Individual competition indices for conifer plantations

Individual competition indices for conifer plantations

Agriculture, Ecosystems and Environment, 27 (1989) 429-437 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands 429 Individual...

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Agriculture, Ecosystems and Environment, 27 (1989) 429-437 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands


Individual Competition Indices for Conifer Plantations* P. CORONA and A. FERRARA

Centro di Sperimentazione Agricola e Forestale S.A.F. (E.N.C.C. Group), via di Casalotti 300, 00166 Rome (Italy) (Accepted for publication 19 April 1989 )

ABSTRACT Corona, P. and Ferrara, A., 1989. Individual competition indices for conifer plantations. Agric. Ecosystems Environ., 27: 429-437. In the management of sustainable conifer plantations, the development of yield models allowing a proper planning of interventions within a low-input silvicultural system is of major interest. The fundamental hypothesis in most forest plantation yield studies assumes that individual tree growth is dependent upon the competitive influence of neighbouring trees. A critical synthesis of the bestknown types of individual competition indices is presented, chiefly by discussing applicative differences between the 'distance dependent' {spatial) and the 'distance independent' (non-spatial) indices. Experimental preliminary trials show that non-spatial competition indices have a predictive ability no lower than the spatial ones, at least when used for conifer-plantation yield projection. The following simple index proved suitable: N

NSCIMj = ~ D~/D~ i=o where Di is the diameter of the ith competitor and Dj is the diameter of the tree in question. Interactions between individual competition indices, predictive ability and stand attributes, such as density and fertility, have been observed.


Nowadays, a great problem in plantation silviculture is represented by the lack of practical influence of ecological research on plantation production as regards management, technical and economic conditions. In particular, in the management of sustainable conifer plantations, the development of yield models allowing a proper planning of interventions within a low-input silvicultural system is of major interest. *Research work supported by C.N.R., Italy. Special grant I.P.R.A. Subproject 1, Paper no. 1813.


© 1989 Elsevier Science Publishers B.V.


The fundamental hypothesis in most yield studies assumes that individual tree growth is dependent on the competitive influence of neighbouring trees (Smith and Bell, 1983). In fact, artificial stand dynamics are well characterized by the gradual intensification of tree competition with age, as a result of the increasing need on the part of individual trees for life-supporting resources. In this sense, in planning a low-input silvicultural system, one of the major problems is to look for a balance between tree spacing optimization, as a function of the increase in individual needs, and the minimization of anthropic interventions, like thinnings, which can directly reduce competition, improving individual growth. Individual competition indices can be used to quantify competition experienced by a tree and to correlate it to its growth rate. The biological processes involved in competition between trees are extremely complex, so it is difficult to describe them with a single mathematical competition index. However, such indices can provide a measure of the outcome of these processes and have been found useful in predicting tree growth (Daniels et al., 1986). Competition indices can be discerned in two classes on the basis of the primary competition unit used in growth models: 'whole stand model' and 'individual tree model' indices. Measures of competition which are based on the average area occupied or available area per tree, relative to some standard density condition, are collectively referred to as 'whole stand' indices (e.g. Krajicek et al., 1961 ). In young plantations, competition occurs which has an impact on the development of stand structure. In this sense, the predictive ability of 'whole stand' competition indices is questionable, because the use of average tree conditions obscures the causal relationship between inter-tree competition and individual tree growth (Smith, 1977 ). On the other hand, 'individual' indices produce detailed information with more significance in relation to stand structure and future yield. Specifically, individual competition indices can be regarded as stand density measures that reflect the relative level of competition between individual trees for growing space. The purpose of this study is to evaluate the practical use of a new modification of the simple competition index developed by Lorimer (1983), as individual increment predictor for conifers in young plantations. INDIVIDUAL COMPETITION INDICES

The type of competition indices representing a direct outgrowth of the distance-measuring techniques used in ecological sampling are referred to as 'tree size and distance dependent' indices (e.g. Hegyi, 1974; Ellis, 1979). In assessing the relative competitive status, they combine spatial relationships between individual trees in the plantation and tree size, that can be quantified by a measurable characteristic, such as diameter at breast height (DBH), crown


dimensions, height. Tree growing space is assumed to be a circle centered on the tree, with a radius proportional to its size: any other tree inside the circle boundaries is regarded as a competitor. A large number of competition indices based on tree dimensions and distance relationships can potentially be formulated, but generally the indices, including the initial size of the tree of interest (subject tree), show better correlation with observed growth than the ones without the size of the subject tree (Nystroem and Gemmel, 1987). The best-known index of this type is the sum of the ratios of the diameters of a subject tree and its competitors, weighted by the distances from the subject tree (Daniels, 1976). Two interesting modifications Can be introduced into this index, making it independent from plantation age and more responsive to tree spatial patterns (Lorimer, 1983). The first is not to fix the radius of the growing space circle (this radius is currently termed 'search radius', precisely because it is used to look for competitors in the area surrounding the subject tree), estimating it as a constant multiple of the overstory trees' mean crown radius. The second is to relativize inter-tree distances, dividing them by the search radius. Thus, the tree size and distance-dependent competition index (SCI) becomes the following: N

