242 
Fishery Bulletin 99(2) 
eling and robust parameter estima- 
tion to estimate the parameters of 
the von Bertalanffy growth function 
(Fournier et ah, 1990, 1991). Log-like- 
lihood objective functions are com- 
pared by using maximum likelihood 
analyses to identify the parameter set 
for the von Bertalanffy model with 
the best fit. 
The form of the von Bertalanffy 
equation that was used in the MUL- 
TIFAN program is 
u , = m, +(rn N -m,) 
1 -P"" 
1-P' 
where 
hm = 
the mean length of the 
age class j turtles in the 
orth length frequency 
data vset; 
m x = the mean length of the 
first age class; 
rn N - the mean length of the 
last age class; 
p = the Brody growth coef- 
ficient; 
/??(«)- 1 = the number of months 
after the presumed birth 
month of the turtle in 
the orth length-frquency 
data set; and 
N = the number of age classes in the data set. 
among years by month so that samples were sufficiently 
large for length-frequency analyses. 
This parameterization of the von Bertalanffy growth equa- 
tion is derived in Schnute and Fournier ( 1980). 
The MLTLTIFAN length-frequency program has the fol- 
lowing assumptions: 1) growth is described by a von Ber- 
talanffy growth curve; 2) samples represent the structure 
of the population; 3) recruitment occurs in seasonal puls- 
es, 4) the lengths of animals in each age class are normally 
distributed; and 5) the standard deviations of the lengths 
are a simple function of the mean length-at-age. 
MULTIFAN requires that initial values for the follow- 
ing parameters be designated as starting points for the 
iterations: expected number of age classes; expected ini- 
tial K values; mean length of the mode representing the 
youngest age class; standard deviation of a distinct mode; 
and month in which youngest animals recruit to the popu- 
lation. We estimated initial values for expected number of 
age classes as varying between 2 and 30 years, and for K 
as 0.01, 0.05, 0.1, and 0.5/yr. The initial estimate for mean 
length of the youngest age class was 47 cm, and the ini- 
tial standard deviation of mode width was estimated as 
1.5 cm. Because there was a significant trend in standard 
deviation of length-at-age with increasing length, this pa- 
rameter was included in the models reported here. April 
was designated as the month in which youngest turtles 
recruit into the population because the April samples had 
the smallest individuals. The CCL data were combined 
Results 
The length-frequency distributions of loggerhead sea tur- 
tles within the size range of 46 to 87 cm CCL that 
stranded from 1988 through 1995 along the Atlantic coast 
of Florida ( /? = 1 234 ) and along the U.S. coast of the Gulf 
of Mexico (Gulf coast of Florida, Alabama, Mississippi, 
Louisiana, and Texas, n=570) are shown in Figures 1 
and 2, respectively. The two distributions are significantly 
different (Kolmogorov-Smirnov test, Z=3.934, PcO.OOl), 
although the relative patterns are similar. We assumed 
that the length-frequency distributions of stranded sea 
turtles are representative of the length-frequency distri- 
butions of sea turtles in the two regions, although there 
is potential for sampling bias from incidental capture in 
commercial fisheries. 
For loggerhead sea turtles in both the Florida Atlantic 
and the Gulf of Mexico, the MULTIFAN analysis estimat- 
ed that the 46 to 87 cm CCL size range comprises 20 year 
classes (Table 1, Fig. 3). For both geographic regions, vi- 
sual inspection revealed that the models fit the length- 
frequency data well (an example is shown in Fig. 4). We 
were unable to assess annual variation because we com- 
bined data for each month from different years owing 
to small sample sizes. Also, combining data among years 
