COMPETITION, MORTALITY, AND DEVELOPMENT OF SPATIAL PATTERNS IN TWO CANTABRIAN POPULATIONS OF FAGUS SYLVATICA L. (FAGACEAE)

ROZAS, V. & J.A. FERNÁNDEZ PRIETO (2000). Competition, mortality, and development of spatial paneras in two Cantabrian populations of Fagus sylvatica L. (Fagaceae). Anales Jard. Bot. Madrid 58(1): 117-131. In this paper the spatial patterns of size and mortality of European beech (Fagus sylvatica L.) were analy sed in two deciduous forest plots of Northern Spain. ¿i general terms, radial growth of F. sylvatica yields a direct relationship with size and an inverse relation with intraspecific competition while tree mortality seems be related to intraspecific competition. In the overall even-aged population, a lack of a recognisable structure in tree-size distribution, a small-scale regularity of survivors, and a regular pattern of dominant trees was noü'ced. This is a consequence of intense intraspecific competition at local level. In the old-growth plot, the wide repulsión between small and large beeches yields a specific spatial structure in tree-size distribution, showing even-sized groups of trees in different stages. Mortality in this plot occurs mainly within the dense group of small trees, which produces a broad regular pattern among the li ve beech trees. The random spatial pattern of dominant beeches seems to be characteristic of old-growth forests and could be a consequence of either self-thinning processes or exogenous factors.


INTRODUCTION
A common tenet in forest ecology is the assumption that trees of smaller sizes follow a clumped distribution while larger sized ones are randomly or uniformly distributed (SZWAGRZYK, 1992;WARD & al., 1996).The aggregation of small individuáis can be well explained by a variety of causes such as the existence of vegetative reproduction, the occurrence of disturbances that reléase space suitable for new establishment, forestfloor heterogeneity, competition, and others (LEPS & KINDLMANN, 1987).The development of spatial patterns, from aggregation to regularity, is usually interpreted as a consequence of densitydependent processes, so that mortality would take place in the high density zones and consequently a more sparse distribution of surviving trees would be given (KENKEL, 1988).However, evidence of a uniform spatial pattern for the large dominant individuáis has been scarcely documented in natural populations of forest trees (MOEUR, 1993), while examples of a random pattern are quite abundant (SZWAGRZYK, 1992).
The main ecological factor identified as the most important cause of mortality and, thus, of spatial pattern transformation, is the competition between neighbouring trees (LEPS & KINDLMANN, 1987;KENKEL, 1988).The interaction between neighbour individuáis promotes the diversification of tree growth-rates within the same initial size class (WEINER, 1984), giving way to a new size differentiation among individuáis so that the dominant and suppressed categories arise.Such divergence, in addition, tends to increase in the course of time, as the interaction between both given categories is not symmetric (WEINER, 1990).The loss of vigour experienced by underlying trees increases their susceptibility to direct mortality agents (LONG & SMITH, 1984) increasing the probability of those individuáis dying.In monospecific stands constituted by even-aged trees, mortality occurrence is a consequence of intraspecific competition, and leads to a more regular spatial pattern of surviving trees than would be expected when assuming that mortality is a random event (KENKEL, 1988).
In natural forests, substantial differences between the growth rates of trees of the same species are very frequent, particularly in cohorts of shade-tolerant species, which can survive for a long time as underlying individuáis (PETERKEN, 1996).As a result of this, the size hierarchy that is present in this type of forests is a consequence of both the unequal age of trees and the diversification in growth-rates of trees belonging to the same cohort.Another factor which also explains to a certain extent the different spatial patterns of trees, is the regeneration mode of the species, being typical in shade-tolerant species the establishment in a continuous way under the forest canopy (VEBLEN, 1992).Therefore, the relative spatial arrangement of the different size classes can be related to a specific regeneration mode (VEBLEN & al., 1980;MOEUR, 1993).This assertion suggests that quantitative spatial analysis would provide a better knowledge of forest dynamics as a whole than those designs based on the subjective identification of canopy gaps, often considered as independent units (LIEBERMAN & ai, 1989).