SCIj = ~, (Di/Dj. (b.MCR)/Lij) i=O

where Dj = diameter of the jth subject tree; Di = diameter of the ith competitor tree; Lij= distance between ith and jth tree; N--total number of competitors ofjth subject tree; MCR = overstory trees' mean crown radius; b = MCR expansion factor (a 3.5 value is generally recommended). A SCI= 0 indicates an open grown tree (i.e. no competition). With Ceteris paribus, doubling the distance of a competitor from the subject tree reduces the contribution of that tree to the total competition index by 50%, while doubling its diameter doubles its contribution. The computation of this index requires detailed stem coordinates, in addition to diameter and overstory trees' sample crown measurements. It is important to point out that spatial indices have not always been superior to the indices which do not take into account spatial arrangements of individual trees, at least for yield projection in plantations (Martin and Ek, 1984). Clearly, the main advantage of non-spatial indices is that the mapping of stem location is not needed, so they are not only more easily computable, but should also be more suitable in long-term forecasting than spatial indices (Nystroem and Gemmel, 1987). Many non-spatial individual competition indices have been developed. An interesting one is that proposed by Lorimer (1983): N

NSCIj = • D,/Dj i=0

432 This index, easily computable in the field, considers both the relative size of the subject tree to competitors as well as stand density level, since it increases as the number of competitors increases. The competitors can be selected with the same procedure as SCI: the main difference is that all competitors contribute equally, without regard to the spatial distribution around the subject tree. However, what should be taken into account is the fact that the interaction between individual trees is generally assumed to be proportional to basal areas rather t h a n diameters (Hatch et al., 1975). In this sense, it is more acceptable, from a biological viewpoint, to modify the NSCI index as follows: N

NSCIMi= ~ Di/Dj 2 2 i=0

The SCI, NSCI and NSCIM indices seem to be a good compromise between yield forecasting significance and mensuration costs. In the present study, their effectiveness as predictors of individual tree increment has been compared. Meanwhile, it was deemed interesting also to test the effectiveness of the selected indices in relation to different levels of stand fertility and density treatments. EXPERIMENTAL METHODS The experimental trials were carried out within an 11-year-old Pinus radiata D. Don plantation established near Mount Arci in the centre of Sardinia (Italy). The plantation is located at 700-750 m a.s.l., on a 5-15%, N - N E facing, slope. Mean annual temperature is around 13.5°C. Mean annual rainfall is about 1100 mm, mainly concentrated between November and April. The bioclimate is humid-Mediterranean, with cool winters. Soil parent material is made up of trachytic rocks, with sandy loam/sandy clay loam soils, moderately deep and very stoney. The plantation, set up according to a square design with a 2.5m tree spacing, presented a density of 1400-1500 trees ha -1 at the age of 11 (1982), with an average height of 9-10 m. At the same age, an experimental thinning was carried out, according to a design based on the following 3 density treatments: standing volume selective removal by some 25% ( T r e a t m e n t A); standing volume mixed (systematic + selective ) removal by some 35 % (Treatment B); no removal (control, T r e a t m e n t C). Each t r e a t m e n t was repeated in 4 stand fertility classes. The experimental plots had an area of 0.2 ha each, for a total of 2.4 ha; the plot attribution to a fertility class was made on the basis of the mean annual volume increment measured in each plot before thinning (i.e., first c l a s s = l l m 3 ha -1 y e a r - l ; second class=12 m 8 ha -1 year-~; third class = 13 m 3 h a - 1 y e a r - 1; fourth class-- 14 m 3 h a - 1 y e a r - 1). Plot measurements were repeated annually until 1986. Statistical indicators of the principal variables at the first measurement are reported in Table 1.

