Diversity metrics

Background.--Diversity measures have been used extensively in a variety of ecological applications. They originally gained popularity as measures of plant and animal species diversity. There has been a proliferation of diversity indices and we will make no attempt to review them here. FRAGSTATS computes 3 diversity indices. These diversity measures are influenced by 2 components--richness and evenness. Richness refers to the number of patch types present; evenness refers to the distribution of area among different types. Richness and evenness are generally referred to as the compositional and structural components of diversity, respectively. Some indices (e.g., Shannon's diversity index) are more sensitive to richness than evenness. Thus, rare patch types have a disproportionately large influence on the magnitude of the index. Other indices (e.g., Simpson's diversity index) are relatively less sensitive to richness and thus place more weight on the common patch types. These diversity indices have been applied by landscape ecologists to measure one aspect of landscape structure--landscape composition (e.g., Romme 1982, O'Neill et al. 1988, Turner 1990a).

FRAGSTATS Metrics.--FRAGSTATS computes several statistics that quantify diversity at the landscape level. These metrics quantify landscape composition at the landscape level; they are not affected by the spatial configuration of patches. The most popular diversity index is Shannon's diversity index (SHDI) based on information theory (Shannon and Weaver 1949). The value of this index represents the amount of "information" per individual (or patch, in this case). Information is a somewhat abstract mathematical concept that we will not attempt to define. The absolute magnitude of Shannon's diversity index is not particularly meaningful; therefore, it is used as a relative index for comparing different landscapes or the same landscape at different times. Simpson's diversity index (SIDI) is another popular diversity measure that is not based on information theory (Simpson 1949). Simpson's index is less sensitive to the presence of rare types and has an interpretation that is much more intuitive than Shannon's index. Specifically, the value of Simpson's index represents the probability that any two cells selected at random would be different patch types. Thus, the higher the value the greater the likelihood that any 2 randomly drawn cells would be different patch types. Because Simpson's index is a probability, it can be interpreted in both absolute and relative terms. FRAGSTATS also computes a Modified Simpson's diversity index (MSIDI) based on Pielou's (1975) modification of Simpson's diversity index; this index was used by Romme (1982). The modification eliminates the intuitive interpretation of Simpson's index as a probability, but transforms the index into one that belongs to a general class of diversity indices to which Shannon's diversity index belongs (Pielou 1975). Thus, the modified Simpson's and Shannon's diversity indices are similar in many respects and have the same applicability.

Patch richness (PR) measures the number of patch types present; it is not affected by the relative abundance of each patch type or the spatial arrangement of patches. Therefore, two landscapes may have very different structure yet have the same richness. For example, one landscape may be comprised of 96% patch type A and 1% each of patch types B-E, whereas another landscape may be comprised of 20% each of patch types A-E. Although patch richness would be the same, the functioning of these landscapes and the structure of the animal and plant communities would likely be greatly different. Because richness does not account for the relative abundance of each patch type, rare patch types and common patch types contribute equally to richness. Nevertheless, patch richness is a key element of landscape structure because the variety of landscape elements present in a landscape can have an important influence on a variety of ecological processes. Because many organisms are associated with a single patch type, patch richness often correlates well with species richness.

Richness is partially a function of scale. Larger areas are generally richer because there is generally greater heterogeneity over larger areas than over comparable smaller areas. This contributes to the species-area relationship predicted by island biogeographic theory (MacArthur and Wilson 1967). Therefore, comparing richness among landscapes that vary in size can be problematic. Patch richness density (PRD) standardizes richness to a per area basis that facilitates comparison among landscapes, although it does not correct for this interaction with scale. FRAGSTATS also computes a relative richness index. Relative patch richness (RPR) is similar to patch richness, but it represents richness as a percentage of the maximum potential richness as specified by the user (Romme 1982). This form may have more interpretive value than absolute richness or richness density in some applications. Note that relative patch richness and patch richness are completely redundant and would not be used simultaneously in any subsequent statistical analysis.

Evenness measures the other aspect of landscape diversity--the distribution of area among patch types. There are numerous ways to quantify evenness and most diversity indices have a corresponding evenness index derived from them. In addition, evenness can be expressed as its compliment--dominance (i.e., evenness = 1 - dominance). Indeed, dominance has often been the chosen form in landscape ecological investigations (e.g., O'Neill et al. 1988, Turner et al. 1989, Turner 1990a), although we prefer evenness because larger values imply greater landscape diversity. FRAGSTATS computes three evenness indices (Shannon's evenness index, SHEI; Simpson's evenness index, SIEI; modified Simpson's evenness index, MSIEI), corresponding to the three diversity indices. Each evenness index isolates the evenness component of diversity by controlling for the contribution of richness to the diversity index. Evenness is expressed as the observed level of diversity divided by the maximum possible diversity for a given patch richness. Maximum diversity for any level of richness is achieved when there is an equal distribution of area among patch types. Therefore, the observed diversity divided by the maximum diversity (i.e., equal distribution) for a given number of patch types represents the proportional reduction in the diversity index attributed to lack of perfect evenness. As the evenness index approaches 1, the observed diversity approaches perfect evenness. Because evenness is represented as a proportion of maximum evenness, Shannon's evenness index does not suffer from the limitation of Shannon's diversity index with respect to interpretability.

Limitations.--The use of diversity measures in community ecology has been heavily criticized because diversity conveys no information on the actual species composition of a community. Species diversity is a community summary measure that does not take into account the uniqueness or potential ecological, social, or economical importance of individual species. A community may have high species diversity yet be comprised largely of common or undesirable species. Conversely, a community may have low species diversity yet be comprised of especially unique, rare, or highly desired species. Although these criticisms have not been discussed explicitly with regards to the landscape ecological application of diversity measures, these criticisms are equally valid when diversity measures are applied to patch types instead of species. In addition, diversity indices like Shannon's index and Simpson's index combine richness and evenness components into a single measure, even though it is usually more informative to evaluate richness and evenness independently.