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Structure and Dynamics of forest stands
Intro to Spatial Analyses
Forest structure
Forest stand structure is the
vertical and horizontal
organization of plants
(Kimmins1996; Franklin et
al.1981)
"the physical and temporal
distribution of trees in a stand”
(Oliver and Larson)
The forest structure
With the word structure we mean how the various
components of a forest community are distributed in space
and time and how they are functionally organized (there are
several synonyms: pattern, texture, …).
There are some different meanings: spatial, temporal, species
composition.
Forest structure
Stand:
group of trees showing a relatively homogeneous
structure and composition and that grow under the same climatic
and soil environment.
Stand structure:
the vertical, horizontal and temporal
organization of plants within a forest.
Forest stand dynamics:
the study of the structural
changes in time within a forest stand.
Stand development: the part of the stand dynamics dealing
with the changes of forest stand structures in time.
Cohort:
a group of trees developing after a single disturbance,
commonly consisting of trees of similar age. The group could be
either small or large.
BIODIVERSITY
With the term biodiversity we meant mainly to describe the
variability at genetic, species and ecosystem level.
Recently this concept has been extended to consider even the
variability of structures and processes. (Franklin 1988, Franklin et
al. 1989).
Noss (1990) and Franklin (1993) suggest that there are
biodiversity features related to composition, structure and function
operating at various hierarchical levels and linked to most of the
biological processes we can find in the forest.
BIODIVERSITY
Strutural diversity
Stand structure is an important element of stand biodiversity
(MacArthur and MacArthur 1961, Willson 1974).
There is often a positive correlation between elements of
biodiversity and measure of the variety and/or complexity of
structural components within an ecosystem.
Ecosystems containing stands with a variety of structural
components are considered likely to have a variety of resources
and species that utilize these resources (Pretzsch 1997, Brokaw
and Lent 1999).
FOREST STRUCTURE
Species
diversity
Variations in tree
dimensions
Distance-independent
measure to characterize forest
structure at
stand-level
Spatial
distribution
Distance-dependent
measure to describe
forest structure
Species composition, density, dimension, age
Spatial structure
It refers to the vertical
(vertical
structure
or
stratification) or horizontal
(horizontal structure or
texture) organization of a
forest stand
Vertical structure
In each forest we can see several layers at different height. These layers can
be few or many and have a sharp or fuzzy transition between them.
Vertical structure
Dominant
Co-Dominant
Co-Dominant
Intermediate
Intermediate
Suppressed
Shrubs
Ground Cover
Vertical Structure
Mixed forest (more than one species): generally with a multilayered structure with the lower layers taken by shade-tolerant
species.
Pure forest (only one species): multi-layered stands only with
shade-tolerant species, regeneration can survive. Shadeintolerant species often show mono-layered stand, trees that
are shade intolerant can not survive in the understories.
Chronological structure
a) establishment
70
Norway spruce
50
stone pine
Trees
40
30
20
10
1570
1600
1630
1660
1690
1720
1750
1780
1810
1840
1870
1900
1930
1960
1990
0
Decades
b) releases
70
60
50
40
30
20
10
Decades
1570
1600
1630
1660
1690
1720
1750
1780
1810
1840
1870
1900
1930
1960
0
1990
Forest communities are not
static but change in time
according to the pulses of
internal
and
external
drivers.
60
% Abrupt growth releases
The processes of birth,
growing, development and
death of a tree give raise of
the population dynamics
and therefore of the
communities.
Stand structure
size vs time
Spruce
Stone pine
Larch
80
N° di piante
N
60
40
20
0
5
N° di piante
N
15
25
35
45
55
65
Diameter
(cm)
Classi di class
d130 (cm)
80
60
40
20
0
15
45
75
105
135
165
Classi
di età(year)
(anni)
Age class
195
225
255
Horizontal structure
It is more complex than the vertical one.
Vegetation can be distributed in many different ways according to:

composition,

macro- and micro-climate conditions,

trees, shrubs and grasses distribution,

macro- and micro- morphology,

vegetative or seed propagation,

seed features and dispersal (wind, animals).
Tobler’s First Law of Geography
• Everything is related to everything else but
near things are more related than distant
things
Generally true with discrete data; definitely true with
continuous data
We call this “spatial dependence”
Can we see Tobler’s law in action?
Waldo Tobler (1930 -
)
Lung cancer for white male in USA
Spatial inequalities in São Paulo
Per capita income
Jobs/ populations
Source: Fred Ramos (CEDEST/Brasil)
Illiterate / population
Gwynns Fall Crime Data
Temperature in the athmosphere
Spatial analyses
Every event leaves behind a footmark within the forest stand.
The spatial structure represents an archive useful to reconstruct
the processes involved in building the structure itself.
“The first step in understanding ecological
processes is to identify patterns”
Fortin et al.2002
Spatial analyses
1 - Point pattern analyses or spatial distribution analyses
With sampling units
Without sampling units
2 - Surface pattern analyses or spatial structure analyses
With sampling units
Without sampling units
Spatial analyses
1 - Point pattern analyses or spatial distribution analyses
Defines the spatial distribution of points
Random– Uniform - Clustered
2 - Surface pattern analyses or spatial structure analyses
Defines the spatial structure of points
a) Mainly with quantitative variables
b) Quantify the spatial dependence with the distance
uniform
ofAthe
variables
B random
c) Draw
a structural
function
C aggregate
(randomly
distributed)
D aggregate (evenly distributed)
E aggregate (patchy distributed)
Spatial structure analyses
Spatial analyses
Sampling area is essential for results
Point patter or distance analyses
Nearest Neighbor
K-Order Nearest Neighbor
Linear Nearest Neighbor
Ripley’s K
Need to identify second-order characteristics of the
distances between points
First order
properties identify the global, or dominant pattern of
distribution – where is it centered, how far it spreads,
any orientation
Second order (local) identify sub regional, or neighborhood
patterns within the overall distribution.
Ripley’s K
• Similar to NNI by providing information about
the average distance between points
• But, it allies to all orders cumulatively, not just
a single order, and applies to all distances of
the study area
Ripley’s K
• If a spatially random distribution of N points
exists, the expected number of points inside
radius ds is given as
N
Pts  K (d s )
A
where N is the sample size, A is the total area, and K(ds ) is
the area of a circle defined by radius d s
Ripley’s K
K (d s ) 
A
N
2
 I (d )
ij
i
j
where I (dij ) represents the number of point j within distance
d s , summed over all points, i.
• A circle is iteratively drawn, and the points are
counted.
• The circle is increased a small distance
Ripley’s K
clustering
L(d)
random
segregation
distance
Ripley’s K
Univariate Ripley’s K
K (d s ) 
Bivariate Ripley’s K
A
K 12(d ) 
n1n 2
A
wk
2 
i
j ij ij
n
3
attraction
clustered
1
no interaction
random
L(d)
-1
repulsion
segregated
-3
0 2 4 6 8 10 12 14 16 18 20
distance (m)
n1
n2
 w
i 1 j 1
ij
k ij
Spatial analyses
1 - Point pattern analyses or spatial distribution analyses
With sampling units
Without sampling units
2 - Surface pattern analyses or spatial structure analyses
With sampling units
Without sampling units
The Autocorrelation
Autocorrelation: basic trait of all variables for which
it is possible to measure the distribution in time (serial
autocorrelation) or space (spatial autocorrelation).
3
2.5
mm
2
1.5
1
0.5
0
1900
1910
T
1920
T+1
1930
T+2
1940
1950
Distance class
Spatial autocorrelation
• Correlation of a field with itself
Low
High
Maximum
Quantifying the spatial autocorrelation
Global
Local
Moran’s I, Geary’s c
n  wij  xi  x x j  x 
n
I (d ) 
LISA, local G, local I
n
i 1 j 1
ij
j
i
1
(n  1)
z(d ) 
i j
j
2
i 1
E( I )  
j
j
n
W  ( xi  x )
 c (d ) X
G*
X
 c (d ) X

X
ij
Gi
I (d )  E[ I (d )]
var[ I (d )]
j
j
j
j
i j
Global versus Local Indicators
Global
Local
• one statistic to summarize pattern
• location-specific statistics
• clusters
• heterogeneity
• Clustering
• Homogeneity
LISA satisfies two requirements:
1.
indicate significant spatial clustering for each location
2.
sum of LISA proportional to a global indicator of spatial association
Identify Hot Spots
• significant local clusters in the absence of global autocorrelation
• some complications in the presence of global autocorrelation (extra heterogeneity)
• significant local outliers
• high surrounded by low and vice versa
Indicate Local Instability
• local deviations from global pattern of spatial autocorrelation
Understanding the results: Moran

I

1
I
0.5

0
-0.5
-1
0.5
0
-0.5
-1
1
2
3
4
5
6
7
Distance classes

1
8
9
10
1
2
3
4
5
6
7
8
Distance classes
9
10
Understanding the results: Moran

I

1
0.5
0
-0.5
-1
1
2
3
4
5
6
7
Distance classes
8
9
10
Understanding the results: G* di Getis
Birth’s defects in China