The aim of this paper is to test the following hypotheses related to the spatial dispersión and the growth and mortality patterns of the shade-tolerant hardwood species Fagus sylvatica L. in a deciduous forest of Northern Spain: (1) the individuáis belonging to any given size class are randomly distributed, (2) the sizes of neighbouring trees are independent, (3) the increase in basal área is independent of competition intensity and (4) the mortality is not related to competition and it does not give a shift in spatial pattern of the survivors.The decay of dead trees from the studied plots is a main limitation for the proper accomplishment of these objectives.Thus, only those dead trees that could be accurately identified, which represent the most recent mortality, were taken into account.In spite of this restriction, the results obtained allow valid conclusions on the dynamics of the studied populations of Fagus sylvatica, and on the development of its spatial patterns to be drawn.

Study área
The study área is located in the western lowlands of Cantabria, Northern Spain (43°20'N, 4°18'W), and included in the Corona forest and the Oyambre Natural Park, between the towns of Comillas and Cabezón de la Sal.The forest under study has a surface of 110 ha and both European beech (Fagus sylvatica L.) and pedunculate oak (Quercus roburL.)dominate its canopy.Other relevant woody species present are Ilex aquifolium L., Salix atrocinerea Brot., Pyrus cordata Desv., Frangula alnus Mill., Corylus avellana L., Crataegus monogyna Jacq, and Malus sylvestris Mill.The soil of the location is classified as sandy brown earth (GUITIAN & ai, 1985) with parent material of sandstone and clay formed in the lower Cretacean (IGME, 1976).It is located on a hillside North-Northeast oriented, with slopes that range from 8 to 50%, and altitudes from 40 to 240 m.The climate is Atlantic with the summer as the warmest and driest season (ALLUE, 1990), a total annual precipitation of 1400 mm, and 13.5 °C as the average annual temperature.

Sampling
Two rectangular plots, C2 and C3, with a surface of 0.25 ha (50 x 50 m) and 0.30 ha (50 x 60 m), respectively, were located in the forest interior.Stands were selected on the basis of: (1) the existence of populations of Fagus sylvatica composed of an adequate number of trees belonging to a wide size range, (2) the presence of enough dead individuáis within these populations and (3) the existence of a regular topography with a low slope that facilitated the field work and guaranteed a minimal error in the measurements.The plots were divided into quadrats of 10 x 10 m and all living and dead trees with DBH (stem diameter at 1.3 m above ground) s 2 cm were identified, labelled, and their DBH measured.Dead trees category included the standing, windthrown and snapped dead trees, as well as the stumps, which were identified by their bark and wood characteristics.The x and y co-ordinates to the centre of each tagged stem were measured within each quadrat to the nearest 0.1 m.Only the largest stem of the few multi-stemmed trees was measured, and each apparently independent stem was considered as a sepárate individual.

Tree age estimates
All the live Fagus sylvatica trees with DBH > 5 cm were cored with a Pressler increment borer.Trees with DBH < 30 cm were cored at 20 cm above ground, while in trees with DBH > 30 cm cores were taken at 100 cm above ground.Cores were air-dried, mounted, and sanded using successively finer grades of sandpaper until the growth rings were clearly visible.In cores that reached the pith of the tree, its age was estimated either as the number of existing rings in the sample obtained by ring counts, if the core included less than 100 rings, or by crossdating with a master chronology, if the core included more than 100 rings.Crossdating permitted recognition of some absent rings in the samples that could not have been identified by other methods.If the core did not reach the pith, its position was estimated by means of the extensión of two xylematic rays visible on the sample surface.The number of absent rings in the missed segment of the core was estimated by means of an initial growth model calibrated from samples of Fagus sylvatica that reached the pith (ROZAS, 1999).The estimated number of absent rings and the number of rings in the available segment have been summed in order to obtain the overall estimates of tree age.It has been preved that this method of age estímate gives a mean absolute deviation of 8.8 years for incomplete cores of F. sylvatica distant up to 5 cm from the pith (ROZAS, 1999).Mean age difference between 20 and 100 cm above ground is 11 years, which have been obtained from 20 trees cored at both heights.Thus, 11 years were added to age estimates of trees cored at 100 cm abo ve ground in order to obtain all age estimates referred to a height of 20 cm above ground level.

