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Small-scale spatial patterns of trees in a mixed Pinus sylvestris-Fagus sylvatica forest
Fdwst Ecol0g.v 3trd Munagcrrzcrrt, 5 1 ( 1992 ) 30 l-3 15 Elsevier Science Publishers B.V.. Amsterdam
Szwagrzyk.
J.. 1992. Smali-scale
spa; ial patterns
301
of trees tn a mixed Pinzis n’i~,~,.s/!-ls-~agiis qharrca
The fine-scale spatial patterns of trees were analysed in 20 circular plots established in mtxed forests dominated by pine and beech in Ratanica Valley. a small forested catchment in the Carpathian footI.:TT,,, eYqf! locations of indiwduals were recorded in circles of radri .1.11‘ ,,.~ ..n-l. -... r.-” _ hills. YlUihcXi PG!an,. 4 \%::‘ proportional to the sizes of measured trees. Pattern analysis was conducted using modified Ripley’s A’method. Apart from a general patt urn for all trees and For beech and pine scpar>rely. spatial rcla., tronships between th2se two species uere analysed using the K function for bivariate processes. Distribution of theoretical competition intensity measures for the central part ofench plot was calculated using two ‘intluence functions’. The p:-evailing spatial pattern in a! size classes of anaiysed trees was intermediate between purely random and regular. However. statistically significant regular-it,, in tree distribution was recorded only in a feu plots. Clumped distribution was extremely rare. and so a’ere the departures from randomness towards aggregation. Therefore. the hypothesis ofany positive mteractions among Individuals, leading to their clumped distribution. should bc rejected. On the other n md. the role of crowding-dependent mortality in shaping spatial patterns of trees was only partly confirmed by the results. Analyses of spatial relationships be.ween beech and pme revealed that these two species were distributed independently. apart from two cases when a kind of ‘attraction’ between them occurred. Global sums of competitive influences. calcutated wtth two different formulae gave gverally cimilar results: there was a grea? diversity in sums of infllrences both within and among analys;d plots. Nonetheless. high levels of tree crowding were Vera rarely achieved, the majorrty of analysed stands being w!! below the siocking levei which could bc attained under prevailing site conditions.
As competition among forest trees can be watched directly only for relativeiy short periods of time, most conclusions and generalisations are made WI the basis of visible effects of competition (West, I984; Peer ~2 ChristenC’or.ws~~~~&wce to: J, Szwagrzyk. Department of Forest Botany and Nature ricultural University, Ai. 29 Listopada 46. 31-415 Cracow, Poland.
0 1992 Eisevic:
Science
Publishers
B.V. Ail rights
reserved
Conservation,
U378..i i27/SZ/$OS.OU
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302
J SZWGRZYK
sen, 1987; Brand and Magnusson, 1988; Knox et al.. 1989 ). The distribution of trees which have survived the process of self-thinning seems to be one of the most valuable (Welden et al., 19X8), or at least the most conveniently measured, of these effects. Competition among plants, studied intensively for a long time, seldom has been displayed against the actual range of spatial and temporal scales involved. In the case of competition in forest trees the problem becomes especially complicated. Differences in spatial scales between seedlings and canopy trees are enormous (Shugart, 1984), and may discourage any attempt towards more exactly defining the range of the spatial scale of investigations A!though the importance of choosing an appropriate spatial scale for each studied object or phenomenon has been acknowledged by some ecologists long ago. it has been only recently that this problem has been given more attention (Wiens, 1989). Until now. some ecological processes have been studied as if adjustment of spatial and temporal scales of the research to the size and iongevity of investigated organisms did not matter much for the results. Because most past research has related competition in plants to density per unit area., the spatial aspects have largely been neglected both in experiments and in field si .dies. Although such an attitude is natural when dealing with small annual plants (Weiner and Thomas, 1986), focusing attention on individuals and their immediate neighbourhood seems much more appropriate in the case of forest trees (Weiner, 1984; Huston et al.. 1988: tomnicki, 1988 ). The spatial pattern of mature canopy trees is believed to be regular, or close to regular, if crowding-dependent mortaiity actually takes place in the course of self-thinning (Ford, 1975 ). Because examples of regular distributions are rare (Pielou, 1978 ), the distribution of trees in dense. mature forest stands is often cited, along with distribution of shrubs in desert and semi-desert areas. as examples of regular distributions in plants (Prentice and Werger. 1985; Chapin et al., 1989). Although often cited, the regular distribution of trees in forest stands has seldom been documented (Buzykin et al., 1985; Tomppo, 1986; Peet and Christensen, 1987). On the other hand, random or even clumped distributional patterns have been recorded by many studies of forest tree populations (Payandeh. 1974; Biirki, 1981: Abbott, 1984: West, 1984; Armesto et al., 1986; Platt et al.. 1988; Johnson and Fryer, 1989). In the present study I was not concerned with spatial patterns of trees in general, but only with small-scale spatial patterns which reflect interferences among neighbouring individuals (West, 1984: tomnicki, 1988 ). Furthermore, I did not consider spatial patterning in tree seedlings since I assumed this to be governed mainly by microsite mosaic and distribution of seeds, and not by interactions among young individuals (Beatty, 1984: Collins and Good, 1987 ). For seedlings the influence of canopy and subcanopy trees, including saplings, is usually more important than the influence of other seedlings (Woods, 1984; Horn, 1985; Christy, 1986 ). For purely methodological rea-
