39 
Abstract .—The accuracy and pre- 
cision of estimates of catch at age from 
sampled lengths were evaluated for 
three different methods with simulated 
red snapper, Lutjanus campechanus, 
data for 1984-94. The methods in- 
cluded a growth curve, age-length keys, 
and a probabilistic method to classify 
a known total number of fish into ages 
from samples of the length frequency 
of the catch. In the first method, ages 
were estimated from sample lengths 
directly from the growth curve. The 
second method involved expanding the 
sample length frequency to age fre- 
quency by using age-length keys. The 
probabilistic method incorporated the 
cumulative frequency distributions of 
length at age, year-class strength, and 
estimates of prior survival to build age 
probability distributions from sampled 
lengths. The evaluation was based on 
the error in the assigned catch at age 
and on the resulting estimates of num- 
bers at age and fishing mortality aris- 
ing from sequential population analy- 
sis. The probabilistic method was the 
best of the three for the situation evalu- 
ated here, and application of the age- 
length key was better than that of the 
growth model. However, the probabilis- 
tic method requires knowledge of 
growth, the distributions of size at age, 
and recruitment that may not be 
known, or only poorly so. Age-length 
keys require no such ancillary informa- 
tion and may be more practical in most 
situations, but the probabilistic method 
is superior if the data requirements can 
be met. 
Manuscript accepted 31 July 1996. 
Fishery Bulletin 95:39-46 (1997). 
Fish age determined from length: 
an evaluation of three methods 
using simulated red snapper data* 
C. Phillip Goodyear 
Miami Laboratory, Southeast Fisheries Science Center 
National Marine Fisheries Service, NOAA 
75 Virginia Beach Drive, Miami, Florida 33149 
E-mail address: Phil_Goodyear@msn.com 
Age-structured stock-assessment 
methods require estimates of the 
age composition of the catch. In 
stock assessments for Gulf of Mexico 
red snapper, Lutjanus campechanus, 
age compositions are used that are 
estimated from the sampled size 
distribution of the catch with 
growth models (Goodyear * 1 ). The 
application of age-length keys de- 
veloped from age determinations of 
length-stratified samples of the 
catch is a superior method (Ketchen, 
1950; Hoenig and Heisey, 1987 ) that 
has been recently incorporated into 
the data collection program for this 
stock. However, it cannot be readily 
applied retroactively to improve the 
estimates of the age composition of 
historical catch, and it requires sig- 
nificantly more resources than the 
former method. In this paper, I com- 
pare the precision of the estimates 
of the age composition of the catch 
from these two methods with an al- 
ternative, using simulated red 
snapper data. The comparisons in- 
clude both accuracy and precision 
of the estimates of the age composi- 
tion of the catch and the consequent 
estimates of numbers at age and 
fishing mortality arising from their 
application to sequential population 
analysis following the methods of 
Gavaris 2 and Powers and Restrepo 
(1992). 
Methods 
Simulated data 
The population simulation model 
used in this analysis (Goodyear, 
1989) employed 30 discrete ages 
with an instantaneous annual natu- 
ral mortality (M) of 0.2 for all ages 
in the fishery. Each year class was 
further partitioned into growth pla- 
toons (cohorts with identical age but 
different mean lengths). The posi- 
tion of a growth platoon in the dis- 
tribution of size at age was fixed so 
that the larger individuals of a year 
class at age 1 remained larger 
throughout their lifetime. Mean 
lengths (L) at age (A) at the begin- 
ning of January were assumed to be 
equal to the estimates in the 1994 
stock assessment for Gulf of Mexico 
red snapper ( Goodyear 1 ) and to cor- 
respond to the von Bertalanffy 
equation, L=88.24( l-exp(-0. 159 
Miami Laboratory Contribution MIA-94/ 
95-42. 
1 Goodyear, P. 1994. Red snapper in U.S. 
waters of the Gulf of Mexico. National 
Marine Fisheries Service, Southeast Fish- 
eries Science Center, Miami Laboratory, 
Miami, Admin, rep. MIA 93/94-63, 150 p. 
2 Gavaris, S. 1988. An adaptive frame- 
work for the estimation of population 
size. Canadian Atlantic Fisheries Scien- 
tific Advisory Committee Research Docu- 
ment 88/29, 4 p. 