Spatial analysis
Univariate spatial pattern was analysed using the Ripley's K function (UPTON & FINGLETON, 1985;HAASE, 1995), which reflects the type, scale and intensity of the spatial pattern of a set of points from the distances between all of them.K(t) function computes the number of neighbouring trees y that are found within a distance t from each focal tree i. Edge effect was corrected by the weighted method, which assigns a higher weight to peripheral trees in the plot than to central ones.The weight assigned to each tree is inverse to the proportion of circumference centred on point i, that passes through the point j, lying within the plot boundaries (MOEUR, 1993;HAASE, 1995).
Bivariate spatial pattern was analysed using the bivariate extensión of Ripley's K function (UPTON & FINGLETON, 1985), which indicates the type, scale and intensity of the spatial interaction between two sets of points.The function Kn(t) computes the number of type 2 trees within circles of radius t centred at each type 1 tree.Edge effect was corrected by means of the same method as in the univariate analysis.K(t) as well as Kn{t) valúes were calculated each 1 m, for a maximum distance of 25 m, and only sets of points with more than 10 individuáis were analysed.
The spatial randomness hypothesis for univariate analysis was tested by means of Monte Cario methods, simulating random coordinates of the same number of trees as in the analysed sample.A 95% confidence interval for spatial randomness was obtained from high and low K{t) valúes for each distance t calculated in 20 simulations.The spatial independence hypothesis for bivariate analysis was verified by simulating random toroidal shifts of the type 2 trees with respect to the type 1 ones (UPTON & FINGLETON, 1985).A 95% confidence interval for spatial independence was generated from high and low K, 2 (t) valúes for each distance t obtained in 20 simulations.Since often Kn(i) *.Ku(t), the spatial interaction between two sets of trees was calculated as a linear combination of both bivariate analyses (UPTON & FINGLETON, 1985).The random mortality hypothesis was tested by selecting at random and removing trees from the pre-mortality populación composed of the set of live + dead trees (KENKEL, 1988;DUNCAN, 1991).The number of individuáis removed in each simulation corresponded to the number of dead trees in the sample.A 95 % confidence interval for random mortality was given from high and low K(t) and Ku(t) valúes for each distance t attained in 20 simulations.
All obtained results were converted into the functions Uf) = [K(t)/n] m for univariate analysis and Lnit) = [KnWnf 2 for bivariate analysis, in order to linearise the function and stabilise the variance.The interpretation of results was made by plotting L(t) -f or Ln(t) -1 against t, which fit nuil hypothesis to zero valué.For univariate analysis, valúes of L(í) -t above upper boundary of confidence intervals indicate a clumped pattern, whilst valúes below lower boundary indicate a uniform pattern.The extent to which the observed distribution departs from the randomness was calculated by applying the transformation W(t) (SZWAGRZYK, 1992) If a correlogram shows positive autocorrelation at small distance classes, then trees of similar size are grouped together.In order to identify even-sized groups of trees, a measure of association reflecting both spatial proximity and size similarity was calculated between each pair of trees (DUNCAN & STEWART, 1991).Agglomerative hierarchical clustering and nonmetric multidimensional scaling were applied to the symmetrical matrices of association measures in order to group trees of similar size and spatial location.The groups of trees recognised from the cluster and the ordination diagram should be spatially discrete, even-sized and with a different size than adjacent ones (DUNCAN & STEWART, 1991; DUNCAN, 1993).