sons, any considerations of spatial patterns created by factors other than interactions among individuals were excludeci from this study (Franklin et al., 1985 j; different methods must be used to investigate this interesting problem (Wiens, 1989). Until recently, few investigations have dealt with changes in spatial pattern of trees in the course of time and self-thinning (Ford, ! 9’75; West et al., 1989 ). 4lthough establishing such studies is necessary, results will not be available for a long time. Approximate results can be obtained now. however, by comparing spatial patterns of trees in even-aged stands of different ages or by comparing spatiai patterns of trees of different size classes in uneven-aged stands. To this end, calculating sums oftheoretical influences of all the trees within a given distance on a point combines the effects ofspacing and size to produce a single numerical value (Woods, 1984). This approach seems better than methods based on pairs of individuals (Weldi:n and Slauson, 1936), and is similar to the concepts of competition index {Bella, 1971; Arney, 1974; Ek and Monserud, 1974; Da’: et al., 1935 ), and ‘ecological field’ (Walker et al., 1989 ). This method ma; be further improved by incorporating the reiationships between size, shape and spatial arrangement of leaves of different tree species and light conditions on the forest floor beneath their canopies (Morn, 1971). Four hypotheses were examined in the present study. The first pair of alternative hypotheses was as follows: ( 1 ) Competition leads to a more or less regular spacing of trees in the course of time, or (2) ‘Cooperation’ between trees leads to a more clumped spacing of individuals in the course of time. Certainly, there was also a third possibility that distribution of trees would be neither regular nor aggregated but merely random. The first hypothesis had a special consideration in that if trees :vere not distributed regularly this might be due to unequal sizes, and, if Ircc s izcs were taken into account, distributions might be more regular. Although this problem is not easy to solve, I attempted to deal with this subject by conducting separate analyses for various size classes. Regardless of the type of distribution for all species within the plot. distributions may be very different among species. Therefore, a second pair of alternative hypotheses was proposed: ( 3 ) intra-specific competition is more intense than inter-specific competition, and thus tree species should display a kind of mutual ‘attraction’ i.e. individuals of different species should grow close to each other, or (4) the rate of growth determines the outcome ofcompetition (Huston and Smith, 1987), and thus one species normally performs better than the others, i.e. individuals of a single species should grow close to each other. One of the questions which could be also addressed in the present study was the irlflirence of initial spacing of planted trees on spatiai patterns ofma-
ture iudi./iduals. Differences in scafe and in number between seedhngs and rna;ure trees are so large, however, that little cdn be concluded regarding the wa:~ in which the pattern chCangesin the cou.rse of time. Inttial regular pattern may lead to any kind of pattern in mature trees (Ford. I975 ), and regularity can be quite easily lost during self-thinning. STUDY AREA
The research was conducted in Ratanica Valley, a 120 ha forested catchment situated in the Carpathian foothills, 30 km south of Cracow (Fig. 1). Elevation ranges from 300 to 420 m above sea level. Moderately inclined slopes prevail, some intersected by narrow, steep gorges. Flat ridges occur in the upper part of the catchment. The bedrock consists mainly of sandstone, partly covered by layers of loess of variable thickness: podzols (Spodosols in US Dept. Agric. classification) and acid brown soils (inceptisols) are most common. Climate is mild, with average temperature about 7.4”C, and with mean annual precipitation about 800 mm (Sulinski and Kucza, 199 1). Forest stands are dominated by Scats pine (Finus sylvestris k. ) and Eurspean beech (Fagus sylvatica L. ). Most stands are between 60 and 90 years old and even-aged. Stands with a large European larch (Lri;i~ &xi&a WI!.)
.i‘\j’ ‘\\ 1.::~:~;:. .,. ,”
Fig. 1. Location of ahe Ratmica Valley.
\\I
,? ‘...:.‘, .’
::’ .,.
SMkLL-SCALE
SPATIAL
PATTEKNS
OF TREES
305
component occur in some parts of the cat&men-t. Pine and iiarch have been planted since the beginning of the twentieth century, but the origin of beech is not clear. In many stands pine or larch constitute the upper canopy layer and beech dominates in the subcanopy ihrhereas in other stands pine and beech do not differ in height. METHODS
JFethods yfdata collection In I986 a rectangular grid 100 x 100 rn’ was established. At 1 I8 points of intersections of the grid, measurements with a relascope were made in order to obtain an estimate of basal area of different tree species. From the group of 46 points that had a relatively large amount of beech, 20 points were chosen at random for the analysis of spatial pattern of trees. Nested circular plots were established at each of the 20 points in summer ! 987. Each plot consisted of six nested circles, with radii of 3, 5, 7, 13, 19, and 25 m. Within the biggest circle all trees of diameter at 1.3 m (DBH) larger or equal to 3.5 cm were recorded. Thresholds were 15 cm DBH, 7 cm DBH, I .3 m tall, and 0.5 m tall, respectively, for plots with radii of 19 m, 13 m, 7 m and 5 m (Szwagrzyk, 1990 ). Within the smaiiest circle all individuals including 1 year seedlings were recorded. Height of each tree was measured, and its exact location within the plot was determined using a ?heodolite and measuring tape. Living trees, standing dead trees, and stumps of broken or cut trees were recorded. Only stump-, which were not strongly decayed, and thus allowed both identification of species and measurement of diameter were recorded; diameter at ground level was nuhiplied by 0.8 to obtain approximate DBH for stumps. Methods of data analysis Patterns of trees in the 20 mapped plots were analysed with a method based on Ripley’s K function (Ripley, i 98 1; Diggle, 1983 ). This function determines the consistency of empirical distribution of distances among individuals in the plot with the Poisson expectations, and is given by the equation:
where: n is number of trees, Y (E) is the Lebesgue measure on the plane, x, y are points of the Euclidean plane, and d(x, y) is the Euclidean distance of the points x and y. In this study Ripley’s method was used in a slightly modified version. As each analysed plot was divided into the inner circle (A ) and buffer zone (B).
