9598

• UCREFRP Catalog Number: 9598
• Author: Lubinski, K., J. Wiener and N. Bhowmik.
• Title: Regulated Rivers Research and Management.
• USFW Year: 1995.
• USFW - Doc Type: \
• Copyright Material: NO

FISH MONITORING 267
minimum depending on the metric) observed conditions among TVA mainstem reservoirs from 1989 to
1991. The best observed conditions were determined on a metric by metric basis. Separate criteria were
set for each longitudinal zone (inflow, transition and forebay) because of ecological differences among
them (Voigtlander and Poppe, 1989; Dionne and Karr, 1992). Scoring criteria were set for three categories
hypothesized to represent relative degrees of degradation: least degraded, 5; intermediate, 3; and most
degraded, 1. Least degraded conditions represent high values for some metrics and low values for others
(Figure 1), so RFAI scores decrease monotonically with increasing degradation. Assignment of scores
was based on the procedures of Fausch et al. (1984) and Kerans and Karr (1994).
Variation in reservoir rankings, 1989-1992
Concordance of reservoir rankings for RFAI and for individual metric scores were compared among the
four years with Kendall's W. This analysis indicates whether rankings of reservoirs are similar across years.
In the absence of data to indicate new impacts or changes in impacts, we expected relatively similar rankings
over the short period covered by the study.
Bootstrap estimation of variance of RFAI scores
Because the RFAI is calculated from a single random sample of 10 runs, its precision cannot be calculated
directly. The bootstrap algorithm can be used to estimate the variability resulting from slight differences in
collection methods (or measurement error) at a site. The bootstrap method is most commonly used to deter-
mine the confidence interval of a test statistic for which the actual distribution is unknown (Efron, 1981).
The bootstrap algorithm creates new samples by resampling from an original random sample. Random
sampling with replacement continues until the bootstrap sample contains the same number of elements as
the original sample. Bootstrap samples are created and the RFAI is calculated for each new sample until
enough values (1000) for the RFAI are accumulated to approximate its distribution. The probability distri-
bution function for repeated measurement of the ith sampling unit provides an estimate of the measurement
error and can be expressed as (Cochran, 1977)
RFAIiJ = µi + eii
where RFAIij = the RFAI at the ith site on the jth repetition; pi = true value of the RFAI at the ith site; and
eil = the error of measurement at the ith site on the jth repetition.
For the ith site, the measurement error, eii, is estimated from the j repetitions generated by the bootstrap
algorithm. From this empirical distribution of the RFAI at a site, the variance for RFAI is calculated as
(Efron, 1981)
var(RFAI) _ Ei= I (RFAIj - RFAI)2
(n - 1)
where RFAIJ = the value of the RFAI calculated for the jth bootstrap sample; j = 1, ... n; and n = the
number of bootstrap samples.
Limitations of the bootstrap
Three of the 12 metrics (ABUN, FHAI and PDIS) are excluded from bootstrap analysis. ABUN and
FHAI remain constant for each bootstrap sample because no data are available to estimate the variance
of these metrics. Because the variance of these three metrics cannot estimated from the current data, the
total variance of RFAI at a site is underestimated. This technique specifically estimates variance at a sample
site and does not include sampling variability due to differences in sampling locations within the reservoir.
1992 supplementary data set
In response to questions about the effects of temporal variability during the sample season (September to
December) on index scores, supplemental data were collected monthly during the 1992 sampling season from