Radial growth and competition
In each of the core samples, widths of the outermost 5 rings were measured to the nearest 0.01 mm under dissecting microscope, with an incremental measuring device (Velmex measuring stage, Acu-Rite linear encoder, and Metronics digital readout unit linked to a PC).The basal área increment of each tree in the last 5 years (BAI5) was calculated from DBH and the ring widths of the last 5 years, period in which the environmental conditions of the forest have not drastically changed.It was calculated a competition index defined as (modified from LORMER, 1983): basal área of neighbouring trees y.This index was calculated for the focal Fagus sylvatica trees distant at least 5 m from the plot boundaries, being considered as neighbours all trees located at a distance O 5 m from the focal tree.Intraspecific competition index was calculated by considering only the neighbours F. sylvatica, while interspecific competition index was calculated from neighbouring trees belonging to all species except F. sylvatica.2-4.9 5-9.9 10-29.930-80  Both populations of Fagus sylvatica were classified into four size-classes for stratified spatial analysis (table 1).The total number of dead trees in plot C2 was 19, whereas in plot C3 it was equal to 33, with a total proportion of dead trees around 11% in both plots.In plot C2, the size-classes 1 and 2 of F. sylvatica were mainly clumped, the sizeclass 3 showed aggregation and random pattern according to spatial scale, while the size-class 4 exhibited a uniform and random pattern, according to the analysed spatial scale (fig.2a).In plot C3, the size-classes 1 to 3 showed different intensity of dumping, while trees belonging to the size-class 4 were distributed at random in all the spatial scales analysed (fig.2b).

The shape of the DBH distribution of
The correlogram for spatial structure of DBH in the Fagus sylvatica population of plot C2 does not show any significant autocorrelation in all the analysed distances and has not overall significance (fig.3a).In the F. sylvatica population of plot C3 (fig.3b) the correlogram for spatial structure of DBH is highly significant as a whole and the first four distance-classes, from 0 to 10 m, showed significant positive autocorrelation indicating similarity in neighbouring tree diameters at this spatial scale.The correlogram for plot C3 exhibits furthermore significant positive autocorrelation at distance class 8 (20 m) and negative autocorrelation at distance classes 17 to 23 (42.5 to 57.5 m).Four even-sized groups of F. sylvatica were given in plot C3 (table 2).Group 1 included large trees with an average of 48.6 cm in DBH and without dead trees, which dominated half of plot C3 (fig.3c; table 2).Group 2, by contrast, included numerous small trees, with a mean size of 5.7 cm in DBH.A proportion of 88 % of total dead F. sylvatica trees in plot C3 were included in group 2, which dominates the opposite half of the plot (fig.3d; table 2).The other two groups of trees with intermediate diameters were intermixed with the principal groups 1 and 2. Dead F. sylvatica trees included in group 3 (table 2) were underlying individuáis developed under dominant trees belonging to group 1.
In both C2 and C3 plots, age and size of Fagus sylvatica were significantly related (least-squares regression in plot C2: log e (age) = 0.33 log^DBH) + 3.25; r 2 = 0.48; «=118; p < 0.001 and in plot C3: log e (age) = 0.78 log e (DBH) + 2.22; r 2 = 0.79; n = 152; p < 0.001).Therefore, spatial interaction between different size-classes can be used to estímate  the regeneration patterns of the studied tree species (VEBLEN, 1992).In plot C2, live + dead F. sylvatica trees with DBH < 30 cm were spatially independent from the live F. sylvatica with DBH > 30 cm, except at distances of 4 and 5 m, which showed a scarce intensity of repulsión (fig.4a).Spatial interaction between the same groups of F. sylvatica trees in plot C3 was characterised by repulsión from 0 to 17 m, and by independence from 18 to 25 m (fig.4b).
Live Fagus sylvatica trees in plot C2 showed a clumped pattern at all analysed distances and were distributed more regularly than would be expected from random mortality at distances from 0 to 2 m, but did not differ from this hypothesis at higher distances (3 to 25 m; fig.5a).Spatial interaction between the live and dead F. sylvatica trees in plot C2 was characterised by attraction at distances from 0 to 17 m, according to the spatial independence hypothesis.Attraction from the nuil hypothesis of random mortality was also found at distances from 1 to 5 m and 8 to 14 m (fig.5b).In plot C3, live F. sylvatica were clumped at all analysed distances and were more uniformly spaced than would be expected given random mortality at distances of 3 to 24 m (fig.5c).Living and dead F. sylvatica trees in plot C3 showed attraction from spatial independence hypothesis at all analysed spatial scales, and also attraction from that expected given random mortality at distances of3to25m(fig.5d).