J. SZW
306
iGRZYK
where: V(A) is the area of analysed plot (inner circle), and n is the number of trees in the plot. Function K(t) was used as a transformed version L(t), L(t) = (K(t)/n)0.5
(3)
Buffer zones were employed to solve the problem of edge effect. The width of the buffer zone was equal to the difference between the radius of the whole plot and the radius of the inner circle and determined the distance to which the analysis was valid (Galiano, 1982 ). Although some data were lost from the analyses by creating buffer zones, this method seemed proper as it did not require any assumptions concerning the distribution of trees outside the plot. Other methods of analysis (Ripley, 1979; Diggle, 1983; Tomppo, 1986) assume that the distribution of trees outside the plot is similar to the distributi XI inside (Szwagrzyk and Ptak, 199 1). For ascertaining the statistical significance of departures from complete spatia! randomness (CSR), constant approximate contidence intervals were established by accepting the value t 1.42 (A/ (n - 1) )o.5 where: A is the area of the inner circle, and n is the number of trees in the plot, as a reasonable approximation of the 5% significance points (Ripley, 1979; Getis and Franklin, 1987 ). Crossing of the lower or upper limit of the interval was considered a significant departure from randomness. Although the null hypothesis sperifies that there is no significant departure from a random spatial pattern (Poi:son’s distribution), acceptance of the null hypci’lhesis Joes not necessarily mean that the distribution is random since many ‘mndom’ patterns are quite close to regular or clumped distributions. Therefore a quantitative estimator of the situation relative tc ‘ideal randomness’ (complete spatial randomness sensu Diggle, 1983 ) and ‘significant regularity’ or ‘significant clumping IS necessarv. Therefore a W, indicator (Szwagrzyk, 1990) calcu1ate.d to estimate the size of departure for the case of constant confidence intervals was introduced. It was given by the formula: maxIL(t)-tl ws=L:
’
s
xsign(l(t)-:)
(4)
where: max IL(t) --t I is maximal deviation of t( 1) function from the theoI
retical value for Poisson distribution, S is the width of the confidence interval, sign (L(1)--t)=-1.0, if L(t)-t
Shf-tLL-SCALE
SP-\TI4L
PATTEKNSOFTKEES
307
tion, while values larger than 1.O indicated significant clumping. Distribution types presented in Tables t and 2 are as follows: W,< - 1.O, regular; tVK/, - 1.0 and WK.< -0.333, intermediate between CSR and regular; W,2 -0.333 and rWti<0.333, CSR; W,Z0.333 and WA< 1.0, intermediate between CSR and clumped; I%‘,2 1.O, clumped. To examine the relationship between the size of trees and their spatial pattern. individuals in specified size classes were analysed separately or in various combinations. Separate analyses for each size class were in some cases impossible because of a small number of trees belonging to that class, thus TABLE I Results of pattern all living trees
analyses
( if;, indicator)
Class
Number
of plots with specified
Regular distribution Hc0.5 m HZOSm H<1.3m HZl.3m DBHi7cm DBH>7 cm DBIHZl5cm DBHZ35cm
for specified
Intermediate
height (II
) and diameter
(DBH ) classes of
distribution Random distribution
Intermediate
Clumped disiribution
0 0
6 5
0 2
3 2
1 0
0
9
3
3
0
I
14 15 16
5 0 2
0 3 0
0 0 0
2
1
TABLE 2 Results ofpattern analyses pine plus larch trees Tree
Number
( ?l;, indicator)
for specified
of plots with specified
diameter
classes of living beech and
distribution
Regular distrih:Pion
Intermediate
Random distribution
I
15
I
14
DISH2 l5cm Beech Pine plus larch
0 I
DBH 2 35 cm Beech Piik?plus larch
1 0
DBHZ7UTBeech Pint plus larch
(DBH)
intermediate
Clumxd diswixtion
?
I
I
0
I 0
14 12
2 3
3 1
0 0
8 13
2 3
0 0
0 0
comparisons
were made only for those combinations
of size classes that had
enough trees to be analysed in all 20 plots. Sp&_iai relationships among different tree species were analysed using function K(I) for bivariate processes, defmed as:
(5) where: n, is the number of objects of the first type, n, is the number of objects of the second type, x is objects of the first type (first component), y is objects of the second type (second component), and the other symbols are as in the formula ( 2 ), and by testing the independence of both components (species) using the test of random labelling (Diggle, 1983). As the ecological roles of pine and larch are almost the same on the study area, analyses were carried out using pairs of Fagus sylvatica vs. Firms sylxhs plus Lark decidua. To take into account possible effects of both tree distribution and sizes, sums of theoretical influences on a given point of all trees within the plot were calculated using two different functions. Both defined competitive influence of a given tree as positively related to its size and negatively related to the distance from that tree. The first function (IF’, ) was given by a formuia: I,117(2,,,?.,,P,2,?,‘)=Dxer;p(-axR’/D)
(6)
where: f,.l,,.l represents a tree located in a point with coordinates sl, yl; is a point with coordinates x2, ~2; D is diatneier at breast height ( 1.3 m) of a given tree; R is distance from the given tree t to a point p: R = ((xl --x2)“+ (yl--~‘2)‘)~.~; a represents a parameter, in this case a= 1.O. The second function ( FZ) was defined as:
~9,~,~,~
izIn(t,,,,.,,p,z,,.~)=D-hxR
(7)
where: b is a parameter, in this case b=3, and the other symbols are as in Formula (6). The sum of theoretical infiuences i(; was calculated as:
where: I(; represents global influence of trees on a point, and Sz is surrounding (the whole plot ). Sums of theoretical influences were computed for points distributed regularly in a 1 x 1 m2 grid over the central 10x 10 m’ quadrat of each plot. Fig. 2. Bar diagrams of global sums oFinfluences for 20 plots in Ratanica Valley. (A) Values of function Fl ; (B) values of function F2; horizontal axis represents classes of global sums of influence; vertical axis represents numbers of points in each class.
SMALL-SCALE
(178
SP.ATI4L
P4TTERNS
OF TREES
309
310 RESULTS
Patterns qftree distribution Most of the analysed plots and size combinations displayed spatial patterns not dtffering significantly from random. A majority of the results, however, fell between purely random and regular distributions. Purely random and intermediate between random and clumped distributions were less numerous, significantly regular patterns were rare, and significant clumping was found only in one plot (Table 1). Differences among specified size classes were negligible as far as canopy and subcanopy trees were concerned. There was no trend towards more regular distribution of large trees than of the smaller ones. Spatial patterns in saplings were closer to random, and spatial patterns of seedlings, on the average, were almost purely random, although particular cases varied from significantly clumped to regular. A single case of clumped distribution occurred with Frangula alms seedlings. In other plots seedlings were very scarce, and in seven plots no seedlings at all could be found. Very similar results were obtained in analyses of canopy and subcanopy trees carried out separately for beech and for pine plus larch. Despite large differences in ecological roles of those species, spatial patterns of beech and pine plus larch were very similar; distributions intermediate between purely random and regular were most common (Table 2 ). Here also differences in distributional patterns among various size classes were negligible. Statistical analysis of spatial relationships among pine plus larch versus beech was possible in only five plots where both spenies were relatively abundant. Results of those analyses indicated that in the majority of cases beech and pine plus larch were distributed independently. Only in two instances were statistically significant attractions found. Spatial variability ofstand density \vithirzplots Distributions of sums of global influences on points distributed regularly within each plot were variable. There was no typical type of distribution, but rather the shape and the range of the distribution were different in each plot (Figs. 2/a, 2B). DlSCUSSfON
The results of the present study differ from those obtained for beech and spruce-fir stands of Krynica Experimental Forest (Szwagrzyk, 1990) where an obvious trend towards more regular distribution was observed as trees became larger. The prevalence of random spatial patterns of individuals of all size classes in Ratanica Forest is somewhat surprising since canopy trees had
Shl~Li:S(‘~LESPZT19LP~TTERNSOFTREES
311
