This indicates that, in dominant trees, the needle biomass was linearly related to crown projected area and, consequently, the mean needle density (needle biomass per unit of crown projected area) was almost constant and independent of tree age and crown projected area. In the lower tree classes the increase in needle biomass levelled off toward larger crown projected areas, i.e. the mean needle density decreased with increase in crown spread (Fig. 1 b).

Stem biomass and, consequently, total above-ground biomass accumulated in all tree classes considerably faster than linearly with the increase in crown projected area (Figs. lc and ld) . This was a consequence of the continuing accumulation of stemwood during the life-span of the trees. The exponent of


TABLE3

The allometric regression models (eqn. 8) for the relationship between crown projected area and components of above-ground biomass and harvest index for all sample trees and separated into first, second and third tree classes

Y-variable k In (C) C r 2 F P

All tree classes Branches 1.41"** - 0.44** 0.64 0.79 361.93 < 0.00 t Needles 1.13*** 0.01 1.01 0.72 244.73 < 0.001 Stem 1.64"** 1.41"** 4.10 0.77 310.57 < 0.001 Total 1.55*** 1.79*** 5.99 0.79 361.12 < 0.001 HI 0.10"** -- 0.38*** 0.68 0.22 26.47 < 0.001 Tree class 1 Branches 1.31"** - 0.05 0.95 0.83 183.91 < 0.001 Needles 1.03"** 0.47* 1.60 0.77 126.92 < 0.001 Stem 1.76*** 1.03** 2.80 0.80 153.12 < 0.001 Total 1.61 *** 1.61"** 5.00 0.82 169.18 < 0.001 HI 0.15*** -0 .58*** 0.56 0.55 46.88 < 0.001 Tree class 2 Branches 1.19*** - 0.04 0.96 0.70 67.36 < 0.001 Needles 0.78*** 0.64*** 1.90 0.71 69.49 < 0.001 Stem 1.43"** 1.96"** 7.10 0.65 53.74 < 0.001 Total 1.35"** 2.28*** 9.78 0.67 59.38 < 0.001 HI 0.08** - 0.33*** 0.72 0.26 10.13 < 0.01 Tree class 3 Branches 1.09"* - 0 . 3 3 0.72 0.65 31.27 < 0.001 Needles 0.7 I*** 0.16 1.17 0.59 24.37 < 0.00 l Stem 1.66"** 1.29"** 3.63 0.73 47.89 < 0.001 Total 1.50"** 1.70*** 5.47 0.74 49.47 < 0.001 HI 0.16** -- 0.41"** 0.66 0.45 13.98 < 0.01

The statistical significance of the parameters are denoted as P< 0.001***, 0 .01<P<0.001**: 0.05 < P < 0 . 0 1 * .

the allometric equation for stem biomass had the mean value of 1.64, varying between tree classes from 1.76 to 1.43 (Table 3). However, the differences between tree classes in the relationship between stem biomass and crown projected area were rather small (Fig. l c).

For total above-ground biomass, all tree classes combined, the exponent of the allometric equation was close to 1.5 (see eqn. (4 ) ) . In dominant trees the exponent was higher ( 1.61 ) and in co-dominant trees lower ( 1.35 ); in dominated trees the exponent was again close to 1.5. Thus, the total above-ground biomass accumulated in all tree classes faster than linearly, but with a varying rate with the increase in crown projected areas (Fig. l d).

The derived models using crown projected area as a predictor explained 72-79%, 77-83%, 65-71% and 59-74% of the variance in the biomass components of all trees and tree classes 1-3, respectively (Table 3). In general,

2 5 0 T I M O K U U L U V A I N E N

the biomass estimates calculated using crown projected area as a predictor were more reliable in the dominant tree class than in lower tree classes, and the variation thus increased from upper to lower tree classes. The derived models for all tree classes were statistically significant, however.

Harvest index in relation to crown projected area

The harvest index of the trees, i.e. the proportion of stem biomass from total above-ground biomass, increased from smaller to larger and older trees (Table 3 ), due to the continuous accumulation of stem biomass accompanied with simultaneous loss of needles and pruning of branches. This pattern was most clearly seen in dominant trees, in which harvest index increased first rapidly as crown projected area became larger, but settled to an almost constant level with crown projected areas larger than approximately 10 m 2 (Fig. 2 ). The fact that the increase in harvest index in larger and older trees halted, indicates that a balance between stem biomass accumulation, on the one hand, and branch and needle biomass accumulation, on the other, was approached during later stages of tree growth. Crown projected area explained 22, 54, 26 and 45% of the variance in harvest index of all trees and tree classes 1-3, respectively (Table 3).