Mean valúes of age, basal área increment during the last 5 years, and competition índex within the most recent cohort of Fagus sylvatica, indicate an evident pattern of sizedependent variation in these three parameters, results being very similar in both the C2 and C3 plots.The hypothesis of identity in the distribution of these variables within different size classes was verified by means of the Kruskal-Wallis test, due to the heteroscedasticity of data.In plot C2 as well as in plot C3, age and basal área increment of F. sylvatica increased significantly with size, while competition index significantly decreased with size (table 3; H ranged between 16.48 and 71.14; d.f.= 3 and p < 0.001 in the six tests).Besides, mean age of total F. sylvatica trees belonging to the recent cohort was significantly greater in plot C2 than in plot C3 (60.2 vs. 50.1 years; t for unpaired data = 8.54; d.f.= 221; p < 0.001) and mean competition index is significantly greater in plot C3 that in plot C2 (35.5 vs. 29.2;í = 3.47; d.f.= 134; p = 0.001).However, mean basal área increment during the last 5 years did not differ significantly between F. sylvatica trees of the recent cohort either in plots C2 or C3 (í = 0.18; d.f.= 221; p = 0.855).In plot C2, basal área increment of F. sylvatica trees belonging to the recent cohort was related to DBH in a direct way, and inversely related to age (least-squares regression: BAI5 = 7.70 DBH -1.62 Age + 27.13; r L = 0.67; d.f.= 66;p< 0.001), while in plot C3 it was only related to DBH (leastsquares regression: BAI5 = 6.79 DBH -36.31; ^ = 0.76; d.f.= 65;/?< 0.001).
Finally, partial correlations of competition Índices with basal área increment during the last 5 years, were calculated for all F. sylvatica trees belonging to the most recent cohort in the plots C2 and C3 individually, as well as in the sum of both populations as a whole.In all cases, basal área increment showed a significant negative correlation with intraspecific competition, i.e. trees that suffered an intense interaction with conspecifics had slower growth rates (table 4).By contrast, interspecific competition and basal área increment were not significantly related, i.e. radial growth rates

DISCUSSION
The age structure of Fagus sylvatica in plot C2 indicates that this population is predominantly composed of trees younger than 100 years old, having found only 4 trees older than 180 years old.Air photos taken in 1953 clearly show that plot C2 is located in a zone with parkland structure, with large scattered trees and much open space, a structure probably derived from its utilisation as pasture for cattle.The compound shape of F. sylvatica diameter distribution in plot C3 is characteristic of the shade-tolerant species which dominates the overstory of old-growth stands (LORIMER & KRUG, 1983).This happens in plot C3 as in other mature forests mainly constituted by Fagus (KOOP & HILGEN, 1987;OHKUBO & ai, 1988) or shadetolerant Nothofagus species (VEBLEN & al., 1980;STEWART & ROSE. 1990).The age structure in plot C3 shows abundant mature F. sylvatica trees older than 200 years as well as abundant regeneration during the last 80 years.Air photos also show that forest density in plot C3 has been high over the last five decades because this plot is located in a zone with high-forest structure.Establishment of the most recent cohort of F. sylvatica began over 20 years earlier in plot C2 than in plot C3, with an average age for this cohort of 60 years in plot C2 and 50 years in plot C3, both significantly different (see results).However, differences in specific dates of tree establishment did not rend any apparent relationship to contrast between the dynamics of both studied populations.
