1. Structure and Dynamics of forest stands Intro to Spatial Analyses

2. 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)

3. 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.

4. Forest structure

5. 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.

6. 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.

7. 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).

8. Variations in tree dimensions
FOREST STRUCTURE
Species diversity
Variations in tree dimensions
Spatial distribution
Distance-independent measure to characterize forest structure at stand-level
Distance-dependent measure to describe
forest structure

9. Species composition, density, dimension, age

10. Spatial structure
It refers to the vertical (vertical structure or stratification) or horizontal (horizontal structure or texture) organization of a forest stand

11. 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.

12. Vertical structure Dominant Co-Dominant Intermediate Suppressed Shrubs
Ground Cover

13. Vertical Structure
Mixed forest (more than one species): generally with a multi-layered 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. Shade-intolerant species often show mono-layered stand, trees that are shade intolerant can not survive in the understories.

14. Chronological structure
The processes of birth, growing, development and death of a tree give raise of the population dynamics and therefore of the communities.
Forest communities are not static but change in time according to the pulses of internal and external drivers.

15. Stand structure size vs time Spruce Stone pine Larch N
Diameter class (cm) N
Age class (year)

16. 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).

17. 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 ( )

18. Lung cancer for white male in USA

19. Spatial inequalities in São Paulo
Per capita income
Jobs/ populations
Illiterate / population
Source: Fred Ramos (CEDEST/Brasil)

20. Gwynns Fall Crime Data

21. Temperature in the athmosphere

22. 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

23. 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

24. Spatial analyses
1 - Point pattern analyses or spatial distribution analyses
A uniform
B random
C aggregate (randomly distributed)
D aggregate (evenly distributed)
E aggregate (patchy distributed)
Defines the spatial distribution of points
Random– Uniform - Clustered
2 - Surface pattern analyses or spatial structure analyses
Defines the spatial structure of points
Mainly with quantitative variables
Quantify the spatial dependence with the distance of the variables
c) Draw a structural function

25. Spatial structure analyses

26. Spatial analyses
Sampling area is essential for results

27. 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.

28. 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

29. Ripley’s K
If a spatially random distribution of N points exists, the expected number of points inside radius ds is given as

30. Ripley’s K A circle is iteratively drawn, and the points are counted.
The circle is increased a small distance

31. Ripley’s K
distance
L(d)
clustering
segregation
random

32. Ripley’s K Univariate Ripley’s K Bivariate Ripley’s K clustered-3 -1 1 3 2 4 6 8 10 12 14 16 18 20
L(d)
distance (m)
clustered
random
segregated
attraction
no interaction
repulsion

33. 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

34. 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 2 mm
1.5 1
0.5
1900
1910
1920
1930
1940
1950 T
T+1
T+2
Distance class

35. Spatial autocorrelation
Correlation of a field with itself
Low
High
Maximum

36. Quantifying the spatial autocorrelation
Global
Local
Moran’s I, Geary’s c
LISA, local G, local I

37. Global versus Local Indicators
one statistic to summarize pattern
Clustering
Homogeneity
Local
location-specific statistics
clusters
heterogeneity
LISA satisfies two requirements:
indicate significant spatial clustering for each location
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

38.  ‚  ‚ Understanding the results: Moran I I Distance classes

39. Understanding the results: Moranƒ I ƒ
Distance classes

40. Understanding the results: G* di Getis
Birth’s defects in China