Spatial patterns in an old-growth Nothofagus obliqua forest in south-central Chile

Abstract

Data from a 1 ha permanent sample plot in an old-growth Nothofagus obliqua dominated forest were used to study spatial patterns of dead and live trees using the Ripley’s K(t) function. Univariate and bivariate analyses were conducted. We computed confidence envelopes for a random (Poisson) spatial distribution using Monte Carlo simulations. An edge effect correction was applied. The spatial pattern of Aextoxicon punctatum (the dominant species) changed from a random distribution at short spatial intervals of analysis to a clustered distribution at broader spatial scales. N. obliqua appeared to be more regularly distributed, but was not statistically significantly different from a random distribution at 95% confidence. There was a negative interaction (i.e. repulsion) between shorter (generally younger than 100 years) and taller (generally older than 250 years) trees. On the other hand, there was a positive interaction (i.e. attraction) between shorter, younger trees and standing dead trees.

Full text

Spatial patterns in an old-growth Nothofagus obliqua forest
in south-central Chile
Christian Salas
a,
*, Valerie LeMay
b
, Patricio Nu
´n
˜ez
a
, Patricio Pacheco
a
, Alejandro Espinosa
a
a
Departamento de Ciencias Forestales, Universidad de La Frontera, Casilla 54-D, Temuco, Chile
b
Department of Forest Resources Management, University of British Columbia, 2045-2424 Main Mall, Vancouver, BC, Canada V6T 1Z4
Received 10 October 2005; received in revised form 29 April 2006; accepted 29 April 2006
Abstract
Data from a 1 ha permanent sample plot in an old-growth Nothofagus obliqua dominated forest were used to study spatial patterns of dead and
live trees using the Ripley’s KðtÞfunction. Univariate and bivariate analyses were conducted. We computed confidence envelopes for a random
(Poisson) spatial distribution using Monte Carlo simulations. An edge effect correction was applied. The spatial pattern of Aextoxicon punctatum
(the dominant species) changed from a random distribution at short spatial intervals of analysis to a clustered distribution at broader spatial scales.
N. obliqua appeared to be more regularly distributed, but was not statistically significantly different from a random distribution at 95% confidence.
There was a negative interaction (i.e. repulsion) between shorter (generally younger than 100 years) and taller (generally older than 250 years)
trees. On the other hand, there was a positive interaction (i.e. attraction) between shorter, younger trees and standing dead trees.
#2006 Elsevier B.V. All rights reserved.
Keywords: Ripley’s KðtÞfunction; Monte Carlo simulations; Bivariate spatial patterns; Standing dead trees; Stand dynamics
1. Introduction
Lowland Nothofagus obliqua,Laurelia sempervirens, and
Persea lingue dominated old-growth forests are scarce and
ecologically important in south-central Chile. These forests
once covered the central depression (low-elevation, below
400 m) of south-central Chile (between 38and 41S latitude)
(Schmithu
¨sen, 1956; Donoso, 1995). They were largely cleared
for agriculture (Veblen et al., 1996) and only some remnants of
these forests now exist (Donoso, 1995). They now occur either
as private estates, such as with the forest studied by Veblen et al.
(1979), or as areas retained by research institutions, such as the
forest studied by Ramı
´rez et al. (1989a,b) and Frank (1998).
The area of these forests is estimated as less than 2% (C.
Donoso, personal communication) of the N. obliqua–N. alpina–
N. dombeyi forest type described by Donoso (1995). However,
some stands are more ecologically limited, occurring as small
isolated islands or as stands greatly altered through human
disturbance, leaving about 4000 ha of this forest type. N.
obliqua dominated old-growth forests are uneven-aged, have
multiple height strata, and, in successional terms, they are close
to a steady-state condition (Veblen et al., 1979; Donoso, 1995).
This forest ecosystem is characterized as being unique in the
world, with both large timber volumes (Donoso, 1995) and high
biodiversity (Frank, 1998; Salas, 2001). However, they are not
represented in Chile’s national system of protected areas
(SNASPE).
Even though these forests have been considered important
for Chilean conservational initiatives (Mun
˜oz et al., 1996), little
research exists for these lowland Nothofagus dominated old-
growth forests. Some research has been conducted on floral
composition (Ramı
´rez et al., 1989a,b; Frank, 1998), tree
regeneration (Veblen et al., 1979), and structure and dynamics
(Veblen et al., 1980; Donoso, 1995; Frank and Finckh, 1998).