mce been planted at a more-or-less regular spacing. Nonetheless, no matter how large the initial spacing, it would not be large enough to maintain a regular distribution in mature stands. The results presented above did not support the hypothetical cooperation among trees leading to clumped distribution ofindividuals. On the other hand, the alternative hypothesis - that competition leads to a more regular spacing - was neither disproved nor strongly corroborated. Rather the rc5ult.s supported the least informative possibility that spatial patterns of individual trees do not clearly reflect competition occurring in the course of growth of a forest stand. Such processes as iaterai growth of branches directed towards gaps in forest canopy weaken the results of crowding-induced mortality, for example, by allowing trees growing close to each other to develop their crowns in directions of adjacent gaps (Runkle and Yetter. 1987; Koop, 1989). Adjustment of the size, shape and spatial distribution of tree crowns to the actual free space in forest canopy may to a certain extent obscure the influence of the distribution of tree stems on competition intensity (Wierman and Oliver, 1979; Brand and Magnussen. 1958 ). Results concerning inter-species reiationships were not informative. Only five out of 20 plots located in mixed forests had sufficient numbers of pine and beech to allow statistical analysis of spatial relationships: this fact suggests that trees growing close to each other are normally of the same species. In the five analysed plots, however. the results suggested a long-lasting coexistence of beech and pine. This is possible as long as pines are, due to age or faster initial growth, at least slightly taller than the beeches. and the situ&ion with beech and larch is similar. Nevertheless, usually either beech or pinelarch are locally more abundant, and patches where the density of both species is more or less equal, are relatively scarce. The fact that significant departures from randomness in spatial patterns of trees were so few focuses attention on other mechanisms which could influence competition processes in forest stands. It is noteworthy that individual trees in forest stands cannot be considered equal even within a specified size class (Muston and Smith, 1987) 1There is perhaps a small fraction of individuals which are predisposed to grcsw faster than the others because of their genetic superiority or because of especially favourable conditions of establishment and early growth, and which thus have greater chances of survival (Weiner and Thomas, 1986: tomnicki, 1988 ). There is no reason to suppose that the distribution of such ‘promising’ individuals in a stand is other than random. Thus even very intensive crowding-depe?adznt mortality among trees cannot create a significantly regular pattern in mature trees: no matter how close and how many neighbours they have. “promising’ individuals will eventually survive and dominate their neighbours , as rhe competition is in their case typica!ly one-sided (Perry, J985: Weiner and Thomas. 1986: Pukkala ZXPV~ Kolstriim. 1987; Knox et al., 1989).
The results of the influence functions analyses raise the question of why high sums of influence in tree stands ofRatanicz. Valley are so rarely attained. The results show that these sums may be as large as i 80 (Figs. 2A, 2B). Examinatiou of distributions of global sums of influence suggests that forest stands have their biomass distributed very unevenly, with many patches being relatively empty. even though they are not ‘gaps’ in the classical, literary meaning. This resembles strongly the results obtained with the method of ‘closure values’ in a neotropical rain forest (Lieberman et al., 1989 ); relative density of forest was very diverse, ranging from very dark to very light patches, but with the majority of places being intermediate. The actual density is onI> a partial realisation of the maximum density, possible under given site conditions (Brand and Magnus>en, 1988 ). This seems to be an easily overlooked feature of natural and semi-natural forest stands: the overall pattern is not regular and the actual density of tree biomass within a plot is not as big as in intensively managed forest plantations (Farnum et al., 1983; Perry and Maghembe, 1989). The yield as well as productivity in such stands will never match the levels obtained in intensively managed forest plantations on similar sites. CONCLUSIONS
The role of self-thinning in shaping the actual pattern of trees is not clear. The fact that the majority of individual tree distribution patterns did not differ significantly from the random distribution suggests. that crowding-dependent mortality is not intense enough to produce reguiar patterns in mature trees. On the other hand, visible departures towards regularity in virtually all plots, and statistically significant regularity in a few plots seemed to support rhe role of distance-dependent competition in determining the spatial distribution of individuals. ACKNOWLEDGEMENTS
This work has been completed due to the assistance of numerous people: Hreneusz Dziasek made- the relascope measurements; Romek Borowiec, Pawel Czarnota, Jadwiga Czerwczak, Marek Czerwczak, Leszek Kobak and Jan Loch he!ped with field measurements: Jerzy Ptak wrote original computer programs and provided advice concerning mathematical methods and terminology; Craiyna Tarko typed the vast field data onto computer files: Jan Bodziarczyk drew the figures. Thanks are also due to Elibieta Pancer-Koteja and Wojciech Rdiariski for their useful comments on the text, and two anc:nymous reviewers for their help in streamlining the origina! manuscript. This Sudy was a part of the research project CFBP.04.10.05.03.08.
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Johnson, EA. and Fryer, 6.1.. 1989. Population dynamics in !odgepoie pine-Engelmann spruce forests. Ecology. 70: 1335-i 345. Knox, R.C.. Peet, R.K. and Christensen, N.L., 1989.Population dynamics in loblolly pine stands: changes in skewness and size inequality. Ecology, 70: 1153- 1166. Koop. H.. 1989. Forest Dynamics. SILVI-STAR: A Comprehensive Moniloring System. Springer, Berlin, 229 pp. Licberman, M., Lieberman, D. and Peralta, R., 1989. Forests are not just Swiss cheese: Canopy stercometry of non-gaps in tropical forests. Ecology, 70: 550-552. tomnicki, A.. 1988. Population Ecoiogy of Individuals. Princeton University Press, Princeton. NJ. 223 pp. Payandeh. B.. 1974. Spatiai patterns of trees in the major forest types of northern Ontario. Can. J. For, Res.. 4: 8-14. Peet, R.K. and Christensen, N.L., 1987. Competition and tree death. Bioscience, 37: 586-595. Perry. D.A.. 1985. The competition process in forest stands. In: M.G.R. Cannel1 and J.E. Jackson (Editors). Attributes of Trees as Crop Plants. Instittite of Terrestrial Ecology. Abbots Ripton. pp. 481-506. Perry. D.A. and Maghembe, J., 1989. Ecosystem Concepts and Current Trends in Forest Management: Time for Reappraisal. For. Ecol. Manage., 26: 123-140. Pielou, E.C., 1978. Population and Community Ecology. Gordon and Breach, New York, 424 PP. Plate. W.J.. Exam G.W. and Rathbun, S.L., 1988. The population dynamics of a long-lived conifer (I’!tll/.sjiil:ir.:rri.,i. Am. Nat.. I3 I: 49 l-525. Prentice. I.C. and Werger. M.J.. 1985. Clump spacing in a desert dwarf shrub community. Vegetatio, 63: 133-139. Pukkala, T. and KolstrGm. T.. 1987. Competition indices and the prediction of radial growth in Scats pine. Silva Fenn., 21: 55-67. Ripley. B.D., 1979. Tests of‘randomness’ for spatial point patterns. J. R. Stat. Sot.. B, 41: 368374. Ripley, B.D.. i 98 1. Spatial Statistics. John Wiley, New York. 252 pp. Runkle. J.R. and Yetter, T.C.. 1987. Treefalls revisited: gap dynamics m the southern Appalachians. Ecology. 68: 417-424. Shugart, H.H.. 1984. A Theory of Forest Dynamics. Springer, New York, 276 pp. Suliriski. J. and Kucza, J., 1991. Element! Srodowiska geograficznego i bilans wodny potoku Ratanica (The geographical features arid water balance of Ratanica catchment). Ekoi. Poi.. in press. S7wagrzyk. J., 1990. Regeneration of forest related io the spatial structure of trees: A study of two forest communities in Western Carpathians, southern Poland. Vegetatio. 89: 1 l-22. Szwagrzyk, J. and Ptak, J.. 1991. Ana+ struktury przestrzennej populacji i zbiorowisk oparte na znajomoSci r3zmieszczenia osobmkliw (.Analyses of spatial structure of populations anti communities based on mapped point pattxns of individuals). (In Polish, with English summary.) Wiad. Ekol.. 37: 107-124. Tomppo. E.. 1986. Models and methods for analysing spatial patterns of trees. Comm. Inst. For. Fenn.. 138. i-65. Walker. J.. Sharpe ?.J.H., Penridge. L.K. and Wu. PI.. 1989. Ecological field theory: the concept and field tests $2gctatio. 83: 81-95. Weiner. J.. 1984. Neighbourbood interference amongst Piizzt.7rrgi& individuals. J. Ecol., 72: 183-195. Weiner. J. and Thomas, SC.. 1986. Size varlabllity and competition in plant monocultures. 0;kos 7 1I-: _.‘I. . , 47._..
