Rocha-Olivares; Age, growth, and mortality of Lutjanus peru 
565 
Month 
Figure 3 
Percentage of translucent margins of the whole otoliths of Lutjanus peru. Sample sizes 
are shown next to symbols. 
Observed length-at-age 
data were obtained from 
whole-otolith readings for 
most fishes (n=1170) and 
from sectioned-otolith read- 
ings for the largest speci- 
mens (rc=10). To correct for 
within-year growth, ages 
were assigned as follows. 
Since translucent margin 
deposition on the otolith 
peaks in July (Rocha Oli- 
vares and Gomez Munoz, 
1993; Fig. 3), only fishes 
caught during this month 
were assigned integer ages. 
For the rest, subsequent 
growth was accounted for 
by assigning fractional ages 
in proportion to the elapsed 
time (e.g. a fish with two 
annuli caught in January 
was assigned 2.5 years). 
Length-weight relation- 
ships were fitted to the data 
and used to calculate the 
von Bertalanffy asymptotic 
weight (W m ). Growth perfor- 
mance <|) = log 10 ( K) + 2/3 logjoOFJ was computed 
from the growth parameters (Manooch, 1987). 
All coefficients of determination reported for non- 
linear models were computed by using the following 
expression (Draper and Smith, 1981): 
were used to obtain approximate estimates (Pauly, 
1980; Ralston, 1987). A mean bottom temperature of 
14°C was assumed for calculating M. This tempera- 
ture prevails throughout most of the Gulf at depths 
between 100 and 300 m (Maluf, 1983). 
R 2 = 1- 
Yj { y~y )2 
^(y-y ) 2 
Results 
where y = observed values; 
y = predicted values; and 
y = mean values. 
Mortality 
An age-length key was constructed from whole- 
otolith ages for the sexes combined and applied to 
the length-frequency distributions to construct popu- 
lation age distributions by sex. Total mortality rate 
(Z) was determined from the descending limb of the 
resulting catch curves for males, females, and pooled 
sexes. Hoenig’s ( 1983) combined regression equation 
was used to obtain another estimate of Z. Owing to 
the lack of data concerning fishing effort and the 
unavailability of unfished areas, no direct estima- 
tion of the natural mortality rate (M) was possible. 
Instead, empirical relationships between M and K 
Population parameters and 
morphometric relations 
During the sampling period L. peru abundance was 
variable, and in some months (e.g. March and De- 
cember 1989 and July to August 1990), sample size 
was small because of limited supply. Sex determina- 
tion was possible for only 13.1% of the specimens used 
for length-frequency distributions (males:females= 
1:0.84; H 0 = 1:1 ratio, Xc=2.85, P=0.091). In the bio- 
logical sampling, the sex ratio was 1:0.85 (H 0 = 1:1 
ratio, x 2 =5.36, P=0.021 ), indicating that no bias was 
introduced in the length-frequency sampling with 
only gonad fragments. 
Macroscopic gonad differentiation occurs in L. peru 
between 30 and 35 cm TL (Table 1 ). A significant frac- 
tion of the catch included individuals smaller than 
50 cm TL (38% of a total of 2171 kg of gutted fish). 