Spatial distributions and spatial patterns (both vertical and
horizontal) of trees in forests are important elements for
understanding forest ecosystem dynamics (Veblen et al., 1979),
and the potential for ecological understanding has not been
fully recognized (Franklin et al., 2002). Nevertheless, few
studies on the spatial distributions of trees have been conducted
in these forests (Veblen et al., 1979, 1980, 1981). The focus of
these studies has been on analysing spatial patterns of
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Forest Ecology and Management 231 (2006) 38–46
* Corresponding author. Present address: School of Forestry and Environ-
mental Studies, Yale University, 360 Prospect Street, New Haven, CT 06511-
2189, USA. Tel.: +1 203 432 9398; fax: +1 203 432 3809.
E-mail address: christian.salas@yale.edu (C. Salas).
0378-1127/$ – see front matter #2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.foreco.2006.04.037

regeneration, commonly the focus of studies on spatial patterns
in forests (Tomppo, 1986). However, knowledge of the spatial
distributions of trees would be useful in: (1) understanding
inter- and intra-species relationships; (2) designing silvicultural
regimes that mimic natural processes; (3) forest inventory
planning and design (Tomppo, 1986); (4) improving stand
dynamics models by including inter-tree (and inter-species)
measures of competition.
A spatial point pattern is a set of locations, irregularly
distributed within a region of interest, which have been
generated by some unknown spatial process (Diggle, 1983).
Many methods and indexes have been developed to interpret
and assess spatial distributions (Greig-Smith, 1952; Clark and
Evans, 1954; Morisita, 1957; Pielou, 1959; Ripley, 1977, 1979,
1981). These methods can be classified into three main groups,
depending upon the type of data required (Ripley, 1981):
(1) Quadrat (plot) counts, where fixed-area sample plots are
established and the number of points (e.g., trees or
seedlings) is counted within each plot (e.g., Greig-Smith,
1952). Based on quadrat count data, Fisher et al. (1922)
proposed the sample variance-to-mean ratio as an index of
dispersion, and Morisita (1957) developed an index of
randomness.
(2) Nearest distance methods, where the distance between the
subject (e.g., tree) and its nearest neighbour (nearest
neighbour distances) (Clark and Evans, 1954) or the
distance from a point to its nearest neighbour (point to
nearest distances) (Pielou, 1959) is determined. Neighbours
other than the nearest neighbour may be also be used.
(3) Mapped data, where the location of each object (e.g., tree) is
recorded, and used to indicate spatial pattern. Ripley’s KðtÞ
function (Ripley, 1977, 1979, 1981) can be used to examine
patterns using mapped point data. Although a number of
different methods have been applied, this approach has been
most commonly applied in ecological spatial pattern
analyses in recent years (Liebhold and Gurevitch, 2002).
Variograms and correlograms can also be useful for spatial
pattern analyses (Duncan and Stewart, 1991; Garcı
´a, 1992),
although these methods are more commonly used for
continuous rather than point processes.
As pointed out by Moeur (1993), researchers have used both
quadrat and distance methods for assessing forest spatial
patterns. Both quadrat and distance methods are largely affected
by sampling procedures. Payandeh (1970) tested the quadrat,
nearest neighbour, and point-to-plant methods, and stated that the
point-to-plant distance performed best, even though all behaved
well. However, Condes and Martinez (1998) showed that the
aggregation index commonly used with the quadrat method is not
efficient. Moreover, quadrat methods are greatly affected by the
plot size (Payandeh, 1970; Pielou, 1977; Diggle, 1983; Tomppo,
1986), and by the proportion of plots without points (i.e. zero
counts). Nevertheless, the variance-to-mean ratio based on
quadrat plots is still widely used (Tomppo, 1986), since data
collection and analysis are relatively straightforward. Analysing
the distribution of nearest neighbour distances may give insights
to competition and other processes (Moeur, 1993). However,
important patterns and processes might exist beyond the nearest
neighbour, and would be missed if only the nearest neighbour
distances are examined. As pointed out by Haase (1995), both
quadrat and distance methods have been frequently modified,
resulting in an increasing number of approaches. However,
problems remain in using these methods. Ripley’s KðtÞfunction
(Ripley, 1977, 1979, 1981) overcomes many of the problems
cited by Haase (1995). Since Ripley’s KðtÞfunction uses
distances between all possible pairs of trees, via increasing the
radius from the target tree, spatial patterns at many scales can be
more easily detected, which is particularly useful for forests with
very high spatial variability (Moeur, 1993).
