Shertzer and Williams: Reef fishes off the the southern United States 
259 
that best represent all objects. Clusters are created 
by assigning each object in the data set to its nearest 
representative (i.e., medoid). 
As with any nonhierarchical method, the number 
of clusters k must be specified a priori. We applied a 
range of values and selected the k most concordant with 
the data, as quantified by highest average silhouette 
width. The silhouette width of each species measures 
its goodness of clustering. For any given k, silhouette 
widths averaged over species within clusters indicate 
relative strength of assemblages; across k, the highest 
average width computed from all species corresponds to 
the optimal number of clusters (Rousseeuw, 1987). To 
examine uncertainty in the optimal number, a bootstrap 
procedure was applied in which columns (vessel-months) 
of the original data matrices were resampled with re- 
placement to produce /i = 1000 bootstrapped matrices 
of the original dimension, and then n = 1000 average 
silhouette widths were recomputed for each k. 
The hierarchical cluster analysis was included to 
provide a comparison with clusters computed by £-me- 
doids and to quantify associations among species, as 
represented by dendrograms. The hierarchical analysis 
was based on the linkage method of McQuitty (McCune 
and Grace, 2002). 
Indices of abundance 
Indices of abundance were computed to examine 
synchrony of dynamics among stocks and thus, to 
investigate the basic assumption that an indicator spe- 
cies could be used to infer dynamics of other species 
in the assemblage. This investigation focused on the 
three strongest assemblages (i.e., strongest coherence 
among members), as measured by average silhouette 
widths from the cluster analysis. Because the strongest 
assemblages were examined, this investigation is a 
best-case scenario. If strongly associated populations 
do not exhibit synchronous dynamics, one should not 
assume that weakly associated populations do otherwise. 
Ideally, indices of abundance should be computed 
from fishery independent data; however, for many spe- 
cies here, such data were unavailable or insufficient. In 
this study, indices were computed from the headboat 
data set. Fishing effort from headboats is applied gener- 
ally toward many species, rather than toward specific 
targets. Because effort is nondirected, any confounding 
effects of density-dependent catchability are likely to 
be minimized, and in this regard, headboat data are 
similar to fishery-independent data. 
Indices of abundance were computed from catch and 
effort data in units of number of fish landed per angler- 
hour. Data were considered from 1978, the first year of 
full area coverage, to 2005. For each species, a trip was 
included only if a species from the relevant assemblage 
was landed. Thus, many trips were excluded, and some 
trips were included that had effort but zero catch. This 
approach represents effective effort more accurately 
than if all trips were included (a situation that would 
inflate the assumed effort) or if trips were restricted to 
those that landed the species in question (a situation 
that would deflate the assumed effort). 
To compute indices of abundance, catch and effort da- 
ta were standardized using a generalized linear model 
(Hardin and Hilbe, 2001). The explanatory variables for 
the model were year, month, and geographic area. To 
ensure adequate sample sizes by geographic area, sam- 
pling areas were aggregated into four regions: North 
Carolina, South Carolina, Georgia-northern Florida, 
and southern Florida (south of Cape Canaveral). The 
response variable was catch per effort, assumed to be 
distributed with delta-lognormal error structure (Lo et 
ah, 1992; Stefansson, 1996; Maunder and Punt, 2004). 
In this structure, the proportion of positive values is 
modeled with binomial error, and positive values them- 
selves are modeled with lognormal error. Indices were 
not computed for species that were caught in fewer 
than 20% of trips on the relevant assemblage, to avoid 
estimation error associated with inflation of zero values 
(Lampert, 1992). Because this criterion excludes rarely 
caught species, evidence of synchrony in our results 
should be viewed as a necessary but not sufficient con- 
dition for the use of indicator species. 
Synchrony in dynamics between any two stocks was 
measured by the Spearman’s rank correlation coeffi- 
cient, computed both from 1) the indices of abundance 
and 2) the first-differenced time series of log-abun- 
dances {z t )\ 
z t = \ogU t -logU t _ 1 = \og^ J -> (3) 
U t - 1 
where U t = the index value of a stock at time t. Positive 
correlation of the indices themselves would indicate 
similar trends in abundance over time. The use of first 
differences, as in Equation 3, rather than raw or relative 
abundance, puts emphasis on annual population growth 
rates and may reduce spurious correlation (Bjprnstad 
et al., 1999). Positive correlation of growth rates would 
indicate that stocks not only have similar patterns of 
productivity (growth, recruitment, and mortality), but 
that they also respond similarly to interannual variation 
in fishing effort or catchability. 
Significance levels of correlation coefficients were 
obtained nonparametrically with n = 10,000 randomiza- 
tions of z t (Prager and Hoenig, 1989; Edgington, 1995; 
Bjprnstad et al., 1999). A coefficient that ranks suffi- 
ciently high in relation to the randomizations could be 
considered significantly positive, and a coefficient that 
ranks low, significantly negative. Significance was de- 
termined with a two-tailed test at the a=0.1 level with 
Bonferroni correction. 
Results 
Species assemblages 
Multidimensional scaling did not reveal strongly isolated 
groups of species in ordination space (Fig. 1). It did, 
however, reveal consistency of ordination in the sense 
