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).

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

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 Intermediate Suppressed Shrubs Ground Cover

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.

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.

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

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 Illiterate / population Source: Fred Ramos (CEDEST/Brasil)

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 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

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

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

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

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

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 2 mm 1.5 1 0.5 1900 1910 1920 1930 1940 1950 T T+1 T+2 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 LISA, local G, local I

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

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

Understanding the results: Moran ƒ I ƒ Distance classes

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