Most of the spatial pattern studies in natural Chilean forests
have been conducted using point-to-plant measures, nearest
neighbour methods (Barasorda, 1977; Morales, 1981; Alvarez,
1982; Peters, 1985), or Morisita’s index (Veblen et al., 1979,
1980). These methods have resulted in difficult interpretations
of spatial patterns for old-growth Nothofagus trees, largely due
to the small numbers of the trees in these stands (Barasorda,
1977; Alvarez, 1982; Peters, 1985) and to the use of relatively
small plot sizes (Veblen et al., 1979, 1980). Alternatively,
Ripley’s KðtÞfunction (Ripley, 1977, 1979, 1981) is
particularly useful for forests with very high spatial variability
since spatial patterns at many scales can be more easily
detected. Ripley’s KðtÞfunction has been applied to N.
obliqua–N. alpina second-growth (Martin, 1995), evergreen
(Gutie
´rrez, 2002), and Gomortega keule (Villegas et al., 2003)
forests, with some success. No study of the spatial distribution
of Nothofagus old-growth forests using Ripley’s KðtÞfunction
was found in the literature.
In this study, we use Ripley’s KðtÞfunction to examine
spatial patterns of trees in mature N. obliqua forest remnants in
Rucamanque, near the city of Temuco, a forest considered
important for Chilean conservation goals (Mun
˜oz et al., 1996).
The main reason for examining these spatial patterns is to gain
insights into inter-tree competition, and to spatial relationships
related to stand structure. This information could be used to
inform management practice (e.g., to mimic natural spatial
patterns) and to alter models of stand dynamics.
2. Data
2.1. Study area
We studied a stand of 18.3 ha, in Rucamanque (38390S,
72350W), at 376 m of altitude, County of Temuco, Cautı
´n
province, IX Region, Chile. This stand is part of a 230 ha late
successional stage forest, dominated by shade-tolerant tree
species, with scattered 260–460-year-old N. obliqua trees
(Salas and Garcı
´a, 2006). This old-growth stand averages
590 trees/ha, 93.7 m
2
/ha of basal area, and 1096.7 m
3
/ha total
volume, with the most abundant tree species being Aextoxicon
punctatum.N. obliqua constitutes about 20% of the volume and
basal area, with approximately 30 trees/ha and diameter at
breast height (dbh) values over 70 cm (Fig. 1). Stands of this
type are remnants of the original sub-type of the N. obliqua–N.
alpina–N. dombeyi forest type according to Donoso (1995).
C. Salas et al. / Forest Ecology and Management 231 (2006) 38–46 39

Botanically, this type of forest is classified as the Lapagerio–
Aextoxiconetum punctatii association according to Oberdorfer
(1960). Further details about ecology of these species can be
found in Veblen et al. (1979, 1996),Veblen and Schlegel
(1982), and Donoso (1994, 1995).
This forest has had very limited human intervention
(Ramı
´rez et al., 1989a,b; Salas, 2001, 2002). The site falls
in Growth Region 1 of Donoso et al. (1993), which represents
the best growth rates over the natural range of N. obliqua. The
high productivity of the site is due to very rich soil features and
climatic conditions that promote tree growth for this species
(Frank, 1998; Salas, 2001).
2.2. Measurements
A 1 ha permanent square sample plot was established in this
stand in 2002. The plot was located in an average stand
condition based on information from four other 1000 m
2
permanent sample plots established in the same stand. The
coefficients of variation for these four plots were 31.8, 23.3, and
23.6% for the number of trees, basal area, and stand volume,
respectively. The established 1 ha permanent sample plot
represents a natural (i.e. with minimum human intervention)
density condition. On all live and dead standing trees with
dbh 5 cm, species, dbh, and crown class were measured.
When trees were multi-stemmed, each stem was considered a
separate tree, if the stem-division was 1.3 above ground. Total
height (h) was measured on 238 trees, selected with probability
proportional to basal area in each diameter class. For non-
sampled height trees, total height was imputed using species-
specific height–diameter equations. Gross volume was esti-
mated with group-species equations fitted by Salas (2002) for
Rucamanque. The location of each tree was recorded, via
conventional measurements of distance, slope, and azimuth.
The position of each tree on a Cartesian plane was later
determined using trigonometric relationships.
