Spatial structure of the regeneration of Scots pine under two silvicultural
systems.
F. Montes, M. Pardos and I. Cañellas
1
CIFOR-INIA. Ctra. de la Coruña km 7.5 28040 Madrid Spain
e-mail: fmontes@inia.es
_____________________________________________________________________
Abstract
This paper is focused in the assessment of the effects of Silviculture on the
structure of two even-aged Scots pine stands across a rotation period .
For this purpose, 2 plots of 0.5 ha in different aged stands were established
in two Scots pine forests with different management systems in the Central
Mountain Range of Spain. To asses the spatial pattern the L(d) function
were employed. To analyse the spatial relationship between the mother
trees and the recruitment, a function derived from K(d) function was used.
In Valsaín forest, the shelterwood fellings are carried out gradually over a
irregular spaced stand, leading to a mixture of several cohorts and a cluster
spatial pattern at 15-20 m for the stem distribution during the shelter phase.
The regeneration showed repulsion from the old crop at very short
distances and at distances greater to 15 m. In Navafría forest, the regular
distribution of the trees and the short period used to regenerate the stand
led to a positive spatial association between the mother trees and the
seedlings at large scale.
_____________________________________________________________________
Introduction
The regeneration process is a key factor that determines the structure of the forest, and
its knowledge is of great importance for sustainable forest management. Several
approaches focussed on different scales and different stand features have been used
to assess forest structure. The spatial pattern can be analysed using the Ripley’s K(d)
function if mapped data are available at stand level (Moeur, 1993; Kuuluvainen, 1996;
Aldrich, 2003), as well as the geostatistical tools at broader scales or when data are
taken in sample points (Denslow, 2000). However, there are not suitable tools to
analyse the spatial relationship between the stem pattern and the spatial distribution of
seedlings or saplings, because of the different scale of both processes that require
different sampling strategies (Goreaud & Pélissier, 2003).
This paper is focused in the assessment of the effect of Silviculture and the stand
structure on the regeneration process in two Scots pine forests that stand for the most
commonly used management methods for the species in the Central Mountain range of
Spain (Montes et al. 2005). For that purpose, a new function termed Krx(d), that allows
to analyse the spatial relationship between a point process and a sampled variable,
was derived from the intertype Krs(d) function for points belonging to two classes, to
analyse the relationship between stems and seedlings or saplings during the
regeneration process.
Material and methods
Study site
Two 5000 m2 plots were installed, one at the beginning of the regeneration period, in a
81-100 years old stand, in Navafría, and the other in a 0-20 years old stand, in Valsaín
accompanied by a residual crop of mother trees. In each plot, all the stems (trees with
diameter at breast height (DBH) larger than 10 cm) were positioned through their xy
coordinates, the saplings (higher than 1.30 m height and DBH less than 10 cm) were
counted in 2x2 m2 quadrats throughout the plot and the seedlings were positioned in
four 25 m2 subplots (divided in a hundred 0.25 m2 plots).
L(d) function
The spatial pattern of seedlings and stems was analysed using the Ripley’s K(d)
function (Ripley, 1977). K(d) was calculated from the equation:
λK (d ) = ∑ in=1 ∑ nj =1
δ ij (d )
n
⎡1 if d ij ≤ d
⎣0 if d ij > d
δ ij (d ) ⎢
, i ≠ j,
(1)
where λ is the density of stems per unit area, dij the distance from tree i to tree j, and n
the number of trees in a circular area of radius d. The K value is compared to 95%
quantiles of a Poisson distribution obtained through 99 simulations of the Poisson
process (Ripley, 1977). To deal with the boundary effect of the plot, δij(d) was replaced
by ωij(d), which is 0 if stems i and j are more distant than d, and in other case gives the
fraction contained within the plot of a circumference centred in i that falls over j.
The transformation Lˆ (d ) , which linearizes the K function and stabilizes its variance,
was used:
Lˆ (d ) =
Kˆ (d )
π
−d
(2)
Spatial relationship between sapling density and stems spatial distribution: Krx(d)
function
In order to analyse the spatial relationship between a spatial point pattern (as is the
stem distribution in the experimental plots) and a continuous spatial variable (as is the
sapling or seedling density in quadrats) a modification of the K(d) function that allows to
characterize the negative or positive spatial association between the point distribution
and the variable values was developed (Eq. 3).
K rx
⎛ N n
⎡ (x − x )⎤ n N
⎡ (x j − x )⎤ ⎞
⎜ ∑∑ ω ij ( d ) ⋅ ⎢ j
+ ∑∑ ω ji ( d ) ⋅ ⎢
⎥
⎥ ⎟⎟
⎜ i =1 j =1
s
s
x
x
⎣
⎦ j =1 j =1
⎣
⎦⎠
=⎝
N
n
n N
∑∑ ω rs (d ) + ∑∑ ω sr (d )
r =1 s =1
∑ (x
n
s x2 =
j =1
(3)
s =1 r =1
− x)
2
j
n
(4)
where N is the number of stems, n is the number of samples were the variable was
measured, xj is the value of the variable in the sample j and ωij is calculated as
described for the K(d) function.
