Tagliafico et al: Exploitation and reproduction of Aetobatus narinari in the Los Frailes Archipelago, Venezuela 
309 
for weight. Statistical differences between these func- 
tions were established with an E-test from the analysis 
of the residual sum of squares, in a manner similar to 
the one proposed by Chen et al. (1992). 
Differences in the proportions by sex for juveniles, 
adults, and embryos were estimated monthly by using 
a chi-square test ( % 2 ) with Yates’s correction (Zar, 1996). 
To determine the reproductive period for A. narinari, 
the proportions of immature and mature males and the 
proportions of females in different reproductive stages 
were examined monthly. Also, we estimated the mean 
and range of embryo lengths. Fecundity was deter- 
mined by the number of embryos per uterus, and the 
size at birth was determined from the largest observed 
embryos. 
The length at which 50% of individuals were mature 
was estimated for males and females by a logistic function: 
where M f = the fraction of mature individuals; 
a = the change in slope of M { as a function of 
length intervals (Lj); and 
b = the length at 50% maturity (L 50 ). 
Parameter estimates for a and b were obtained by 
maximizing the log-likelihood function and assuming a 
binomial error distribution (Welch and Foucher, 1988). 
Confidence intervals were estimated by joint likelihood 
profiles (Venzon and Moolgavkar, 1988). Parameter es- 
timates and confidence intervals were calculated with 
the statistical software R, vers. 2.13.0 (R Development 
Core Team, 20 1 1 1 ). 
Results 
Effort, catch, and catch per unit of effort 
In the 29-month sampling period, 413 fishing trips 
directed at A. narinari were analyzed. Sampling yielded 
55.9 metric tons and 1352 individuals. A subsample of 
1167 individuals, 846 females and 321 males, was mea- 
sured for biological data. 
The largest numbers of fishing trips per month, 
with more than 30 trips per month, were observed 
during the months of February, April, and May 2006 
and February 2007 (Fig. 1A). For 2006 and 2007, the 
number of trips in the first 6 months of each year 
corresponded to 73% and 69% of the total number of 
trips made in each year, respectively. Highest catches 
in 2006 and 2007 occurred in months with most fish- 
ing effort (Fig. IB). Catches in the first 6 months 
represented 81% and 62% of total annual catch for 
the years 2006 and 2007, respectively. Approximately 
1 Mention of trade names or commercial companies is for 
identification purposes only and does not imply endorsement 
by the National Marine Fisheries Service, NOAA. 
23% of the total number of trips during the study 
period resulted in no catch. In all years of this study, 
November was the month with the highest proportion 
(>50%) of trips with no catch. 
Data on catch per unit of effort (CPUE) in number of 
fish caught per trip did not show a clear trend during the 
study period. Minimum values were observed in Novem- 
ber 2006 and 2007 (Fig. 2A), and maximum values were 
observed in October 2005; January, April, September, 
and December 2006; and July and October 2007. The 
overall mean CPUE for the study period was 3 individu- 
als per trip. The distribution of numbers of fish caught 
per trip shows that -85% of trips yielded 0-6 individu- 
als, with 7-21 individuals caught during the remaining 