3. Methods
3.1. Statistical analysis
We used Ripley’s KðtÞfunction (Ripley, 1977, 1979, 1981)
to examine tree spatial arrangements. Since this method
considers the distances between all pairs of point (trees) in the
plane (Moeur, 1993; Haase, 1995), more detailed analyses of
interactions among points, both within a class of points (i.e.
same species, whole stand level) and also between separate
point populations (i.e. between species 1 and 2), were possible
(Moeur, 1993). The function counts the number of neighbour
trees within a circular plot of radius t, centered at each tree in
the study area. This process is repeated using increasingly
larger values (radii) of t.
For both univariate (i.e. within a class of points) and
bivariate (i.e. between two class of points) analyses, only
groups with more than 10 trees in the permanent sample plot
were used (e.g., single species as a group, or all live trees as a
group). All the analyses were conducted using the software
package Spatial Point Pattern Analysis (SPPA), Version 2.0.3,
created by Dr. Peter Haase.
3.1.1. Univariate analysis
We determined the spatial distribution for live trees by
species, specifically: A. punctatum,N. obliqua,P. lingue, and
Laureliopsis philippiana. For each species, the Ripley’s KðtÞ
function (Ripley, 1976, 1981) was calculated as
ˆ
KðtÞ¼ A
n2X
n
i¼1X
n
j¼1
1
wij
ItðuijÞ;(1)
where Ais the plot size (m2), nthe number of trees measured for
the plot, uij the distance (m) between the ith subject tree and the
jth tree, Ita counter, equal to 1 if uij t(the tree is within the
circular plot of radius t) or 0 otherwise, and wij is an edge
correction factor. The edge effect arises from the unobserva-
bility of points outside the 1 ha plot.
Ripley’s KðtÞvalues were computed both from the ith to the
jth tree and vice versa. KðtÞvalues can be interpreted as the
expected number of trees within distance tof an arbitrary tree
(Tomppo, 1986; Moeur, 1993). Edge effects were corrected
using the following expression proposed by Haase (1995):
wij ¼12 cos 1ðe1=uijÞþ2 cos 1ðe2=uijÞ
2p;(2)
where wij is the correction factor for ith border tree and its jth
neighbour tree, e1and e2the distances to the two closer borders
from the ith tree, and cos 1refers to the inverse cosine function.
We used 0.5 m as the interval for incrementing t, starting
with t¼0:5, and ending with a maximum value of t¼50 m,
following the recommendation of Haase (1995), to minimize
edge problems and approximation errors in the location
measurement of trees (Hanus et al., 1998). Also, beyond 50 m,
we expected interactions between trees to be minimal (i.e.
Moeur, 1993 used 12.2 m (40 ft)). To facilitate the interpreta-
tion of the resulting Ripley’s KðtÞfunction, Besag (1977)
C. Salas et al. / Forest Ecology and Management 231 (2006) 38–4640
Fig. 1. Diameter distribution for all live trees of each major species and for all
species combined (inset).

proposed an estimator ˆ
LðtÞresulting in a linear pattern of L
versus tunder a Poisson (random) spatial process. This was
slightly modified by Ripley (1979, 1981). We used the
following estimator (Ripley, 1979):
ˆ
LðtÞ¼ ffiffiffiffiffiffiffiffiffi
ˆ
KðtÞ
p
st:(3)
The estimator ˆ
LðtÞalso stabilizes the variance and gives an
expected value equal to 0 for a Poisson (random) spatial
distribution (Besag, 1977; Ripley, 1979). Therefore, ˆ
LðtÞindi-
cates the difference between the number of trees within in a
circular plot of radius tand the number of trees expected under
a Poisson (random) spatial process (Hanus et al., 1998).
Monte Carlo simulations were conducted to test the null
hypothesis of a Poisson process, suitable for unknown
distributions and for smaller sample sizes and commonly used
with spatial indices (Besag and Diggle, 1977). For each
simulation, each tree was randomly relocated over the
permanent sample plot, then the ˆ
LðtÞwas computed for each
t. Following Haase (1995), we conducted 19 simulations. Based
on the resulting empirical distribution of ˆ
KðtÞ, a 95%
confidence envelope over twas computed for ˆ
KðtÞunder a
random spatial process.
Based on the confidence envelope under a random process,
three different outcomes are possible. If the values of ˆ
LðtÞare
inside of the confidence envelope, the observed spatial
distribution is likely random. If ˆ
LðtÞis larger than the upper
values of the confidence envelope, the distribution is aggregated
or clustered. Finally, if ˆ
LðtÞfalls under the lower limit of the
confidence envelope, the distribution is likely uniform or
regular.