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Welden, C.W. and Slauson, W.L., 1986. The intensity of competition versus its importance: An overlooked distinction and some implications. Q. Rev. Biol., 6 1: 23-44. Welden, C.W., Slauson, W.L. and Ward, R.T., 1988. Competition and abiotic stress among trees and shrubs in northwest Colorado. Ecology, 03: i566- 1577. West, P.W., 1984. Inter-tree competttion and small-scale pattern in monoculture ofEl;c&~&; obliqua L’Herit. Aust. J. Ecol., 9: 405-4 1I. West, P.W., Jackett, D.R. and Borough, C.J., 1989. Compe?itive process in a monoculture of Pinus rudiuta D. Don. Oecologia, 8 1: 57-6 I. Wiens, J.A., 1989. Spatial scaling in ecology. Funct. Ecol., 3: 385-397. Wterman, C.A. and Oliver, CD., 1979. Crown stratification in even-aged mixed stands of Douglas %-western hemlock. Can. J. For. Res., 9: l-9. Woods, K.D., 1984. Patterns of tree replacement: canopy effects on understory pattern in hemlock-northern hardwood forests. Vegetatio, 56: 87-107.
Szwagrzyk.
J.. 1992. Smali-scale
spa; ial patterns
301
of trees tn a mixed Pinzis n’i~,~,.s/!-ls-~agiis qharrca
The fine-scale spatial patterns of trees were analysed in 20 circular plots established in mtxed forests dominated by pine and beech in Ratanica Valley. a small forested catchment in the Carpathian footI.:TT,,, eYqf! locations of indiwduals were recorded in circles of radri .1.11‘ ,,.~ ..n-l. -... r.-” _ hills. YlUihcXi PG!an,. 4 \%::‘ proportional to the sizes of measured trees. Pattern analysis was conducted using modified Ripley’s A’method. Apart from a general patt urn for all trees and For beech and pine scpar>rely. spatial rcla., tronships between th2se two species uere analysed using the K function for bivariate processes. Distribution of theoretical competition intensity measures for the central part ofench plot was calculated using two ‘intluence functions’. The p:-evailing spatial pattern in a! size classes of anaiysed trees was intermediate between purely random and regular. However. statistically significant regular-it,, in tree distribution was recorded only in a feu plots. Clumped distribution was extremely rare. and so a’ere the departures from randomness towards aggregation. Therefore. the hypothesis ofany positive mteractions among Individuals, leading to their clumped distribution. should bc rejected. On the other n md. the role of crowding-dependent mortality in shaping spatial patterns of trees was only partly confirmed by the results. Analyses of spatial relationships be.ween beech and pme revealed that these two species were distributed independently. apart from two cases when a kind of ‘attraction’ between them occurred. Global sums of competitive influences. calcutated wtth two different formulae gave gverally cimilar results: there was a grea? diversity in sums of infllrences both within and among analys;d plots. Nonetheless. high levels of tree crowding were Vera rarely achieved, the majorrty of analysed stands being w!! below the siocking levei which could bc attained under prevailing site conditions.
As competition among forest trees can be watched directly only for relativeiy short periods of time, most conclusions and generalisations are made WI the basis of visible effects of competition (West, I984; Peer ~2 ChristenC’or.ws~~~~&wce to: J, Szwagrzyk. Department of Forest Botany and Nature ricultural University, Ai. 29 Listopada 46. 31-415 Cracow, Poland.
