188
Elements of Spatial Data Analysis in Ecological Assessments
into two main sections: (1) general considerations
and issues in spatial analysis and (2) an overview
of approaches in spatial analysis. It is not the intent of this chapter to describe at length all possible techniques and how they relate to each other;
this information is available in other publications,
which are cited in the relevant sections. The scope
of this chapter is to describe approaches appropriate for some of the questions of interest in the spatial analysis of EA data.
The basic methodologies for spatial data analysis presented in this chapter apply to both environmental and social sciences for three main reasons.
First, EAs consider linked environmental and social systems. Second, data are generally observational rather than experimental in EAs and therefore present similar issues in their analysis and
interpretation, regardless of whether they are environmental or social. Third, environmental and social analyses are often directed at similar spatial
scales and data structures, so methods applicable to
the spatial analysis of one type of data should also
be applicable to other types.
13.2 General Considerations and
Issues in the Spatial Analysis
of EA Data
The analysis of spatial patterns has become increasingly prevalent in the investigation of environmental and social data (Haining, 1990), because
most phenomena of interest are structured by forces
that have spatial components (Bell et aI., 1993; Legendre and Legendre, 1998). For example, ecologists examine the spatial patterns of single species
or assemblages of species to understand the mechanisms that control their distributions; soil scientists study the movement of water, a driver of soil
genesis and landscape evolution, to understand the
causal agents of pedogenic variability and many
practical aspects of soil behavior; social scientists
study the settlement patterns of human populations
and the impact of societal values to understand the
extent to which human populations shape and are
shaped by their environment. In this section, we
discuss general considerations and issues that may
arise in analyzing spatial data. Specific information
regarding the sampling and storage of such data is
provided in Chapters 5 to 8 and 11. A full presentation of the subject matter treated in this section
is found in Haining (1990).
13.2.1 Importance and Nature of Spatial
Structure in EA Data
Spatial structure in EA data sets has three main
sources: measurement error, continuity effects
(e.g., spatial heterogeneity), and space-dependent
processes. Determining which of these sources is
present in any given data set has implications for
the analysis of EA data, indicating the types of spatial patterns that should be expected and the types
of models that best represent such patterns (Haining, 1990).
Measurement errors have several origins. First,
instrument precision can alter our ability to accurately quantify spatial structure at a given scale.
Second, such errors can be generated by observerdependent bias. For example, if a large region is
divided into subregions for surveying purposes,
each with a different survey team, even the smallest team-dependent bias can generate discontinuities at subregion boundaries (Milne, 1959; Haining, 1990). Third, remotely sensed data (see
Chapter 10) can also suffer from spatial dependency effects induced by instruments. Although
rapid progress is being made in hardware improvement and in modeling satellite data (see
Chapter 10; also, Quattrochi and Goodchild, 1997),
it is still important to carefully consider this type
of error in EA data sets (Craig, 1979; Labovitz and
Masuoka, 1984). Finally, measurement errors can
propagate themselves from one scale to another
(Heuvelink, 1998).
Three important related concepts to consider in
the spatial analysis of EA data are continuity effects,
homogeneity, and heterogeneity. Spatial continuity
of patterns is due to the spatial continuity in the
events (i.e., processes) that generates the patterns and
are responsible for their spatial distribution, including boundaries between patterns, pattern shape, and
the scale at which patterns are generated (see Chapter 2; also, King, 1997). Spatial variation in the distribution of a pattern or process is described using
the two opposing concepts of homogeneity (i.e., the
absence of variation), and heterogeneity (i.e., composed of different parts; see Kolasa and Rollo, 1991;
Dutilleul and Legendre, 1993; Legendre and Legendre, 1998). The analysis of sharp boundaries
(Fortin et al., 1996) between contrasting patterns
(i.e., spatial heterogeneity) is a central aspect of EA
spatial analysis.