3.1.2. Bivariate analysis
The bivariate version of Ripley’s KðtÞfunction was used to
investigate potential spatial relationships among two groups of
trees, specifically:
(1) live trees <15 m tall (group 1, the shortest height class)
versus live trees 35 m and taller (group 2, the tallest height
class),
(2) all live trees versus standing dead trees, and
(3) live trees (group 1) versus standing dead trees.
A number of indices (or methods) can be used to indicate
vertical diversity (Staudhammer and LeMay, 2001),butfew
give both vertical and horizontal diversity (LeMay and
Staudhammer, in press). One way to indicate both vertical
and horizontal diversity is to divide trees into relevant height
strata, and use these to calculate a bivariate spatial index. The
20 m interval between the two vertical strata provided
separation into understory versus overstory trees. The bivariate
Ripley’s KðtÞfunction indicated spatial relationships between
these height strata. This bivariate spatial pattern is also
reflective of stand dynamics, since trees in the shorter height
class were younger (mostly less than 100 years), whereas trees
in the taller class were older (more than 250 years). Also, a
similar approach was used by Moeur’s (1993) study and,
therefore, comparisons were possible. The interactions
between live and dead trees were also of interest, in particular,
whether shorter live trees might be associated with standing
dead trees, indicating regeneration in proximity to standing
dead trees.
The bivariate version of Ripley’s KðtÞfunction was used to
detect the degree of repulsion, attraction, or indifference
between the two groups (Andersen, 1992; Haase, 2001;
Lotwick and Silverman, 1982). The estimators ˆ
K12ðtÞand
ˆ
K21ðtÞof the pooled distribution for each of the two groups of
interest were calculated (Lotwick and Silverman, 1982). First,
ˆ
K12ðtÞ, the interaction (or in this case spatial association)
between groups 1 and 2, was calculated as
ˆ
K
12ðtÞ¼ A
n1n2X
n1
i¼1X
n2
j¼1
1
wij
ItðuijÞ;(4)
where n1and n2are the numbers of trees in groups 1 and 2,
respectively, and uij is the distance (m) between the ith subject
tree of group 1 and the jth tree of group 2.
The interaction between groups 2 and 1 was then calculated
using
ˆ
K
21ðtÞ¼ A
n1n2X
n1
i¼1X
n2
j¼1
1
wji
ItðujiÞ;(5)
and, finally, the bivariate index was calculated using
ˆ
K12ðtÞ¼n2ˆ
K
12ðtÞþn1ˆ
K
21ðtÞ
n1þn2
:(6)
By a similar argument as before, we also calculated
ˆ
L12ðtÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffi
ˆ
K12ðtÞ
p
st:(7)
As for the univariate case, a 95% confidence envelope for a
random spatial process was found using Monte Carlo simula-
tions. For this bivariate case, when values of ˆ
L12ðtÞare inside
the confidence envelope, the two groups are considered inde-
pendent (no interaction). If ˆ
L12ðtÞis greater than the upper limit
of the confidence envelope, the two groups are positively
associated, meaning there is an attraction between the two
groups. Finally, if ˆ
L12ðtÞfalls under the lower limit of the
confidence envelope, the association between the two groups is
negative, indicating a repulsion between the two groups of
trees.
4. Results
4.1. Stand characterization
Stand variables are summarized in Table 1 (see also Fig. 1).
These statistics are similar to those reported for this type of
forest in Veblen et al. (1979), and to those given for a similar
forest in Veblen et al. (1980) where N. dombeyi plays the
ecological role of N. obliqua in Rucamanque. However, a much
larger plot size was used for our study.
C. Salas et al. / Forest Ecology and Management 231 (2006) 38–46 41

C. Salas et al. / Forest Ecology and Management 231 (2006) 38–4642
Table 1
Stand variables summary by species and over all species
Number of trees Basal area (m
2
/ha) Gross volume (m
3
/ha)
Live Standing dead Live Standing dead Live Standing dead
A. punctatum 437 30 68.5 3.41 706.3 30.2
N. obliqua 21 12 17.2 6.77 248.8 33.4
P. lingue 17 5 2.6 0.23 33.5 1.9
L. philippiana 108 2 1.1 0.01 8.6 0.1
Other 78 6 5.7 1.01 63.1 9.3
Total 661 55 95.1 11.4 1060.3 74.9
Fig. 2. (a) Locations map of all live trees in a 100 m 100 m permanent sample plot at Rucamanque Forest, Chile. (b) Ripley’s KðtÞresults. The sample statistic ˆ
LðtÞ
is shown as a solid line, whereas the pointwise 95% confidence envelope for a random spatial process is given as dotted lines.
