3.1 The Observed-to-Expected (O/E) Index
The standard metric derived from RIVPACS-type predictive modeling
approaches is the observed-to-expected ratio (O/E), a single-metric index that
compares the observed taxonomic richness at a study site to the expected richness
under minimally impaired conditions. The O/E ratio indicates the degree of
“taxonomic completeness” (sensu Hawkins [91]) of the test site. O/E values
less than one indicate that taxa expected to be present if the sites were unimpaired
are absent.
Following biotic classification of reference sites, RIVPACS employs Multiple
Discriminant Analysis (MDA) to develop linear functions that best describe the
relationships of natural environmental variables to the biotic classes. The discriminant functions are used to determine the distance, in environmental variable space,
of the test site to the biotic reference classes, which in turn are used to estimate the
probabilities that the test site belongs in each reference class (referred to here as
class probabilities). For all native taxa in the study region, the proportion of
reference sites within a given biotic class where a taxon is present represents the
probability of observing that taxon at a site in that class (referred to as the
probabilities of capture). The probabilities of capture of a given taxon within
each reference class, and the class probabilities of the test site for each reference
site, are used to estimate the probability of capturing the taxon at the test
site assuming unimpaired conditions. The expected richness at the test site
(the E in O/E) is given by summing probabilities of capture at the test site for all
taxa (see Fig. 3 and Table 3 for additional details).
O/E values greater or less than one indicate departures from what is predicted
under unimpaired conditions. Simpson and Norris [92] recommended that O/E
values below the tenth percentile of the reference site distribution indicate impairment, with the extent of impairment increasing as the ratio decreases. They also
postulated that O/E values greater than one may indicate areas of exceptionally high
natural biodiversity or those subject to mild impairment that artificially increases
richness.
A common modification to the basic framework is to exclude rare taxa from the
analysis, as their inclusion can result in a site receiving an O/E score near one when
the assemblage observed deviates considerably from statistical expectations.
Several authors have indicated that excluding taxa with probabilities of capture
less than 0.5 (producing the O/E 0.5 index) improves accuracy and precision [72, 93,
94]. As an alternative, Van Sickle [93] adapted the Bray–Curtis dissimilarity
measure to compare observed and expected assemblages (referred to as BC) and
showed that BC was generally more accurate than O/E for identifying impairment
across a wide range of assemblages and study systems. O/E 0.5 and BC indices
developed for Appalachian stream macroinvertebrate assemblages exhibited similar accuracy and precision [75].
246
A.L. Garey and L.A. Smock
The standard metric derived from RIVPACS-type predictive modeling
approaches is the observed-to-expected ratio (O/E), a single-metric index that
compares the observed taxonomic richness at a study site to the expected richness
under minimally impaired conditions. The O/E ratio indicates the degree of
“taxonomic completeness” (sensu Hawkins [91]) of the test site. O/E values
less than one indicate that taxa expected to be present if the sites were unimpaired
are absent.
Following biotic classification of reference sites, RIVPACS employs Multiple
Discriminant Analysis (MDA) to develop linear functions that best describe the
relationships of natural environmental variables to the biotic classes. The discriminant functions are used to determine the distance, in environmental variable space,
of the test site to the biotic reference classes, which in turn are used to estimate the
probabilities that the test site belongs in each reference class (referred to here as
class probabilities). For all native taxa in the study region, the proportion of
reference sites within a given biotic class where a taxon is present represents the
probability of observing that taxon at a site in that class (referred to as the
probabilities of capture). The probabilities of capture of a given taxon within
each reference class, and the class probabilities of the test site for each reference
site, are used to estimate the probability of capturing the taxon at the test
site assuming unimpaired conditions. The expected richness at the test site
(the E in O/E) is given by summing probabilities of capture at the test site for all
taxa (see Fig. 3 and Table 3 for additional details).
O/E values greater or less than one indicate departures from what is predicted
under unimpaired conditions. Simpson and Norris [92] recommended that O/E
values below the tenth percentile of the reference site distribution indicate impairment, with the extent of impairment increasing as the ratio decreases. They also
postulated that O/E values greater than one may indicate areas of exceptionally high
natural biodiversity or those subject to mild impairment that artificially increases
richness.
A common modification to the basic framework is to exclude rare taxa from the
analysis, as their inclusion can result in a site receiving an O/E score near one when
the assemblage observed deviates considerably from statistical expectations.
Several authors have indicated that excluding taxa with probabilities of capture
less than 0.5 (producing the O/E 0.5 index) improves accuracy and precision [72, 93,
94]. As an alternative, Van Sickle [93] adapted the Bray–Curtis dissimilarity
measure to compare observed and expected assemblages (referred to as BC) and
showed that BC was generally more accurate than O/E for identifying impairment
across a wide range of assemblages and study systems. O/E 0.5 and BC indices
developed for Appalachian stream macroinvertebrate assemblages exhibited similar accuracy and precision [75].
246
A.L. Garey and L.A. Smock