X I,I C~

Z

co UJ

I

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0

• •

• : • . .

• 0 °

o o

I I I I I I

5 10 15 20 25 30

CROWN PROJECTED AREA, M 2

Fig. 2. The relationship between harvest index (stem dry-matter/total above-ground biomass) and crown projected area in dominant trees.

CROWN PROJECTED AREA AND ABOVE-GROUND BIOMASS IN NORWAY SPRUCE 2 5 1

Effect of crown shape on biomass density

The analysis of covariance with tree age, altitude of the site, harvest index and crown-shape ratio as covariates, and tree class as the classification variable, showed that crown-shape ratio had a significant effect on the biomass density of all above-ground tree components, i.e. branches, needles, stem, and, consequently, on the total biomass density per unit of crown projected area (Table 4). This indicates that tree morphology had an effect on how a tree accumulated biomass with respect to its growing area.

Tree age had a significant effect on branch, stem and total biomass density, while the altitude of site had an effect only on stem biomass density of a tree. Neither of these variables had a significant influence on needle biomass den-

TABLE 4

The analysis o f covar iance on the m e a n dens i ty o f branch, needle, s tem and total b iomass per uni t o f crown projected area (kg m -x, n = 96) , with tree age, a l t i tude o f site, crown shape ratio and harves t index as covar ia tes and tree class as the classif icat ion variable

Source o f var ia t ion s s DF MS F P

Branches With in + residual 9.42 88 0.11 Tree age 6.68 1 6.68 62.39 < 0.00 I Alt i tude o f site 0.02 1 0.02 0.20 0.655 Crown shape ratio 4.83 1 4.83 45.14 < 0.00 I Harves t index 0.40 1 0.40 3.74 0.056 Tree class 5.67 3 1.89 17.65 < 0.001 Needles With in + residual 1.58 88 0.02 Tree age 0.05 1 0.05 2.87 0.094 Alt i tude o f site 0.01 1 0.01 0.39 0.534 Crown shape ratio 0.98 1 0.98 54.44 < 0.001 Harves t index 0.00 1 0.00 0.00 0.962 Tree class 1.40 3 0.47 25.95 < 0.001 Stem With in + residual 26.21 88 0.30 Tree age 21.24 1 21.24 71.30 < 0.001 Alt i tude o f site 1.44 1 1.44 4.83 0.031 Crown shape ratio 11.21 I 11.21 37.63 < 0.001 Harves t index 9.68 1 9.68 32.50 < 0.001 Tree class 10.33 3 3.44 11.56 < 0.001 Total With in + residual 6.59 88 0.07 Tree age 3.68 1 3.68 49.09 < 0.001 Alt i tude o f site 0.07 1 0.07 0.90 0.346 Crown shape ratio 4.00 1 4.00 53.37 < 0.001 Harves t index 4.06 1 4.06 54.18 < 0.00 I Tree class 4.08 3 1.36 18.16 < 0.001


sity. The harvest index had an effect on the branch, stem and, consequently, on total biomass density, but no effect on needle biomass density. The tree class, in turn, had a clear effect on the density of all the components of above- ground biomass. In particular, the needle biomass density of the trees appeared to be rather insensitive to such factors as altitude of site, harvest index and tree age, but very sensitive to crown shape and tree class.

To assess the direction of the effect of these variables on the biomass density values, regression equations were derived (Table 5 ). Narrow crown shape indicated high biomass density values for all components of above-ground biomass. Also, the effect of harvest index was clear and, as could be expected from the definition of harvest index, a high harvest index indicated high stem and total biomass densities, but low branch biomass values per unit of crown projected area. Branch biomass density increased with tree age and decreased

TABLE5

Regression coefficients for the variables that in the analysis of covariance (see Table 4) proved to have a significant effect on the biomass density values

Y-Variable Regression X-Variable t-value for coefficient coefficient

Branch mass/crown projected area - 2.086 Harvest index - 2.038 + 0.463 Crown shape ratio 4.883 - 0 . 3 9 5 Tree class - 4 . 9 0 5 + 0.044 Tree age 6.823 +0.574 Constant 0.806

r :=0 .572 , F = 30.37, P < 0.001 Needle mass/crown projected area

+ 0.464 Crown shape ratio 5.961 - 0.345 Tree class - 5.302 + 0.778 Constant 2.668

r2=0.503, F=47.15 , P<0.001 Stem mass/crown projected area

+ 26.019 Harvest index 2.574 + 3.859 Crown shape ratio 4.749 -0 .011 Altitude - 2.589 - 2.740 Tree class - 3.832 + 0.470 Tree age 7.903