To set the boundaries of the 95% confidence interval of a independent distribution of
the stems and the sapling density or the seedling density, a Montecarlo test was
carried out, simulating 99 random distribution of stems and assigning each time
randomly the measured values of the variable to the samples.
Results
Spatial pattern of stems
In Navafría the mother trees, during the regeneration fellings, show a regular spatial
pattern at shorter scales, till 8 m approximately. In Valsaín, the mother trees show a
cluster pattern at scales between 8 and 20 m when the regeneration fellings start. At
the end of the regeneration period, the cluster pattern of the young stems at shorter
scales overlaps the cluster pattern at larger scales of the mother trees (Figure 1).
Valsaín
1.50
1.00
1.00
0.50
0.50
L(d)
L(d)
Navafría
1.50
0.00
-0.50
0.00
-0.50
-1.00
-1.00
0
10
20
0
Distance (m)
10
20
Distance (m)
Figure 1. Analysis through the L(d) function of the spatial pattern of the stems in the
experimental plots of Navafría and Valsaín.
Spatial relationship between seedlings and stems
Figure 3 shows the Krx(d) function in the plots of Navafría and Valsaín, for the spatial
arrangement of the mother trees and the seedling density in 4 randomly distributed
plots of 25 m2 divided in 100 quadrats of 0.25 m2. In Navafría, seedlings show positive
spatial relationship with mother trees at scales between 10 and 20 m. In Valsaín plot,
the young strata form dense patches, giving a negative spatial relationship between
stem density and seedling density at short distances and beyond 15 m.
Valsaín
0.30
0.20
0.10
Krx(d)
Krx(d)
Navafría
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
0.00
-0.10
-0.20
-0.30
0
10
Distance (m)
20
0
10
20
Distance (m)
Figure 2. Analysis through the Krx(d) function of the spatial relationship between the
stems and the seedling density in the experimental plot of Navafría, where
regeneration fellings have just started, and in the experimental plot in Valsaín, at the
end of the regeneration period.
Spatial relationship between saplings and stems in the experimental plot of Valsaín
Figure 3 shows the Krx(d) function, for the spatial arrangement of the sapling density in
the 2×2 m2 quadrats in Valsaín’s plot. It can be seen the negative spatial association
between saplings and the dense patches of young stems in all the analysed range.
1-20 years
0.10
Krx(d)
0.05
0.00
-0.05
-0.10
0
10
20
Distance (m)
Figure 3. Analysis through the Krx(d) function of the spatial relationship between the
stems and the sapling density in experimental plot of Valsaín.
Discussion
In this paper the Lrx(d) function is proposed to find the spatial relationship between the
pattern of the stems and the structure of continuous variables such as sapling density.
This function may have many applications in forest ecology research, because the
trees form a point pattern associated with continuous variables, such as soil properties
or slope, or to determine the spatial structure of other vegetation strata or fungus
populations which are measured using density samples. The Lrx(d) function is
independent of the sampling location where the spatial continuous variable is
measured because it is divided by the sum of the terms ωij(d). The value of the Lrx(d)
function depends only on the value of the variable and the local density of trees,
eliminating the effect of the interaction between the location of the samples and the
point pattern. The value of the function depends on the spatial association between
high values for the variable and the local density of the point pattern. The variable
standardization through the expression
(x
j
−x
sx
) in eq. 3 gives values close to 0 under
the assumption of spatial independence between the variable and the point pattern.
Silviculture play an important role in the establishment process. In Navafría, the old
stand is felled completely in a 20 years period, keeping a homogeneous distribution of
the mother trees throughout the regeneration area. The low density of the stand at the
beginning of the regeneration period favours the establishment of a dense herb layer,
that hinders the success of natural regeneration, and often soil labour is required. The
competence of herb layer, as far as the lack of mother trees’ protection from hard
climatic conditions, lead to the positive spatial relationship between mother trees and
seedlings in Navafría. Similarly, after a geostatistical analysis of the spatial structure of
regeneration and the radiation conditions determined by the upper strata, Denslow et
al. (2000) concluded that the regeneration pattern is independent from the highest
radiation conditions. For the germination and development of the seedlings to occur,
the radiation level would need to be above a certain threshold, but other factors such
as the substrate (Pardos et al., 2004) or grazing (Aldrich et al., 2003) determine the
spatial pattern of the regeneration. As the negative spatial association that the Krs(d)
function shows between stems and saplings at large scales indicates, low density is
required for seedling performance. Once the seedlings are established, it is necessary
to eliminate both the shade and the competition from mother trees to permit stand
development. In Valsaín, the regeneration period often extends during 40 years, and
the fellings lead to a mosaic of dense gaps and clear gaps. The resulting structure is
formed by several cohorts originating by different regeneration events at the first life
stages of the stand. Natural regeneration is favoured by the microclimatic conditions
gradient that the heterogeneous structure provides.
Acknowledgments
The authors wish to thank to Javier Donés and Juan Carlos Martín their help and
knowledge of the studied forest, and to Angel Bachiller and Enrique Garriga for their
collaboration in the field work. This study has been supported by the projects AGL
2000-1545 and AGL 2004-07094-CO2.01/FOR
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