433 TABLE 1 Statistical indicators for some variables at the first m e a s u r e m e n t in the 12 sample plots

Diameter at breast height (cm) N u m b e r of trees (n h a - 1) S t a n d basal area (m s h a - 1) DBH i n c r e m e n t (cm y e a r - 1) IBA i n c r e m e n t (cm 2 year -1 )





8.6 825 16.55 0.16 10.18

21.9 1520 32.90 1.43 203.40

16.21 1125 24.50 0.48 13.32

3.26 275 5.15 0.25 10.24

After thinning, 5 sample trees were randomly selected in each plot, whose detailed stem coordinates and DBH measurements were recorded. The growing area of each sample tree was assumed to be a circle centered on the tree, with a search radius equal to 3.5 times the plot overstory trees' mean crown radius. Both detailed coordinates and DBH of the trees inside the boundaries of the growing area (trees assumed to be competitors) were recorded yearly. The 3 competition indices under examination (SCI, NSCI and NSCIM) were evaluated and compared after the methodology developed by Daniels et al. (1986). The correlation coefficients between the indices and DBH and individual basal area (IBA) increments, measured on the sample trees, were calculated. Simple correlations provide useful comparisons, but it must be noted that, in practice, individual competition indices are generally used when other increment predictors, like tree size and stand density, are already known. Therefore, the predictive contribution of the indices in the presence of tree DBH and stand density indicators was investigated by multiple linear regression procedures. RESULTS

All the indices examined prove to be well correlated with DBH and IBA increments (Table 2). Correlation coefficients are similar to those found by Smith and Bell (1983) and Daniels et al. (1986), using more complex indices. Correlations are negative, since the indices represent a competitive stress on growth. According to Martin and Ek (1984), the spatial index (herein, the ratio of tree diameters divided by inter-tree distance) is not more correlated with increment than the simple ratio of diameters only; moreover, the proposed modification of Lorimer's non-spatial index gives this latter a slightly higher correlation than the above-mentioned spatial index. The presence of 3 different stand densities interferes with increment-competition relationships. In fact, for each index, the correlation with IBA increment varies with the residual stand density after thinning: the higher the stand




Comparison of correlation coefficients between individual competition indices and the annual increment of Monterey pine in the young plantation examined Index

Correlation coefficient ~, with increment in DBH



- 0.520

- 0.572



- 0.520

- 0.574

~Correlation coefficients are all significant

(P < 0.01; n = 60).






+ *


o o -0.60



~" 20



I 25

I 30

residual basal area rn2 * h a "1 (A,B,C = density treatments)

Fig. 1. Correlation coefficients between individual competition indices and IBA increment as function of stand density.


density, the higher the ability of the indices to explain IBA increment variation (Fig. 1). Correlations, however, show a slight trend to decrease with stand fertility. This phenomenon might suggest that competition interacts more considerably with individual growth in stands established in low fertility sites, if the fertility range examined were not so limited (Fig. 2). Improvement of the indices potential in IBA prediction was obtained by multiple linear models including progressively, besides the indices, tree DBH, basal area ha -1 and tree number ha -1 (Table 3). While the number of trees h a - 1 contributes little in the presence of DBH and competition indices, the addition of the stand basal area proves more useful to increase increment-

435 -0.75




oo -0.60

-0.55 11


stand productivity







113 rna * h a "1 * y i 1

Fig. 2. Correlation coefficients between individual competition indices and IBA increment as a function of stand fertility.


Comparison of squared multiple correlation coefficients between Monterey pine IBA annual increment (cm 2 year -I ) and individual competition indices in the presence of tree size and stand density Index


Squared multiple correlation coefficients for model including1:




0.418 0.415 0.410 0.358

0.425 0.421 0.415 0.368

0.453 0.451 0.438 0.385

1D = tree diameter at breast height; N T = number of trees h a - 1; SBA = stand basal area h a - 1. 2Fit without the index as a check on the index predictive contribution.

explained variability.However, by subjecting all the mentioned predictors to stepwise regression procedure, only D B H and individual competition indices are selected. (Stepwise regressions were tested with a tolerance value equal to 0.01 and an F significance levelfor predictor deletion or inclusion equal to 0.5.) The contribution ranking of SCI and N S C I M in multiple correlations is reversed with respect to their ranking in simple correlations;in fact,SCI, that is


based on a more complex structure, obviously presents a slightly lower collinearity degree with subject tree DBH, the other main increment predictor, than NSCIM does. The individual increment variation explained by the equations elaborated might not seem very high, but it is to be noted that the study, representing only a preliminary investigation, was conducted on a limited number of samples. On the other hand, the multiple correlation coefficients obtained by other authors in similar research are of the same values (e.g. Smith and Bell, 1983; Martin and Ek, 1984; Daniels et al., 1986). DISCUSSION AND CONCLUSIONS