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sen, 1987; Brand and Magnusson, 1988; Knox et al.. 1989 ). The distribution of trees which have survived the process of self-thinning seems to be one of the most valuable (Welden et al., 19X8), or at least the most conveniently measured, of these effects. Competition among plants, studied intensively for a long time, seldom has been displayed against the actual range of spatial and temporal scales involved. In the case of competition in forest trees the problem becomes especially complicated. Differences in spatial scales between seedlings and canopy trees are enormous (Shugart, 1984), and may discourage any attempt towards more exactly defining the range of the spatial scale of investigations A!though the importance of choosing an appropriate spatial scale for each studied object or phenomenon has been acknowledged by some ecologists long ago. it has been only recently that this problem has been given more attention (Wiens, 1989). Until now. some ecological processes have been studied as if adjustment of spatial and temporal scales of the research to the size and iongevity of investigated organisms did not matter much for the results. Because most past research has related competition in plants to density per unit area., the spatial aspects have largely been neglected both in experiments and in field si .dies. Although such an attitude is natural when dealing with small annual plants (Weiner and Thomas, 1986), focusing attention on individuals and their immediate neighbourhood seems much more appropriate in the case of forest trees (Weiner, 1984; Huston et al.. 1988: tomnicki, 1988 ). The spatial pattern of mature canopy trees is believed to be regular, or close to regular, if crowding-dependent mortaiity actually takes place in the course of self-thinning (Ford, 1975 ). Because examples of regular distributions are rare (Pielou, 1978 ), the distribution of trees in dense. mature forest stands is often cited, along with distribution of shrubs in desert and semi-desert areas. as examples of regular distributions in plants (Prentice and Werger. 1985; Chapin et al., 1989). Although often cited, the regular distribution of trees in forest stands has seldom been documented (Buzykin et al., 1985; Tomppo, 1986; Peet and Christensen, 1987). On the other hand, random or even clumped distributional patterns have been recorded by many studies of forest tree populations (Payandeh. 1974; Biirki, 1981: Abbott, 1984: West, 1984; Armesto et al., 1986; Platt et al.. 1988; Johnson and Fryer, 1989). In the present study I was not concerned with spatial patterns of trees in general, but only with small-scale spatial patterns which reflect interferences among neighbouring individuals (West, 1984: tomnicki, 1988 ). Furthermore, I did not consider spatial patterning in tree seedlings since I assumed this to be governed mainly by microsite mosaic and distribution of seeds, and not by interactions among young individuals (Beatty, 1984: Collins and Good, 1987 ). For seedlings the influence of canopy and subcanopy trees, including saplings, is usually more important than the influence of other seedlings (Woods, 1984; Horn, 1985; Christy, 1986 ). For purely methodological rea-
sons, any considerations of spatial patterns created by factors other than interactions among individuals were excludeci from this study (Franklin et al., 1985 j; different methods must be used to investigate this interesting problem (Wiens, 1989). Until recently, few investigations have dealt with changes in spatial pattern of trees in the course of time and self-thinning (Ford, ! 9’75; West et al., 1989 ). 4lthough establishing such studies is necessary, results will not be available for a long time. Approximate results can be obtained now. however, by comparing spatial patterns of trees in even-aged stands of different ages or by comparing spatiai patterns of trees of different size classes in uneven-aged stands. To this end, calculating sums oftheoretical influences of all the trees within a given distance on a point combines the effects ofspacing and size to produce a single numerical value (Woods, 1984). This approach seems better than methods based on pairs of individuals (Weldi:n and Slauson, 1936), and is similar to the concepts of competition index {Bella, 1971; Arney, 1974; Ek and Monserud, 1974; Da’: et al., 1935 ), and ‘ecological field’ (Walker et al., 1989 ). This method ma; be further improved by incorporating the reiationships between size, shape and spatial arrangement of leaves of different tree species and light conditions on the forest floor beneath their canopies (Morn, 1971). Four hypotheses were examined in the present study. The first pair of alternative hypotheses was as follows: ( 1 ) Competition leads to a more or less regular spacing of trees in the course of time, or (2) ‘Cooperation’ between trees leads to a more clumped spacing of individuals in the course of time. Certainly, there was also a third possibility that distribution of trees would be neither regular nor aggregated but merely random. The first hypothesis had a special consideration in that if trees :vere not distributed regularly this might be due to unequal sizes, and, if Ircc s izcs were taken into account, distributions might be more regular. Although this problem is not easy to solve, I attempted to deal with this subject by conducting separate analyses for various size classes. Regardless of the type of distribution for all species within the plot. distributions may be very different among species. Therefore, a second pair of alternative hypotheses was proposed: ( 3 ) intra-specific competition is more intense than inter-specific competition, and thus tree species should display a kind of mutual ‘attraction’ i.e. individuals of different species should grow close to each other, or (4) the rate of growth determines the outcome ofcompetition (Huston and Smith, 1987), and thus one species normally performs better than the others, i.e. individuals of a single species should grow close to each other. One of the questions which could be also addressed in the present study was the irlflirence of initial spacing of planted trees on spatiai patterns ofma-
ture iudi./iduals. Differences in scafe and in number between seedhngs and rna;ure trees are so large, however, that little cdn be concluded regarding the wa:~ in which the pattern chCangesin the cou.rse of time. Inttial regular pattern may lead to any kind of pattern in mature trees (Ford. I975 ), and regularity can be quite easily lost during self-thinning. STUDY AREA
The research was conducted in Ratanica Valley, a 120 ha forested catchment situated in the Carpathian foothills, 30 km south of Cracow (Fig. 1). Elevation ranges from 300 to 420 m above sea level. Moderately inclined slopes prevail, some intersected by narrow, steep gorges. Flat ridges occur in the upper part of the catchment. The bedrock consists mainly of sandstone, partly covered by layers of loess of variable thickness: podzols (Spodosols in US Dept. Agric. classification) and acid brown soils (inceptisols) are most common. Climate is mild, with average temperature about 7.4”C, and with mean annual precipitation about 800 mm (Sulinski and Kucza, 199 1). Forest stands are dominated by Scats pine (Finus sylvestris k. ) and Eurspean beech (Fagus sylvatica L. ). Most stands are between 60 and 90 years old and even-aged. Stands with a large European larch (Lri;i~ &xi&a WI!.)
.i‘\j’ ‘\\ 1.::~:~;:. .,. ,”
Fig. 1. Location of ahe Ratmica Valley.
\\I
,? ‘...:.‘, .’
::’ .,.
SMkLL-SCALE
SPATIAL
PATTEKNS
OF TREES
305
component occur in some parts of the cat&men-t. Pine and iiarch have been planted since the beginning of the twentieth century, but the origin of beech is not clear. In many stands pine or larch constitute the upper canopy layer and beech dominates in the subcanopy ihrhereas in other stands pine and beech do not differ in height. METHODS
JFethods yfdata collection In I986 a rectangular grid 100 x 100 rn’ was established. At 1 I8 points of intersections of the grid, measurements with a relascope were made in order to obtain an estimate of basal area of different tree species. From the group of 46 points that had a relatively large amount of beech, 20 points were chosen at random for the analysis of spatial pattern of trees. Nested circular plots were established at each of the 20 points in summer ! 987. Each plot consisted of six nested circles, with radii of 3, 5, 7, 13, 19, and 25 m. Within the biggest circle all trees of diameter at 1.3 m (DBH) larger or equal to 3.5 cm were recorded. Thresholds were 15 cm DBH, 7 cm DBH, I .3 m tall, and 0.5 m tall, respectively, for plots with radii of 19 m, 13 m, 7 m and 5 m (Szwagrzyk, 1990 ). Within the smaiiest circle all individuals including 1 year seedlings were recorded. Height of each tree was measured, and its exact location within the plot was determined using a ?heodolite and measuring tape. Living trees, standing dead trees, and stumps of broken or cut trees were recorded. Only stump-, which were not strongly decayed, and thus allowed both identification of species and measurement of diameter were recorded; diameter at ground level was nuhiplied by 0.8 to obtain approximate DBH for stumps. Methods of data analysis Patterns of trees in the 20 mapped plots were analysed with a method based on Ripley’s K function (Ripley, i 98 1; Diggle, 1983 ). This function determines the consistency of empirical distribution of distances among individuals in the plot with the Poisson expectations, and is given by the equation:
where: n is number of trees, Y (E) is the Lebesgue measure on the plane, x, y are points of the Euclidean plane, and d(x, y) is the Euclidean distance of the points x and y. In this study Ripley’s method was used in a slightly modified version. As each analysed plot was divided into the inner circle (A ) and buffer zone (B).