Lack of spatial structure of Fagus sylvatica population in plot C2 is shown by both the spatial pattern analyses for different size classes (fig.2a) and the spatial correlogram of DBH (fig.3a).Trees with less than 30 cm in DBH are distributed with small aggregation intensity or in a random way, while the largest size class presents a random or regular pattern of small intensity, depending on the spatial scale chosen.Furthermore, F. sylvatica population of C2 presents a mortality pattern which is also characteristic of density dependence: dead trees are only present in the smaller size classes, live trees show a uniform pattern at very short distance, and live and dead trees show spatial attraction at short and mean distances.Thus, F. sylvatica mortality in plot C2 occurs not at random, and is a consequence of intraspecific competition between trees located in cióse proximity (ANTONOVICS & LEVIN, 1980; KENKEL, 1988), specifically at distances from 0 to 2 m.
The greatest part of Fagus sylvatica trees in plot C2 belong to the cohort established without space limitation.Therefore development of this cohort was similar to that expected from classic models, based on the study of monocultures on homogeneous substrate (ANTONOVICS & LEVIN, 1980;WEINER, 1984;KENKEL, 1988).In consonance with a widely accepted and experimentally ratified model, interaction between neighbour trees belonging to the same cohort was not symmetrical.According to the model, competition would increase growth rate variability and, by so much, magnify size differences between cióse neighbours from those expected with scarce (or without any) competition (WEINER, 1990).In agreement with these hypotheses, the sizes of neighbour F. sylvatica in plot C2 were independent, and basal área increments were directly proportional to size, therefore the asymmetrical intraspecific competition indeed contributed to increase differences in size of neighbouring trees along the development of the most recent cohort.Size differences between adjacent trees permitted the large sized individuáis to reach a dominant position in the canopy, increasing their capacity to continué growing and confining underlying individuáis to grow in an increasingly reduced space (OLIVER & LARSON, 1996).Therefore, small-sized trees in the plot C2 presented little radial growth since they were subjected important competition intensity on a small spatial scale, and died when competition with larger neighbours was intense enough.
The size-class 4 of Fagus sylvatica in plot C2 included 9 trees younger than 80 years, 5 trees of 80 to 120 years in age, and 4 trees older than 180 years.Thus, the bivariate pattern obtained in figure 4a indicates only independence between different size-classes in this population, but it is not related to the spatial interaction between different cohorts and therefore indicates nothing on regeneration pattern of F. sylvatica in plot C2.The not very intense clumped pattern of the small-sized trees in plot C2 is not a consequence of regeneration limited to concrete zones, but of the growth rate diversification between neighbouring trees as a result of asymmetrical competition.The prevalent uniform pattern in the greatest sizeclass could be a consequence of intraspecific competition on radial growth and mortality, since the stochastic processes of tree losses by wind or decline of dominant trees has not had any incidence yet in plot C2.A similar spatial structure has been described in plots with a scarce disturbance regime (MOEUR, 1993) in which the competition processes that lead toward an increasingly regular distribution while increase the size of trees are expressed without participation of exogenous factors that could modify the final pattern.
In plot C3 die smaller size classes of Fagus sylvatica were clumped, while bigger trees showed a random pattern, which is in agreement with resulte obtained in other old-growth forests (VEBLEN & al., 1980;NAKASHIZUKA & NUMATA, 1982a, 1982b;OHKUBO & ai, 1988;DUNCAN, 1993;TAYLOR & al., 1996).Although spatial pattern analyses in some of the above mentioned publications were made by means of different methods than Ripley's £function (Morisita's index and Iwao's method), all their results suggest that the main spatial pattern of large trees in old-growth forests is random or near random.The existence of a random pattern is a normal result of the transformation of an initial clumped pattern caused by self-thinning (LEPS & KINDLMANN, 1987).
Therefore, it is incorrect to deduce the independence of individuáis within a forest stand from the observed random pattern since competition between neighbouring trees does not necessarily origínate regular spatial patterns.Furthermore, it is very probable that past competition between trees could be not reflected in the current spatial distribution of live trees (SZWAGRZYK, 1992).The influence of exogenous factors along the history of plot C3, such as disturbances that might have eliminated dominant trees of the main canopy, could have conditioned the final pattern, making it depart from the one expected, if only the competition had exerted its effect.Thus, the effects of self-thinning as well as some exogenous factors acting on tree growth and mortality are sufficient to explain the random pattern of large F. sylvatica trees inplotC3.