- 26.844 Constant - 3.432 r2=0.755, F= 55.49, P < 0,001

Total mass/crown projected area + 26.019 Harvest index

+ 4.650 Crown shape ratio - 3.983 Tree class + 0.464 Tree age

- 38.504 Constant r2 =0.742, F = 65.40, P < 0.001

2.574 5.210

- 5 . 2 5 3 7.597

- 5 . 7 4 9

CROWN PROJECTED AREA AND ABOVE-GROUND BIOMASS IN NORWAY SPRI ICE 2 5 3

with tree class. Stem biomass density increased with age and decreased with altitude, and from upper to lower tree classes.

D I S C U S S I O N A N D C O N C L U S I O N S

The growth and biomass of spruce forests have been studied for several decades (see Schmidt-Vogt, 1986). According to Palumets (1988) the pattern of biomass partitioning in spruce is quite variable, with factors which are known to affect biomass distribution including age, climate, soil conditions, stand structure and genetic properties. It was not surprising, in this respect, that the unexplained share of variance in the models for the relationships between crown projected area and components of above-ground biomass remained considerable, since the study material represented trees from different growing conditions (see Burger, 1953). However, the proportions of explained variance were thought to be sufficient to facilitate the use of the derived models for analysing the biomass-area relationships of the sample tree material.

It is evident that the relationship between total above-ground biomass and crown coverage in trees is a result of the dynamics of each of the components of above-ground biomass in relation to growing space. In this respect, each of the above-ground tree parts behaved differently. Particularly in the dominant spruce trees, an approximately linear relationship existed between crown projected area and needle biomass of the tree. Thus, the mean needle-biomass density of the crown projected area was almost constant, indicating that the growth and mortality of needles per unit of crown projected area approximately balanced each other. This result can be explained if one assumes that needle biomass is regulated in a population-like manner through the birth and death rates of needles (Harper and Bell, 1979; White. 1981; Kellom~iki and V~iis~inen, 1988).

In contrast to needle biomass, the allometric exponent for stem biomass was substantially greater than unity in all tree classes, indicating an increasing slope in changes in stem biomass with increase in crown projected area. This was obviously the result of the continuous accumulation of stem biomass in surviving trees, since mortality of stems occurs only at population level. The fact that the relationship between crown projected area and stem biomass is concave may be attributed to the gradual decline of horizontal expansion of the crown along with age.

The case of branches appeared to be an intermediate of those of needles and stem: branch biomass increased faster than linearly with crown projected area, but the accumulation of biomass occurred more slowly than in the case of stemwood. The processes underlying this pattern are the accumulation of supporting and conducting woody tissue to the living branches through sec- ondary growth and self-pruning of lower branches of the crown.


It becomes clear that, at the individual tree level, biomass-density relationships encompass three intrinsically different but interrelated processes: (i) regulation of needle biomass (number); (ii) regulation of branch number and accumulation of biomass to living branches; and (iii) accumulation of stem biomass. The dynamics of each of these components of above-ground biomass of the tree have different response times in the forest, but they are interrelated through the pipe-model principle. It is reasonable to assume that growth and death of needles implies formation and release of transport and support structure, respectively, in branches and stem (Valentine, 1985; M~ikel~i, 1986 ).

Needle biomass is regulated mainly by the birth and death rate of needles on a time-scale ranging from months to years. Branch biomass is determined both by the mortality and birth of branch units and by the accumulation of biomass into neeedle-bearing branches. Both of these phenomena are dependent on needle dynamics, but function on a longer time-scale of several years. At tree level, stem biomass only accumulates, but the rate of biomass accumulation is regulated by branch and needle dynamics.

The decrease in branch and needle biomass densities from dominant to more suppressed tree positions obviously reflects the hierarchy of resource consumption in a tree stand. Lower light levels decrease the quantity of needles that can be maintained and, consequently, also branch growth per unit land area. In addition, the broad horizontally extended crown shapes of the suppressed trees (e.g. Horn, 1971 ) may decrease branch and needle biomass in relation to crown projected area. The relationship between stem biomass and crown projected area, however, showed much less variation between tree classes, indicating an approximately constant efficiency of space occupancy in this respect.