J. SZW
306
iGRZYK
where: V(A) is the area of analysed plot (inner circle), and n is the number of trees in the plot. Function K(t) was used as a transformed version L(t), L(t) = (K(t)/n)0.5
(3)
Buffer zones were employed to solve the problem of edge effect. The width of the buffer zone was equal to the difference between the radius of the whole plot and the radius of the inner circle and determined the distance to which the analysis was valid (Galiano, 1982 ). Although some data were lost from the analyses by creating buffer zones, this method seemed proper as it did not require any assumptions concerning the distribution of trees outside the plot. Other methods of analysis (Ripley, 1979; Diggle, 1983; Tomppo, 1986) assume that the distribution of trees outside the plot is similar to the distributi XI inside (Szwagrzyk and Ptak, 199 1). For ascertaining the statistical significance of departures from complete spatia! randomness (CSR), constant approximate contidence intervals were established by accepting the value t 1.42 (A/ (n - 1) )o.5 where: A is the area of the inner circle, and n is the number of trees in the plot, as a reasonable approximation of the 5% significance points (Ripley, 1979; Getis and Franklin, 1987 ). Crossing of the lower or upper limit of the interval was considered a significant departure from randomness. Although the null hypothesis sperifies that there is no significant departure from a random spatial pattern (Poi:son’s distribution), acceptance of the null hypci’lhesis Joes not necessarily mean that the distribution is random since many ‘mndom’ patterns are quite close to regular or clumped distributions. Therefore a quantitative estimator of the situation relative tc ‘ideal randomness’ (complete spatial randomness sensu Diggle, 1983 ) and ‘significant regularity’ or ‘significant clumping IS necessarv. Therefore a W, indicator (Szwagrzyk, 1990) calcu1ate.d to estimate the size of departure for the case of constant confidence intervals was introduced. It was given by the formula: maxIL(t)-tl ws=L:
’
s
xsign(l(t)-:)
(4)
where: max IL(t) --t I is maximal deviation of t( 1) function from the theoI
retical value for Poisson distribution, S is the width of the confidence interval, sign (L(1)--t)=-1.0, if L(t)-t
Shf-tLL-SCALE
SP-\TI4L
PATTEKNSOFTKEES
307
tion, while values larger than 1.O indicated significant clumping. Distribution types presented in Tables t and 2 are as follows: W,< - 1.O, regular; tVK/, - 1.0 and WK.< -0.333, intermediate between CSR and regular; W,2 -0.333 and rWti<0.333, CSR; W,Z0.333 and WA< 1.0, intermediate between CSR and clumped; I%‘,2 1.O, clumped. To examine the relationship between the size of trees and their spatial pattern. individuals in specified size classes were analysed separately or in various combinations. Separate analyses for each size class were in some cases impossible because of a small number of trees belonging to that class, thus TABLE I Results of pattern all living trees
analyses
( if;, indicator)
Class
Number
of plots with specified
Regular distribution Hc0.5 m HZOSm H<1.3m HZl.3m DBHi7cm DBH>7 cm DBIHZl5cm DBHZ35cm
for specified
Intermediate
height (II
) and diameter
(DBH ) classes of
distribution Random distribution
Intermediate
Clumped disiribution
0 0
6 5
0 2
3 2
1 0
0
9
3
3
0
I
14 15 16
5 0 2
0 3 0
0 0 0
2
1
TABLE 2 Results ofpattern analyses pine plus larch trees Tree
Number
( ?l;, indicator)
for specified
of plots with specified
diameter
classes of living beech and
distribution
Regular distrih:Pion
Intermediate
Random distribution
I
15
I
14
DISH2 l5cm Beech Pine plus larch
0 I
DBH 2 35 cm Beech Piik?plus larch
1 0
DBHZ7UTBeech Pint plus larch
(DBH)
intermediate
Clumxd diswixtion
?
I
I
0
I 0
14 12
2 3
3 1
0 0
8 13
2 3
0 0
0 0
comparisons
were made only for those combinations
of size classes that had
enough trees to be analysed in all 20 plots. Sp&_iai relationships among different tree species were analysed using function K(I) for bivariate processes, defmed as:
(5) where: n, is the number of objects of the first type, n, is the number of objects of the second type, x is objects of the first type (first component), y is objects of the second type (second component), and the other symbols are as in the formula ( 2 ), and by testing the independence of both components (species) using the test of random labelling (Diggle, 1983). As the ecological roles of pine and larch are almost the same on the study area, analyses were carried out using pairs of Fagus sylvatica vs. Firms sylxhs plus Lark decidua. To take into account possible effects of both tree distribution and sizes, sums of theoretical influences on a given point of all trees within the plot were calculated using two different functions. Both defined competitive influence of a given tree as positively related to its size and negatively related to the distance from that tree. The first function (IF’, ) was given by a formuia: I,117(2,,,?.,,P,2,?,‘)=Dxer;p(-axR’/D)
(6)
where: f,.l,,.l represents a tree located in a point with coordinates sl, yl; is a point with coordinates x2, ~2; D is diatneier at breast height ( 1.3 m) of a given tree; R is distance from the given tree t to a point p: R = ((xl --x2)“+ (yl--~‘2)‘)~.~; a represents a parameter, in this case a= 1.O. The second function ( FZ) was defined as:
~9,~,~,~
izIn(t,,,,.,,p,z,,.~)=D-hxR
(7)
where: b is a parameter, in this case b=3, and the other symbols are as in Formula (6). The sum of theoretical infiuences i(; was calculated as:
where: I(; represents global influence of trees on a point, and Sz is surrounding (the whole plot ). Sums of theoretical influences were computed for points distributed regularly in a 1 x 1 m2 grid over the central 10x 10 m’ quadrat of each plot. Fig. 2. Bar diagrams of global sums oFinfluences for 20 plots in Ratanica Valley. (A) Values of function Fl ; (B) values of function F2; horizontal axis represents classes of global sums of influence; vertical axis represents numbers of points in each class.