Four important types of processes may generate
spatial structure in an environmental or social attribute (Haining, 1990): (1) diffusion, a general
term describing a process in which some attribute
Elements of Spatial Data Analysis in Ecological Assessments
into two main sections: (1) general considerations
and issues in spatial analysis and (2) an overview
of approaches in spatial analysis. It is not the intent of this chapter to describe at length all possible techniques and how they relate to each other;
this information is available in other publications,
which are cited in the relevant sections. The scope
of this chapter is to describe approaches appropriate for some of the questions of interest in the spatial analysis of EA data.
The basic methodologies for spatial data analysis presented in this chapter apply to both environmental and social sciences for three main reasons.
First, EAs consider linked environmental and social systems. Second, data are generally observational rather than experimental in EAs and therefore present similar issues in their analysis and
interpretation, regardless of whether they are environmental or social. Third, environmental and social analyses are often directed at similar spatial
scales and data structures, so methods applicable to
the spatial analysis of one type of data should also
be applicable to other types.
13.2 General Considerations and
Issues in the Spatial Analysis
of EA Data
The analysis of spatial patterns has become increasingly prevalent in the investigation of environmental and social data (Haining, 1990), because
most phenomena of interest are structured by forces
that have spatial components (Bell et aI., 1993; Legendre and Legendre, 1998). For example, ecologists examine the spatial patterns of single species
or assemblages of species to understand the mechanisms that control their distributions; soil scientists study the movement of water, a driver of soil
genesis and landscape evolution, to understand the
causal agents of pedogenic variability and many
practical aspects of soil behavior; social scientists
study the settlement patterns of human populations
and the impact of societal values to understand the
extent to which human populations shape and are
shaped by their environment. In this section, we
discuss general considerations and issues that may
arise in analyzing spatial data. Specific information
regarding the sampling and storage of such data is
provided in Chapters 5 to 8 and 11. A full presentation of the subject matter treated in this section
is found in Haining (1990).
13.2.1 Importance and Nature of Spatial
Structure in EA Data
Spatial structure in EA data sets has three main
sources: measurement error, continuity effects
(e.g., spatial heterogeneity), and space-dependent
processes. Determining which of these sources is
present in any given data set has implications for
the analysis of EA data, indicating the types of spatial patterns that should be expected and the types
of models that best represent such patterns (Haining, 1990).
Measurement errors have several origins. First,
instrument precision can alter our ability to accurately quantify spatial structure at a given scale.
Second, such errors can be generated by observerdependent bias. For example, if a large region is
divided into subregions for surveying purposes,
each with a different survey team, even the smallest team-dependent bias can generate discontinuities at subregion boundaries (Milne, 1959; Haining, 1990). Third, remotely sensed data (see
Chapter 10) can also suffer from spatial dependency effects induced by instruments. Although
rapid progress is being made in hardware improvement and in modeling satellite data (see
Chapter 10; also, Quattrochi and Goodchild, 1997),
it is still important to carefully consider this type
of error in EA data sets (Craig, 1979; Labovitz and
Masuoka, 1984). Finally, measurement errors can
propagate themselves from one scale to another
(Heuvelink, 1998).
Three important related concepts to consider in
the spatial analysis of EA data are continuity effects,
homogeneity, and heterogeneity. Spatial continuity
of patterns is due to the spatial continuity in the
events (i.e., processes) that generates the patterns and
are responsible for their spatial distribution, including boundaries between patterns, pattern shape, and
the scale at which patterns are generated (see Chapter 2; also, King, 1997). Spatial variation in the distribution of a pattern or process is described using
the two opposing concepts of homogeneity (i.e., the
absence of variation), and heterogeneity (i.e., composed of different parts; see Kolasa and Rollo, 1991;
Dutilleul and Legendre, 1993; Legendre and Legendre, 1998). The analysis of sharp boundaries
(Fortin et al., 1996) between contrasting patterns
(i.e., spatial heterogeneity) is a central aspect of EA
spatial analysis.
Four important types of processes may generate
spatial structure in an environmental or social attribute (Haining, 1990): (1) diffusion, a general
term describing a process in which some attribute