Landscape Metrics for Categorical Map Patterns
Instructor: K. McGarigal
Assigned Reading: Turner et al. 2001 (Chapter 5); McGarigal (Lecture notes)
Objective: Provide an overview of common landscape metrics and insights into their use and interpretation. Highlight importance of selecting the “right” metric for the “right” problem.
Topics covered:
1. Introduction and overview: distribution statistics
2. Area & edge metrics
3. Shape metrics
4. Core area metrics
5. Contrast metrics
6. Aggregation metrics
7. Diversity metrics
8. General considerations
1. Taxonomy of metrics
Landscape metrics exist at the patch, class (patch type) and landscape level. At the class and landscape level, some of the metrics quantify landscape composition, while others quantify landscape configuration. Landscape composition and configuration can affect ecological processes independently and interactively. Thus, it is especially important to understand for each metric what aspect of landscape pattern is being quantified. In addition, many of the metrics are partially or completely redundant; that is, they quantify a similar or identical aspect of landscape pattern. In most cases, redundant metrics will be very highly or even perfectly correlated. For example, at the landscape level, patch density (PD) and mean patch size (MPS) will be perfectly correlated because they represent the same information. These redundant metrics are alternative ways of representing the same information; they are available as metrics because the preferred form of representing a particular aspect of landscape pattern will differ among applications and users. It behooves the user to understand these redundancies, because in most applications only 1 of each set of redundant metrics should be employed. It is important to note that in a particular application, some metrics may be empirically redundant as well; not because they measure the same aspect of landscape pattern, but because for the particular landscapes under investigation, different aspects of landscape pattern are statistically correlated. The distinction between this form of redundancy and the former is important, because little can be learned by interpreting metrics that are inherently redundant, but much can be learned about landscapes by interpreting metrics that are empirically redundant.
Many of the patch metrics have counterparts at the class and landscape levels. For example, many of the class metrics (e.g., mean shape index) represent the same basic information as the corresponding patch metrics (e.g., patch shape index), but instead of considering a single patch, they consider all patches of a particular type simultaneously. Likewise, many of the landscape metrics are derived from patch or class characteristics. Consequently, many of the class and landscape metrics are computed from patch and class statistics by summing or averaging over all patches or classes. Even though many of the class and landscape metrics represent the same fundamental information, naturally the algorithms differ slightly. Class metrics represent the spatial distribution and pattern within a landscape of a single patch type; whereas, landscape metrics represent the spatial pattern of the entire landscape mosaic, considering all patch types simultaneously. Thus, even though many of the metrics have counterparts at the class and landscape levels, their interpretations may be somewhat different. Most of the class metrics can be interpreted as fragmentation indices because they measure the configuration of a particular patch type; whereas, most of the landscape metrics can be interpreted more broadly as landscape heterogeneity indices because they measure the overall landscape pattern. Hence, it is important to interpret each metric in a manner appropriate to its scale (patch, class, or landscape).
Landscape metrics are typically grouped loosely according to the aspect of landscape pattern measured – but note that these groupings are done for mostly for convenience as these are not independent aspects of landscape pattern and most metrics can fall into more than one group – as follows:
• Area & edge metrics
• Shape metrics
• Core area metrics
• Contrast metrics
• Aggregation metrics
• Subdivision metrics
• Isolation metrics
• Diversity metrics
Within each of these groups, metrics are further grouped into patch, class, and landscape metrics.
2. Distribution Statistics
Patch metrics can be summarized at the class and landscape levels using a variety of distribution statistics that provide first- and second-order statistical summaries of the patch metrics for the focal class or the entire landscape, such as: (1) mean, (2) area-weighted mean, (3) median, (4) range, (5) standard deviation, and (6) coefficient of variation. The difference between the mean and the area-weighted mean in this context is especially important as discussed below.
Metrics applied to categorical patch mosaics (under the “landscape mosaic model” of landscape structure) fundamentally represent the structure of the landscape as defined by its patch structure. Clearly, patches are the basic building blocks of categorical patch mosaics and, as such, most metrics derive from the spatial character and distribution of the patches themselves. However, most patch-based metrics can be summarized at the class and landscape levels to reflect the character and distribution of individual patches over a broad extent. Indeed, in most applications, the objective involves characterizing the patch structure for a single focal class or for the entire patch mosaic across the full extent of the landscape, rather than focusing on individual patches. Despite the common objective of characterizing the class or landscape structure, metrics differ in whether they offer a “patch-based” or “landscape-based” perspective of landscape structure. This is perhaps best illustrated by the difference between class and/or landscape distribution metrics based on the simple arithmetic mean or the area-weighted mean.
Mean versus area-weighted mean
Metrics based on the mean patch characteristic, such as mean patch size (AREA_MN) or mean patch shape index (SHAPE_MN), provide a measure of central tendency in the corresponding patch characteristic across the entire landscape, but nevertheless describe the patch structure of the landscape as that of the average patch characteristic. Thus, each patch regardless of its size is considered equally (i.e., given equal weight) in describing the landscape structure. Consequently, metrics based on the mean patch characteristic offer a fundamentally patch-based perspective of the landscape structure. They do not describe the conditions, for example, that an animal dropped at random on the landscape would experience, because that depends on the probability of landing in a particular patch, which is dependent on patch size.
Conversely, metrics based on the area-weighted mean patch characteristic, such as the areaweighted mean patch size (AREA_AM) and area-weighted mean patch shape index (SHAPE_AM), while still derived from patch characteristics, provide a landscape-based perspective of landscape structure because they reflect the average conditions of a pixel chosen at random or the conditions that an animal dropped at random on the landscape would experience. This is in fact the basis for the subdivision metrics of Jaeger (2000) described later.
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