Fig. 3. Ripley’s KðtÞresults for standing live trees for: (a) Aextoxicon punctatum, (b) Nothofagus obliqua, (c) Persea lingue, and (d) Laureliopsis philippiana. The
sample statistic ˆ
LðtÞis shown as a solid line, whereas the pointwise 95% confidence envelope for a random spatial process is given as dotted lines.

The main species, by decreasing basal area, are: A.
punctatum,N. obliqua,L. philippiana,L. sempervirens,P.
lingue,andEucryphia cordifolia (Tab l e 1). Species within
the class ‘‘others’’ are primarily E. cordifolia,Gevuina
avellana,andLomatia dentata. The stand is an old-growth
forest with a reversed J-shaped distribution of tree diameters
when pooled for all species (inset in Fig. 1). This is a typical
feature for uneven-aged and multi-species stands (Donoso,
1995), with a high concentration of smaller, younger trees,
showing that there is abundant regeneration of shade-tolerant
species, especially of the very shade-tolerant, A. punctatum
and L. philippiana (Fig. 1). N. obliqua occur as emergent
trees, as well do E. cordifolia.A. punctatum,L. sempervirens,
and P. lingue are dominant and codominant canopy tree
species, but A. punctatum is present in all height strata. L.
philippiana is mainly concentrated in the smaller diameter
classes and in sub-intermediate and intermediate crown
classes.
4.2. Univariate analysis
The map of tree spatial positions for all live trees did not
show any obvious clustering (Fig. 2 a). However, the plot of
ˆ
LðtÞover tfor the 1 ha plot indicates that ˆ
LðtÞis larger than
expected under a random spatial distribution, indicating
significant clustering (P<0:05) at all levels of t(Fig. 2b).
The maximum level of aggregation occurs at around 30 m.
The four species shown in Fig. 3 have very different spatial
patterns. A. punctatum showed a random distribution until 33 m
and a clustered distribution for this and larger distances
(Fig. 3a). N. obliqua showed a clear trend toward a regular
spatial distribution for over the 22 m of distance (Fig. 3b), but
this was not significantly different from a random distribution
(P>0:05). P. lingue showed a random distribution (Fig. 3c),
but there was some evidence of a trend toward a clustered
distribution with distances between 3 and 9 m, and other
distances, but this was not significant. L. philippiana clearly
showed a clustered spatial distribution (P<0:05), with highest
values at 26.5 m (Fig. 3d).
4.3. Bivariate analysis
There was a negative interaction (repulsion) between short
(<15 m tall) and tall trees (35 m and taller) (Fig. 4 a). Shorter,
younger trees were less frequent near tall live trees (t9 m),
likely because of shading, and competition for other resources.
There was evidence of a positive interaction (attraction)
between live and standing dead trees (Fig. 4b), indicating a
tendency for trees to regenerate close to dead standing trees.
This is supported by Fig. 4c, which shows that shorter, younger
trees are associated with dead standing trees at all but the
farthest spatial distances.
5. Discussion
5.1. Stand characterization
Stand features similar to that of this study were reported both
by Veblen et al. (1979, 1980) and by Alvarez (1982) for forest
remnants in other locations in Chile, and also by Salas (2001)
for the average condition of old-growth Rucamanque forests.
The current structure is a result of a long-term process of
successional dynamics. After disturbance, N. obliqua dom-
inates the structure and composition, as it is an early seral
(pioneer) and shade-intolerant species (Veblen et al., 1996).
After a long period of time, in the case of Rucamanque forest
approximately 450 years (Salas and Garcı
´a, 2006), the most
shade-tolerant (A. punctatum and L. philippiana)(Figueroa and
Lusk, 2001) and other semi-shade-tolerant species (P. lingue
and L. sempervirens) dominate the stand structure (Donoso,
1995). In this stand, A. punctatum was the dominant species
C. Salas et al. / Forest Ecology and Management 231 (2006) 38–46 43
Fig. 4. Ripley’s KðtÞresults for the interaction of: (a) live trees <15 m tall with
live trees 35 m and taller, (b) live trees with standing dead trees, and (c) live
trees <15 m tall with standing dead trees. The sample statistic ˆ
LðtÞis shown as
a solid line, whereas the pointwise 95% confidence envelope for a random
spatial process is given as dotted lines.

