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Fishery Bulletin 96(3), 1 998 
Maximum use of the visual survey data required 
statistical intercalibration of the sampling efficiency 
of each diver. We used multiple regression analysis 
(Neter et al., 1996) to estimate relative sampling ef- 
ficiency by adapting the “fishing power” model of 
Robson (1966) 
C(d,t) = F(d,t)N(t)i;(d,t) = q(d)f(d,t)N(t)i;(d,t) 
C(d,t) 
■» . = q(d)N (d,t), 
f(d,t) 
( 1 ) 
where C(d,t) = the fish count of diver d at reef date t; 
Nit) = the average population size at reef 
date t; 
q(d) = the coefficient of sampling efficiency 
for diver d; 
f(d,t) = the nominal survey effort of diver d 
at reef date t, and 
%(d,t) = a log normally distributed error 
variable. 
To account for any sampling bias that may have been 
introduced by differences among divers, a simple log- 
linear transformation of Equation 1 makes it pos- 
sible to obtain minimum variance estimates of rela- 
tive sampling efficiency, given fish counts by species, 
by diver, and by reef date. Data used for model de- 
velopment were derived from a series of controlled 
experiments conducted during a 9-day sampling ex- 
pedition to the Dry Tortugas during June 1994. A 
matrix of estimated efficiency coefficients for divers 
by species was used to adjust an individual diver’s 
results in relation to a standard-normal diver, here 
the most experienced diver in the group. After stan- 
dardization, all the individual visual “catch-per-unit- 
of-effort” measurements were comparable over time 
and space (Ault et al. 2 ). Spatial and temporal pat- 
terns in abundance and correlative linkages to habi- 
tat types were qualitatively analyzed with 3-D visu- 
alization software (IDL, 1995) by reef site through- 
out the Florida Keys for various survey years. Mul- 
tivariate statistical analysis (Johnson and Wichern, 
1992; Venables and Ripley, 1994) was used to assess 
variance-covariance and correlation structures be- 
tween reef fish density and selected environmental 
and fish community auxiliary covariates. 
We also used the 1981-95 NMFS headboat catch- 
and-effort data (Bohnsack et al., 1994; Dixon and 
Huntsman, 1992) to provide fishery-dependent popu- 
lation estimates comparable to those from the visual 
2 Ault, J. S., J. A. Bohnsack, and G. Meester. 1998. The rela- 
tive fishing power of divers in tropical reef fish visual 
surveys. Unpubl. manuscript. 
survey. Headboat data provide total numbers of in- 
dividuals in the catch as well as total weight in the 
catch by species by year. 
Stock assessment indicator variable 
A stock assessment indicator variable is a quantita- 
tive measure that reflects the status of a population 
subjected to fishing or other environmental changes. 
Because reef fishes integrate aspects of the coastal 
ocean environment over their lifetime, a robust mea- 
sure of population “health” or status can provide a 
sensitive indicator of direct and indirect stress on 
the stock, and perhaps on the regional marine eco- 
system (Fausch et al., 1990). Population health for 
reef fish communities can best be described with the 
metabolic-based pool variable “average length in the 
exploitable phase of the stock.” Therefore, to assess 
the health of each of the s stocks in the reef fish com- 
munity over the past two decades, the statistic “av- 
erage length in the exploitable phase of the stock,” 
L ( t ), was found for each stock by integrating between 
the population age limits from t ' ( minimum age at first 
capture) to t x (oldest age in the stock), written as 
t k 
F(t)J N(a,t)L{a,t)da 
F(t)J N(a,t)da 
t ' 
where N(a,t) = abundance for age class a at time t; 
L(a,t) = length for class a at time t; and 
Fit) = the instantaneous fishing mortality 
rate at time t. 
Estimates of the mean, variance, and 95% confidence 
interval of the mean were computed by the methods 
of Sokal and Rohlf ( 1969). 
To estimate the annual total instantaneous mor- 
tality rate Zit) for each fish stock in each year t from 
population size structure and abundance statistics, 
we used a length-based method (Ault and Ehrhardt, 
1991; Ehrhardt and Ault, 1992) particularly appli- 
cable to reef fish population dynamics 
Z(t)(L' - L(t)) + K(L„ - Lit)) 
Z{t)(L x - Lit)) + K(L„ - Lit)) ’ <3) 
where, L x 
_V 
Lit) 
maximum size; 
the length at first capture; 
the average size in the exploitable 
phase in year t; and 