The correlogram of Fagus sylvatica size in plot C3 shows positive autocorrelation at small distance classes, no autocorrelation at intermediate distance classes and negative autocorrelation at large distance classes (fig.3b), which indicates a spatial gradient in tree diameter distribution (LEGENDRE & FORTÍN, 1989).This result agrees with the spatial arrangement of the two principal groups of trees identified, with large diameter dominance in a half of the plot while small diameter trees domínate the other half.Similar results have been obtained in other spatial autocorrelation analyses of size (SAKAI & ODEN, 1983) and age (DUNCAN & STEWART, 1991) in natural tree populations.The gradient structure of DBH seems to be related to the regeneration pattern of F. sylvatica in plot C3, which occurred segregated frora the mature trees of their own species.This is quite a logical conclusión, because size-class 4 of F. sylvatica in plot C3 was composed of a 64 year old tree, a 175 year tree, and 33 mature trees of more than 200 years.For this reason, the bivariate pattern of figure 4b is an adequate indicator of the large spatial repulsión with which the regeneration occurred in relation to the mature trees.
Fagus species are always more shadetolerant than the other coexisting deciduous trees throughout the entire north hemisphere (PETERS, 1992), F. sylvatica being the most shade-tolerant broadleaf tree species in Europe (PETERKEN, 1996).However, the regeneration of different Fagus species is very difficult under a canopy of their own species, mainly due to the great capacity of light assimilation that adult Fagus trees possess.Therefore, Fagus regeneration takes place mostly in canopy gaps and less dense canopy zones, in which young trees reach often large densities (NAKASHIZUKA & NUMATA, 1982a, 1982b;KOOP & HILGEN, 1987;OHKUBO & al., 1988).Thus, the highly organised spatial structure of F. sylvatica population in plot C3 would be mainly a consequence of the occurrence of regeneration as a density-dependent process along the last 80 years.Tree regeneration took place segregated from the previous cohort, the size of neighbour trees being similar and, since basal área increment depends to a large extent on tree size, this similarity would have perpetuated over time.
In plot C3 dead trees were found in the smallest size class of the most recent cohort as well as in the smallest size classes of the most ancient cohort (fig.le).That is to say, two types of Fagus sylvatica mortality levéis would coexist in plot C3: (1) tree mortality within the cohort established at 30 to 80 years ago, and (2) mortality of the trees of 170 to 270 years old.Distribution patterns of F. sylvatica trees in plot C3 differed significantly from that expected given random mortality.Both a uniform pattern for live trees and spatial attraction between Uve and dead trees, from that which would be expected from random mortality, were observed in nearly all the analysed distances.Except for very short distances (< 3 m) or very long distances (> 24 m), intraspecific competition produced mortality of F. sylvatica trees in plot C3 (DUNCAN, 1991).Current models predict that if intraspecific competition causes tree mortality live trees will be more uniformly spaced than would be expected from random mortality at small spatial scale (KENKEL, 1988).This was observed in plot C2 and in other natural tree populations (DUNCAN, 1991).Lack of evidence of competition at short distance in the recent cohort of F. sylvatica in plot C3 can be well explained by the great size similarity of neighbouring trees.The existence of tree groups with very similar size was reflected in the highly significant positive autocorrelation at distances up to 10 m (fig.3b).The great majority of dead trees in the F. sylvatica population of plot C3 were found within group 2 and the greatest difference in DBH between the individuáis of this group was around 15 cm (table 2).Therefore, in this case there was not an intense intraspecific competition at small spatial scale exerted by the greater sized trees.F. sylvatica mortality in plot C3 was rather a consequence of the competition exerted by a great number of individuáis of a very similar size, and located in a very wide distance range.
