Models of Landscape Structure - University of Massachusetts Amherst

83 Pages·2014·7.31 MB·English

Models of Landscape Structure
Instructor: K. McGarigal
Assigned Reading: McGarigal (Lecture notes)
Objective: Provide a basic description of several alternative models of landscape structure,
including models based on point, categorical and continuous patterns. Highlight the importance
of selecting a meaningful model for the question under consideration given the constraints of
data availability and software tools available for analyzing pattern-process relationships.
Topics covered:
1. Models of landscape structure
2. Point pattern model
3. Patch mosaic model - island biogeographic and landscape mosaic models
4. Landscape gradient model
5. Graph matrix model
1. Models of Landscape Structure
There are many different ways to model or represent landscape structure corresponding to
different perspectives on landscape heterogeneity. Here we will review five common alternative
models: (1) point pattern model; (2) island biogeographic model based on categorical map
patterns; (3) landscape mosaic model based on categorical map patterns; (4) landscape gradient
model based on continuous surface patterns; and (5) graph-theoretic model.
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The choice of model in any particular application depends on several criteria:
• The ecological pattern-process under consideration and the objective of the analysis
• The spatial character of the landscape with respect to the relevant attributes
• Available spatial data (type, structure and quality)
• Available analytical methods (software tools)
• Available computational resources
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2. Point Pattern Model
2.1. Data Characteristics
Point pattern data comprise collections of the locations of entities of interest, wherein the data
consists of a list of entities referenced by their (x,y) locations. Familiar examples include:
• Map of all trees in a forest stand, perhaps by species
• Map of all occurrences of a focal ecosystem (e.g., seasonal wetland) in a study area
• Map of all detections of an individual of a species during a season or over a lifetime
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2.2. Data Structure
Point pattern data typically are represented using a vector data structure, wherein each point is
referenced by its (x,y) location and occupies no real space. Alternatively, it may be convenient in
some applications (see below) to represent point patterns using a raster data structure, wherein
each point is represented as a cell (or pixel) in a raster grid and thus occupies the space of one
cell. Lastly, it may be useful in some applications to address point patterns using a graph matrix
data structure, which is described later as a special model of landscape structure.
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2.3. Pattern Elements
Point pattern data consist of a single pattern element - points. The points are often
indistinguishable from each other (i.e., unweighted), wherein only the (x,y) location of the points
is of interest. Alternatively, the points may be distinguished from each other on the basis of one
or more attributes (e.g., weights), so that not all points are equal, and this information is then
taken into account in the analysis.
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2.4. Pattern Metrics
The goal of point pattern analysis is typically to quantify the intensity of points at multiple scales
and there are numerous methods for doing so. Here we will review only a few of the more
popular approaches.
(1) 1st-order point patterns
The primary data for point pattern analysis consist of n points tallied by location within an area of
size A (e.g., hundreds of individual trees in a 1-ha stand). The simplest of pattern metrics merely
quantify the number and density of points. However, a plethora of techniques have been
developed for analyzing more complex aspects of spatial point patterns, some based on sample
quadrats or plots and others based on nearest-neighbor distances. A typical distance-based
approach is to use the mean point-to-point distance to derive a mean area per point, and then to
invert this to get a mean point density (points per unit area), Lambda, from which test statistics
about expected point density are derived. There are nearly uncountable variations on this theme,
ranging from quite simple to less so (e.g., Clark and Evans 1954). Most of these techniques
provide a single global measure of point pattern aimed at distinguishing clumped and uniform
distributions from random distributions, but do not help to distinguish the characteristic scale or
scales of the point pattern.
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(2) 2nd -order point patterns – Ripley’s K-distribution
The most popular means of analyzing (i.e., scaling) point patterns is the use of second-order
statistics (statistics based on the co-occurrences of pairs of points). The most common technique
is Ripley's K-distribution or K-function (Ripley 1976, 1977), which we discussed previously as a
scaling technique for point pattern data. Recall that the K-distribution is the cumulative
frequency distribution of observations at a given point-to-point distance (or within a distance
class); that is, it is based on the number of points tallied within a given distance or distance class.
Because it preserves distances at multiple scales, Ripley's K can quantify the intensity of pattern
at multiple scales.
In the real-world example shown here for the distribution of vernal pools in a small region in
Massachusetts, the K function reveals that pools are more clumped than expected under a
spatially random distribution out to a distance of at least 3.5 km, and are perhaps most clumped
at a scale of about 400 m. The scale of clumping of pools is interesting given the dependence of
many vernal pool amphibians on metapopulation processes such as dispersal of individuals
among ponds. For most of these vernal pool-dependent species the pools are highly clumped at
scales corresponding to the range of dispersal distances.
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(3) Local pattern intensity – Kernel estimators
The previous methods provide a numerical summary of the global point pattern; that is, they
provide a quantitative description of the average pattern of points across the entire landscape.
Often times, however, it is more useful to assess the local point pattern and produce a pattern
intensity map. The kernel estimator (Silverman 1986; Worton 1989) is a density estimator, which
we discussed previously as a scaling technique for point pattern data. Recall that a kernel
estimator involves placing a “kernel” of any specified shape and width over each point and
summing the values to create a cumulative kernel surface that represents a distance-weighted
point density estimate. Because we can specify any bandwidth, the kernel estimator can be used
to depict the intensity of point pattern at multiple scales.
In the example shown here, a bivariate normal kernel was placed over each vernal pool in a small
study area from western Massachusetts, and the cumulative kernel surfaces are illustrated here in
three dimensions. The kernel surface on the left results from a bivariate normal kernel with a
bandwidth (standard deviation) of 200m. The one on the right has a bandwidth of 400m. Clearly,
the smaller the bandwidth, the rougher the surface. The peaks represent regions of high vernal
pool density, the troughs represent regions of low vernal pool density.
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