with 72% of the stand basal area (Table 1). The gross volume
was high, due to the large dimensions of the old-growth trees of
N. obliqua and the high density of A. punctatum, representing
90% of the stand volume. A. punctatum trees occur in all
diameter classes (Fig. 1), showing continuous regeneration
(Veblen et al., 1979, 1980). Conversely, N. obliqua was only
represented in the very large diameter classes ( >70 cm) and in
the emergent tree stratum. L. philippiana is the most shade-
tolerant species of this forest type, and, therefore was
represented by a large number of trees in the smaller diameter
classes, with few in the medium and larger size classes. P.
lingue appears to be still regenerating due to its semi-shade-
tolerance, but at a rate far lower than A. punctatum and L.
philippiana, features also reported by Veblen et al. (1979,
1980). Further details about strata composition were reported
by Veblen et al. (1979) for a similar forest and by Ramı
´rez et al.
(1989a,b) and Frank (1998) for Rucamanque.
5.2. Univariate analysis
Clustered spatial distributions are often typical in naturally
regenerated stands (van Laar and Akc¸a, 1997). For very old
forests at Wind River on the Pacific Coast of the USA, North
et al. (2004) found that trees were clustered at all distances. In
Nothofagus forests, shade and semi-shade-tolerant species
established in small gaps, resulting in small groups of juvenile
trees (Veblen et al., 1979). In this study, spatial distribution for
all trees seemed very similar to that of L. philippiana,
suggesting a great influence of this species on the spatial
distribution of trees in the stand.
A. punctatum occurred in larger spatial clusters of trees (in
some cases 40 trees), resulting in evidence of clustering at
larger spatial scales. Clustering also appeared to be present at
shorter distances, although this was not detected as being
different from a random spatial process. Veblen et al. (1979)
also detected a random spatial distribution using Morisita’s
index for A. punctatum with dbh <10 cm. However, they did
not detect clustering at larger scales, possibly due to a smaller
sample plot size, and problems in using Morisita’s index. In
general, the A. punctatum spatial distribution was more
clustered than for P. lingue, indicating that A. punctatum
regenerated in gaps, even though this species is able to
regenerate under a continuous canopy cover (Veblen et al.,
1979).
The spatial distribution of N. obliqua in this type of forest is
likely influenced by their longevity of more than 400 years
(Salas and Garcı
´a, 2006). This very old stand may have started
with 40,000 N. obliqua seedlings/ha (Veblen et al., 1996), but,
through self-thinning, it is now composed of just 20 very large-
crowned N. obliqua trees/ha. There was some evidence of a
regular distribution, but this was not detected as being different
from a random process, possibly due to the small number of
trees. Even though there are few trees, however, 18% of the
stand basal area was represented by this species. N. obliqua is
not able to regenerate under the current conditions of a
continuous canopy cover and little exposed bare mineral soil,
and is frequently replaced by very-shade-tolerant species such
as A. punctatum and L. philippiana (Veblen et al., 1980, 1996).
Unless large disturbance occurs, the early seral species will not
regenerate, and this forest could be considered to be in a steady
state. Veblen et al. (1980) postulated that the emergent crown
classes of N. alpina and N. dombeyi for the Valdivian low-land
forests were established as a consequence of drastic perturba-
tions, rather than from gaps produced by one or two trees
falling. However, Veblen et al. (1979, 1980, 1981) did not
report spatial distribution results for their old-growth Notho-
fagus. The sample plot size for these studies (2400 m
2
) may
have been too small to represent the high spatial heterogeneity
of these forests.
P. lingue showed a random spatial distribution. There was
some evidence of a trend toward clustering, even though not
significant, in ‘‘waves’’ of around 10 m (between 3 and 9, 9 and
19, and 19 and 29 m) up to a distance of 30 m. This
phenomenon creates small (of around 10 m of radii) even-sized
groups of P. lingue trees, growing under a continuous cover of
an uneven-aged stand. Above 38 m, where distances between
the tallest and smallest trees are captured, there was some
evidence of a trend toward regularity (not significant).
Clustered distributions are common for small trees (dbh’s
around 10 cm) located in gaps. The progressive change to a
random distribution in older stages was likely the result of
competition within these clumps, as noted by Veblen et al.
(1979) for P. lingue.