In summary, within the two Fagus sylvatica populations under study, age and size were directly related, and both radial growth and mortality depends on intraspecific competition.However, the notable differences concerning spatial organisation and mortality patterns observed between populations could be a consequence of regeneration development under very different conditions.Recent cohort establishment in one plot occurred without space limitations, due to the scarce presence of mature trees.Size hierarchy in this population, mainly composed of even-aged individuáis, could have been originated by the asymmetric intraspecific competition between neighbouring trees.The main consequence of this is the absence of a recognisable structure in the spatial arrangement of tree size, with great differences in the sizes of neighbouring trees.Thus tree mortality in this population was a result of the asymmetrical competition exerted by large sized trees on adjacent suppressed individuáis.On the other hand, in the population constituted by two welldifferentiated principal cohorts, establishment of new individuáis was limited by the existence of an old-aged cohort that monopolised an extensive área of the plot surface.Thus, tree regeneration was densitydependent, resulting in a size hierarchy mainly conditioned by differences in age, as well as in a clear spatial structure in those groups composed of even-sized trees.Tree mortality pattern, in this case, resulted from the competition exerted by a great number of individuáis very similar in size over a wide distance range.
Fagus sylvatica in the plot C2 is descending monotone, with dead trees included in the fírst two size classes, always narrower than 20 cm in DBH (fig.la).While mature trees older than 200 years are very scarce, the population of F. sylvatica in plot C2 largely consists of trees with ages ranging from 40 to 80 years old (fig.Ib).In plot C3 the DBH distribution is compound, consisting of a steeply descending monotone in the two smallest size classes and a broad peak in the size classes larger than 20 cm (fig.le).Dead trees are found in both the first size-class, ranging from 2 to 10 cm in DBH, and the first two sizeclasses of the wide peak, from 20 to 40 cm in DBH.The age structure of F. sylvatica in plot C3 reveáis two well differentiated cohorts, one composed largely of mature trees 200 to TABLEI DBH CLASSES CONSIDERED FOR THE SPATIAL ANALYSES AND NUMBER OF FAGUS SYLVATICA TREES IN EACH SIZE CLASS where CI is the competition index, BA{ is the basal área of the focal tree i, and BA]

Fig. 3 .
Fig. 3.-Spatial correlograms of Fagus sylvatica DBH in plots C2 (a) and C3 (b).Standard normal deviation z(d) of Moran's /coefficient in 2.5 mdistance classes.Solid points: signifícant spatial autocorrelation at 0.05 level.Theoverall significance level of each correlogram is shown.n.s.: non signifícant.Spatial arrangement of the principal two groups of trees recognised in plot C3, group 1 (c) and group 2 (d), corresponding to the groups detailed in table 2.
Fig. 5.-Spatial analysis of Fagus sylvatica mortality.Univariate analyses for Uve trees in plots C2 (a) and C3 (c).Bivariate analyses of spatial interaction between live and dead trees in plots C2 (b) and C3 (d).Dotted lines: 95% confidence intervals for spatial randomness (univariate) or independence (bivariate) hypotheses.Dashed lines: 95% confidence intervals for random mortality hypothesis.
. For bivariate analysis, valúes of Li2(f) -t above upper boundary of confidence intervals indicate attraction, whilst valúes below lower boundary indicate repulsión.The spatial structure of the DBH variable within each set of trees was analysed by the standard normal deviates z(d) of Moran's / spatial autocorrelation coefficient (UPTON & FINGLETON, 1985).Computation was made at 2.5 m distance classes and only intervals with at least 20 pairs of neighbouring trees were included in the analysis (DUNCAN & STEWART, 1991).The nuil hypothesis of independence in size among neighbouring trees was tested by means of the confidence interval defined by the 0.05 significance level valúes for a standard normal distribution.Valúes of z(d) greater than 1.96 indícate positive autocorrelation, while valúes less than -1.96 indícate negative autocorrelation.An overall test for each correlogram was performed by checking whether at least one valué was significant at the 0.05/k level, where k is the number of distance classes analysed, according to the Bonferroni's criterion for múltiple tests (LEGENDRE & FORTÍN, 1989; DUNCAN & STEWART, 1991).