Besides 'tree size and distance dependent' competition indices, the other most used spatial indices are referred to as 'growing space polygon' (e.g. Moore et al., 1973; Adlard, 1974) and 'growing space overlap' competition indices (e.g. Bella, 1971; Arney, 1974). On the whole, as regards the effectiveness of the indices considered from a practical point of view, it should be remembered that most of the researchers who have made comparative tests between them have found little difference in predictive ability, despite the substantial differences in conceptual design (e.g. Hegyi, 1974; Daniels, 1976; Daniels et al., 1986). Moreover, the present results confirm that the extra time and expense involved in surveying the spatial coordinates of trees may be unjustified for growth prediction, at least in young conifer plantations. The lack of importance of relative inter-tree distances in young plantation dynamics seems to be quite understandable, as there is little or no variability in tree spacing. Yet, in accordance with Martin and Ek (1984), the indication of the relative size of the subject tree, together with some local stand density measurements, might be enough for predicting individual tree growth, even in natural stands, at least in fully-stocked or uniformly thinned stands. However, it is possible that inter-tree distances prove useful for individual growth prediction in irregular stands, where, for instance, wide canopy gaps occur at irregular intervals (Lorimer, 1983). In conventional productive forestry, high yields are usually obtained without paying appreciable attention to how anthropic inputs, like artificial thinnings, interact between trees in the stand. Conversely, when planning low-input silvicultural systems, which should share greater ecological similarity with natural forest ecosystems, it is necessary to know the level of competition experienced by trees in relation to stand density management and growth rates, in order to reproduce, tentatively, natural self-thinning rules. In this sense, the results obtained indicate that, although tree size alone accounts for the largest portion of variation in IBA increment, adding the function of a simple nonspatial competition index considerably improves growth forecasting reliability. This suggests that this type of index can be profitably incorporated into predictive models in progress within yield studies for Italian conifer plantations.

437 ACKNOWLEDGEMENTS The authors gratefully thank Andrea Rossi for his technical assistance and Marco Borghetti for his thoughtful comments.

REFERENCES Adlard, P.G., 1974. Development of an empirical competition model for individual trees within a stand. In: J. Fries (Editor), Growth Models for Tree and Stand Simulation. Royal College of Forestry, Stockholm, pp. 22-37. Arney, J.D., 1974. An individual tree model for stand simulation in Douglas-fir. In: J. Fries (Editor), Growth Models for Trees and Stand Simulation. Royal College of Forestry, Stockholm, pp. 38-46. Bella, I.E., 1971. A new competition model for individual trees. For. Sci., 17: 364-372. Daniels, R.F., 1976. Simple competition indices and their correlation with annual loblolly pine tree growth. For. Sci., 22: 454-456. Daniels, R.F., Burkhart, H.E. and Clason, T.R., 1986. A comparison of competition measures for predicting growth of loblolly pine trees. Can. J. For. Res., 16: 1230-1237. Ellis, R.C., 1979. Response of crop trees of sugar maple, white ash and black cherry to release and fertilization. Can. J. For. Res., 9: 179-188. Hatch, C.R., Gerrard, D.J. and Tappeneir, J.C., 1975. Exposed crown surface area: a mathematical index of individual tree growth potential. Can. J. For. Res., 5: 224-228. Hegyi, F., 1974. A simulation model for managing jack-pine stands. In: J. Fries {Editor), Growth Models for Tree and Stand Simulation. Royal College of Forestry, Stockholm, pp. 74-90. Krajicek, J.E., Brinkman, K.A. and Gingrich, S.F., 1961. Crown competition - a measure of density. For. Sci., 7: 35-42. Lorimer, C.G., 1983. Tests of age-independent competition indices for individual trees in natural hardwood stands. For. Ecol. Manage., 6: 343-360. Martin, G.L. and Ek, A.R., 1984. A comparison of competition measures and growth models for predicting plantation red pine diameter and height growth. For. Sci., 30: 731-743. Moore, J.A., Budelsky, C.A. and Schlesinger, R.C., 1973. A new index representing individual tree competitive status. Can. J. For. Res., 3: 495-500. Nystroem, K. and Gemmel, P., 1987. Models for predicting height and diameter of individual trees in young Picea abies (L.) Karst. stands. Swedish University of Agricultural Science, Department of Silviculture {unpublished), 32 pp. Smith, S.H., 1977. The evaluation of competitive stress index as a measure of stand density for young growth Douglas-fir. Master of Science thesis, Oregon State University, Corvallis, OR {unpublished), 188 pp. Smith, S.H. and Bell, J.F., 1983. Using competitive stress index to estimate diameter growth for thinned Douglas-fir stands. For. Sci., 29: 491-499.