L. philippiana can regenerate well under a continuous
canopy cover, and can reproduce vegetatively, resulting in
clumps (average area of 2206 m
2
, based on a radii of 26 m) of
similar-sized trees. Most of the L. philippiana trees were small
in diameter. Similar results were reported by Peters (1985)
using distance methods. Clumps are also likely due to abundant
regeneration as a result of high seed production and the
establishment of trees in small gaps (Veblen et al., 1979, 1980,
1981).Veblen et al. (1980) found a random distribution for this
species at a large scale of analysis; however, they noted that
their results were confounded by using a small number of trees
in computing Morisita’s index. The high proportion of both L.
philippiana and A. punctatum in this forest is a clear example of
the dynamics of the lowland old-growth Nothofagus forests
(Donoso, 1995), when old-growth Nothofagus are replaced by
very shade-tolerant species.
5.3. Bivariate analysis
The repulsion between short and tall trees found in this study
was also reported by Moeur (1993) for natural uneven-aged
forests in Idaho (USA), as well as by Van Pelt and Franklin
(2000) for understory versus canopy trees in old-growth forests
along the Pacific Coast of the USA. Taller trees in the upper
canopy as a result of a long-term process (around of 450 years
in the Rucamanque’s case) with increasing competitive
capabilities tended to be more randomly distributed. Con-
versely, lower canopy trees tended to be clustered in gaps and
areas around gaps created by the fall of tall, and usually older,
large diameter trees. Similar to the results of this study, North
et al. (2004) found a repulsion between shade-tolerant and
C. Salas et al. / Forest Ecology and Management 231 (2006) 38–4644

shade-intolerant trees in old-growth forests of the Pacific Coast
of the USA. As noted by Lusk and Ortega (2003) for second-
growth Nothofagus stands in Chile, emergent trees often do not
affect the basal area or abundance of canopy trees, when the
overstory canopy is 15–20 m above the lower canopy.
In Chile, few studies on dead trees and their role within the
forest ecosystem have been conducted. However, Franklin et al.
(1987, 2002) and Spiering and Knight (2005) noted that there is
now more emphasis on studying the importance of these dead
trees to forest ecosystem function. In this study, there was
evidence of attraction between live and standing dead trees,
likely the result of regeneration following tree mortality. This
was more clearly shown by the strong spatial attraction between
short, younger trees and standing dead trees (significant for
t<42 m), which was also noted during data collection. This is
a property of a forest with minimal or no human intervention,
where horizontal diversification is occurring (e.g., when gap
development is the dominant process in the forest; Franklin
et al., 2002), in this case, over more than 400 years.
6. Concluding remarks
Univariate and bivariate Ripley’s KðtÞfunctions were used
to identify spatial patterns for trees of different species, and
across vertical height strata for an old-growth N. obliqua forest
in south-central Chile. These functions gave insights on stand
history, as noted in other studies of spatial patterns. Information
on spatial patterns could also be used to improve the
development and use of growth models. Tree-level distance-
dependent growth models are most suited to these complex
forests. In using these models to project growth, tree spatial
positions may not always be available, and instead, an expected
spatial pattern must be supplied. Based on this study, different
spatial patterns would need to be supplied for each species and
vertical stratum in these and other complex forests. Alter-
natively, this spatial information could be used to supplement a
tree-level distance-independent model to increase the precision
without the cost of tree spatial measures. The bivariate
functions were used to examine relationships across height
strata and between live versus dead trees in this study, but other
relationships could be examined, including inter-species
interactions as an aid to modelling successional processes.
Finally, although this study examined spatial patterns for a
single point in time, knowledge of spatial patterns over time
would give further insights into the competitive processes of
these species to better model forest dynamics, and also into
natural spatial patterns of largely undisturbed forests to inform
management decisions.
Acknowledgments
This research was supported by the Direccio
´n de Investiga-
cio
´n y Desarrollo, Universidad de La Frontera, Chile, DIUFRO
Project No. 110201. The first author thanks Dr. Albert Stage for
providing helpful suggestions and critical comments on the
manuscript, as well as Prof. Claudio Donoso (Emeritus
Professor at the Facultad de Ciencias Forestales at the
Universidad Austral de Chile) for his helpful comments about
distribution and succession of old-growth N. obliqua forests.
We thank Iva
´n Araos, Jorge Marinao, and Oscar Castillo for
assistance in data collection. Finally, we thank all those who
provided critical reviews of this manuscript, including three
anonymous reviewers. This publication was prepared while C.
Salas was a graduate student of the Department of Statistics at
the University of Idaho, Moscow, Idaho, USA.
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