Several factors may contribute to the approximate constancy of the stem- biomass-area relationship found in the sample trees from different tree classes. First, stem biomass expresses the total amount of dry-matter allocated to the stem during the life-time of a tree, which includes the period before the sepa- ration of tree classes, while branch and needle biomass reflects more the cur- rent growing conditions of a tree. Secondly, weak and suppressed trees tend to allocate more growth to the stem than dominant ones; large proportional allocation to the stem also limits crown expansion (e.g. Albrektson and Val- inger, 1985 ). Thirdly, physiological and structural modifications of needles as induced by shading - for example increase in specific needle area - obviously increase needle efficiency in light utilization. Fourthly, the decrease in within-tree shading of foliage from bigger dominant to smaller suppressed trees decreases the effect of shading by the dominant tree layer (Pukkala and Kuuluvainen, 1987).

The fact that the share of explained variance in the models between crown projected area and components of above-ground biomass decreased from up-

CROWN PROJ ECTED AREA AND ABOVE-GROUND BIOMASS IN NORWAY SPRUCE 2 5 5

per to lower tree classes can be due to both the varying growing conditions of suppressed trees and to the somewhat arbitrary determination of tree classes.

The consequences of the within-stand competi t ion are most clearly seen in the differentiation of the tree population into tree classes and in the respec- tive modifications in the allometric relationships of the trees. Although it is clear that tree-level and stand-level phenomena are not directly comparable, they are closely related. In this respect, the present study may give some in- sights into the regulation of biomass-density relations in closed stands, as generalized by the 3/2 power law of self-thinning (Yoda et al., 1963). This model deals with the relationship between stand density and mean biomass of the stand members, and defines a limit on the biomass which can be packed into a given space. Obviously, the biomass relationships at the population level are a consequence of population dynamics and individual-level processes in dry-matter accumulation and distribution.

The allometric exponent value of 3/2, as predicted by eqn. (4) was not found in this study for any single component of above-ground biomass in any tree class. In different tree classes the exponents for branch biomass ranged from 1.31 to 1.09 and for needle mass from 1.03 to 0.71; in both cases the exponent values decreased systematicly from dominant to co-dominant and dominated trees. The exponents for stem biomass ranged from 1.76 to 1.43, and for total above-ground biomass from 1.35 to 1.61. In this case, the dominant trees had the highest and co-dominant the lowest values, i.e. with stem biomass the exponent values did not change systematically with tree position in the canopy (Table 3).

Taking into account all tree classes, the exponent for stem biomass was higher, and for branch biomass lower than 3/2, while for needles it approached unity. However, for total above-ground biomass of all tree classes, the value of the exponent of the allometric equation conformed approximately to that predicted by eqn. (4), i.e. 3/2. If we assume a complete canopy cover, this means that the exponent of the self-thinning rule is equal to -3/2.

The fact that the exponent of the allometric equation for stem and total above-ground biomass was greater in dominant trees than in co-dominant and dominated trees indicates that the shaded trees accumulated biomass more slowly in relation to the land area they covered. At the population level, a corresponding phenomenon in the biomass-density regulation is the finding that the slope of the self-thinning rule approaches - 1, if plants are grown in deep shade (Furnas, 1981; Lonsdale and Watkinson, 1982).

It appears, thus, that similar biomass-density relationships as generally found at the population level can be found also at the individual-tree level. Because at tree level the biomass-density relationships arise from the interrelated regulation of needle, branch and stem biomass densities, it seems possible that the biomass-density relationships found at the population level could

2 5 6 TIMO KUULUVAINEN

indicate individual-level relationships of tree allometry (see also Kellom~iki, 1986).

The harvest index of a tree indicates the share of stemwood from total above- ground biomass at a given moment. In small trees, the harvest index increased very rapidly at first with increase in crown projected area. This was apparently a consequence of the initial rapid increase in stem biomass, while branch and needle biomass increased more slowly with increase in crown projected area (see Fig. I ). Evidently, this reflects the increased allocation requirements to stem during the stage of rapid height growth, as predicted by the pipe-model theory (M~ikel~i, 1986).

In dominant trees, however, the relationship between the above-ground biomass components was balanced when the tree had captured a certain amount of living space; the harvest index remained relatively constant for trees with crown projected areas larger than 10 m 2, corresponding to a crown diameter of approximately 3.6 m. This can be understood by considering the development of tree morphology and the internal functional requirements of a tree. Because increase in tree height levels off with the increase in crown spread (Fig. 3), the allocation requirements for height growth (stem) decrease in relation to allocation requirements for horizontal growth (branches, needles). Accordingly, it has been reported that the proportional allocation of dry-matter to needles (and branches) increases in spruce forests toward old-growth stage (Kazimirov and Morozova, 1974). This leads to declining stemwood increment and stabilizing harvest index in older trees.