SMALL-SCALE
(178
SP.ATI4L
P4TTERNS
OF TREES
309
310 RESULTS
Patterns qftree distribution Most of the analysed plots and size combinations displayed spatial patterns not dtffering significantly from random. A majority of the results, however, fell between purely random and regular distributions. Purely random and intermediate between random and clumped distributions were less numerous, significantly regular patterns were rare, and significant clumping was found only in one plot (Table 1). Differences among specified size classes were negligible as far as canopy and subcanopy trees were concerned. There was no trend towards more regular distribution of large trees than of the smaller ones. Spatial patterns in saplings were closer to random, and spatial patterns of seedlings, on the average, were almost purely random, although particular cases varied from significantly clumped to regular. A single case of clumped distribution occurred with Frangula alms seedlings. In other plots seedlings were very scarce, and in seven plots no seedlings at all could be found. Very similar results were obtained in analyses of canopy and subcanopy trees carried out separately for beech and for pine plus larch. Despite large differences in ecological roles of those species, spatial patterns of beech and pine plus larch were very similar; distributions intermediate between purely random and regular were most common (Table 2 ). Here also differences in distributional patterns among various size classes were negligible. Statistical analysis of spatial relationships among pine plus larch versus beech was possible in only five plots where both spenies were relatively abundant. Results of those analyses indicated that in the majority of cases beech and pine plus larch were distributed independently. Only in two instances were statistically significant attractions found. Spatial variability ofstand density \vithirzplots Distributions of sums of global influences on points distributed regularly within each plot were variable. There was no typical type of distribution, but rather the shape and the range of the distribution were different in each plot (Figs. 2/a, 2B). DlSCUSSfON
The results of the present study differ from those obtained for beech and spruce-fir stands of Krynica Experimental Forest (Szwagrzyk, 1990) where an obvious trend towards more regular distribution was observed as trees became larger. The prevalence of random spatial patterns of individuals of all size classes in Ratanica Forest is somewhat surprising since canopy trees had
Shl~Li:S(‘~LESPZT19LP~TTERNSOFTREES
311
mce been planted at a more-or-less regular spacing. Nonetheless, no matter how large the initial spacing, it would not be large enough to maintain a regular distribution in mature stands. The results presented above did not support the hypothetical cooperation among trees leading to clumped distribution ofindividuals. On the other hand, the alternative hypothesis - that competition leads to a more regular spacing - was neither disproved nor strongly corroborated. Rather the rc5ult.s supported the least informative possibility that spatial patterns of individual trees do not clearly reflect competition occurring in the course of growth of a forest stand. Such processes as iaterai growth of branches directed towards gaps in forest canopy weaken the results of crowding-induced mortality, for example, by allowing trees growing close to each other to develop their crowns in directions of adjacent gaps (Runkle and Yetter. 1987; Koop, 1989). Adjustment of the size, shape and spatial distribution of tree crowns to the actual free space in forest canopy may to a certain extent obscure the influence of the distribution of tree stems on competition intensity (Wierman and Oliver, 1979; Brand and Magnussen. 1958 ). Results concerning inter-species reiationships were not informative. Only five out of 20 plots located in mixed forests had sufficient numbers of pine and beech to allow statistical analysis of spatial relationships: this fact suggests that trees growing close to each other are normally of the same species. In the five analysed plots, however. the results suggested a long-lasting coexistence of beech and pine. This is possible as long as pines are, due to age or faster initial growth, at least slightly taller than the beeches. and the situ&ion with beech and larch is similar. Nevertheless, usually either beech or pinelarch are locally more abundant, and patches where the density of both species is more or less equal, are relatively scarce. The fact that significant departures from randomness in spatial patterns of trees were so few focuses attention on other mechanisms which could influence competition processes in forest stands. It is noteworthy that individual trees in forest stands cannot be considered equal even within a specified size class (Muston and Smith, 1987) 1There is perhaps a small fraction of individuals which are predisposed to grcsw faster than the others because of their genetic superiority or because of especially favourable conditions of establishment and early growth, and which thus have greater chances of survival (Weiner and Thomas, 1986: tomnicki, 1988 ). There is no reason to suppose that the distribution of such ‘promising’ individuals in a stand is other than random. Thus even very intensive crowding-depe?adznt mortality among trees cannot create a significantly regular pattern in mature trees: no matter how close and how many neighbours they have. “promising’ individuals will eventually survive and dominate their neighbours , as rhe competition is in their case typica!ly one-sided (Perry, J985: Weiner and Thomas. 1986: Pukkala ZXPV~ Kolstriim. 1987; Knox et al., 1989).
The results of the influence functions analyses raise the question of why high sums of influence in tree stands ofRatanicz. Valley are so rarely attained. The results show that these sums may be as large as i 80 (Figs. 2A, 2B). Examinatiou of distributions of global sums of influence suggests that forest stands have their biomass distributed very unevenly, with many patches being relatively empty. even though they are not ‘gaps’ in the classical, literary meaning. This resembles strongly the results obtained with the method of ‘closure values’ in a neotropical rain forest (Lieberman et al., 1989 ); relative density of forest was very diverse, ranging from very dark to very light patches, but with the majority of places being intermediate. The actual density is onI> a partial realisation of the maximum density, possible under given site conditions (Brand and Magnus>en, 1988 ). This seems to be an easily overlooked feature of natural and semi-natural forest stands: the overall pattern is not regular and the actual density of tree biomass within a plot is not as big as in intensively managed forest plantations (Farnum et al., 1983; Perry and Maghembe, 1989). The yield as well as productivity in such stands will never match the levels obtained in intensively managed forest plantations on similar sites. CONCLUSIONS
The role of self-thinning in shaping the actual pattern of trees is not clear. The fact that the majority of individual tree distribution patterns did not differ significantly from the random distribution suggests. that crowding-dependent mortality is not intense enough to produce reguiar patterns in mature trees. On the other hand, visible departures towards regularity in virtually all plots, and statistically significant regularity in a few plots seemed to support rhe role of distance-dependent competition in determining the spatial distribution of individuals. ACKNOWLEDGEMENTS
This work has been completed due to the assistance of numerous people: Hreneusz Dziasek made- the relascope measurements; Romek Borowiec, Pawel Czarnota, Jadwiga Czerwczak, Marek Czerwczak, Leszek Kobak and Jan Loch he!ped with field measurements: Jerzy Ptak wrote original computer programs and provided advice concerning mathematical methods and terminology; Craiyna Tarko typed the vast field data onto computer files: Jan Bodziarczyk drew the figures. Thanks are also due to Elibieta Pancer-Koteja and Wojciech Rdiariski for their useful comments on the text, and two anc:nymous reviewers for their help in streamlining the origina! manuscript. This Sudy was a part of the research project CFBP.04.10.05.03.08.
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