Norway spruce is characterized by high variability in crown form (Schmidt- Vogt, 1986, p. 37-38 ), which was also displayed by the sample-tree material

'° I 30 •

g • 20 • • Oeo •

~-. I I J

0 10 20 30

CROWN PROJECTED AREA, M 2

Fig. 3. The relationship between tree height and crown projected area in dominant trees.


of this study. It is evident that genetically determined differences in crown architecture regulate the hierarchy of the light-resource utilization between the photosynthesizing components of crown structure (mainly shoots) and, consequently, product ion and allocation of photosynthates (Harper, 1985 ). Accordingly, the crown shape was found to have a strong effect on the biomass projected onto the horizontal crown projection. Narrow-crowned trees had more biomass per unit of crown projected area than broad-crowned trees. This resulted directly from two interacting physical causes, which both acted to increase the amount ofbiomass packed onto a given crown coverage. First, the narrow and deep crowns possessed more needle and branch biomass per unit of crown volume and consequently, they produced more stemwood per unit of crown projected area than broader crowns (Kuuluvainen, 1988 ). Sec- ondly, the geometric shape of narrow and deep crowns obviously depicts smaller horizontal space requirements for equal crown volumes, when com- pared with broad-crowned trees.

The results of this tree-level study support the hypothesis that narrow- crowned Norway spruce are able to accumulate more biomass per unit of occupied land area than broad-crowned trees of the same age. The fact that narrow crown forms were able to maintain higher amounts of light-gathering needle units per occupied land area than broad crown forms, may indicate differences in the efficiency of resource utilization between different tree architectures (e.g. Jahnke and Lawrence, 1965 ).

It is noteworthy that the crown surface area, contributing to interception of diffuse radiation and gas exchange, is greater per unit of crown volume in narrow-crowned trees than in broad-crowned trees. Some evidence suggests that narrow-crowned trees are characterized by less self-shading when com- pared to broader crown shapes (Oker-Blom and Kellom~iki, 1983; Kuuluvai- nen and Pukkala, 1987, 1989). The beneficial within-crown light regime of the narrow-crowned trees, however, is likely to delay self-pruning (Kuuluvai- nen, 1988 ), but will also increase the mean life-span of the photosynthesizing organs. This may increase the efficiency of resource utilization by increasing the productive output of the organs in relation to their building costs.

Are narrow-crowned trees also more efficient in biomass production and accumulation at stand level? Ellison ( 1989; cf. Miyanishi et al., 1979 ) argues that self-thinning is determined by plant morphology, so that the slope of the self-thinning line is steeper for populations of vertically oriented plants in comparison to more horizontally extended plant architectures. Lonsdale and Watkinson ( 1983 ) derived similar results, and concluded that plant architecture affects self-thinning in such a way that the canopy can be deeper and denser the more light is t ransmitted through a given leaf-area index. The competition for light is also apparently a central factor limiting photosynthesis in spruce stands (Schulze et al., 1977) and, thus, inducing density-dependent mortality. There is evidence that, in coniferous trees at high latitudes, a nar-


row crown shape indicates low within-tree competition for light (Kuuluvai- nen and Pukkala, 1987 ), as well as efficient light interception in stand conditions (Pukkala and Kuuluvainen, 1987). In addition, narrow-crowned trees seem to allocate a large proportion of the produced dry-matter to stems (Kel- lom~iki, 1986; Kuuluvainen, 1988 ). In the light of these results and the results of this study, it seems possible that crown architecture affects density-dependent regulation and, consequently, yield of even-aged spruce stands.

Thus, if the aim is to maximize stemwood production, stands of narrow- crowned trees could be more efficient in resource utilization than broad- crowned trees. It appears, however, that the mean tree size and length of branchless stem would be smaller in a stand of narrow-crowned trees, com- pared with a stand of broad-crowned trees (Kellom~iki, 1986; Kuuluvainen, 1988 ). Accordingly, Etwerk ( 1985 ) concluded that the pulpwood production of Norway-spruce stands could be substantially increased by selecting for narrow-crowned trees. However, we need more knowledge of the factors actually regulating dry-matter production and distribution in trees, as well as of the ecological role of tree architecture in maintaining forest stability in varying environments.

ACKNOWLEDGEMENTS

I wish to thank Prof. P. Schmid-Haas for providing complementary material concerning the sample tree data, Prof. Seppo Kellom~iki and Dr. Timo Pukkala for helpful discussions, and two anonymous reviewers for insightful comments and B. Sc.For. Helen Jozefek for revising the English of the manuscript.

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Documents

Relationships between crown projected area and components of above-ground biomass in Norway spruce trees in even-aged stands: Empirical results and their interpretation