96 
PACIFIC SCIENCE, VoL VIII, January, 1954 
ration of the length frequency data may be 
made: 
At some age, perhaps one or two years, an 
age group or year-class is first taken in sig- 
nificant amounts by the fishermen during the 
summer fishing. By the second summer, this 
1946 
1947 
1948 ^ 
D 
cy 
>• 
1949 e 
I- 
1950 
1951 
Fig. 1. Length frequencies of Hawaiian aku, 1946- 
51. The number identifying modal positions is the 
presumed year of origin of the modal group. 
Length in Centimeters 
age group, at a length of 70 to 75 centimeters, 
is again taken and, as a matter of fact, is the 
size group most eagerly sought by the fisher- 
men. This year-class appears again in the 
catch during the third summer but cannot be 
traced thereafter with any certainty from the 
available data. 
The age of the modal group of smallest 
length, that of the youngest year-class fished, 
is of interest. It would appear to be possible 
to form some judgment of this age by fitting 
the observed modal length to a growth curve 
and extending the growth curve toward the 
origin. It is appreciated that the initial growth 
period, during the larval stages, will probably 
not be described by a simple growth curve 
adequate for the later period of growth; hence, 
this approach would not, of course, yield a 
certain answer, but it may, at least, give a 
likely estimate of the age of the fish. A growth 
curve of the type described by Walford (1946) 
was fitted to the length frequency data in the 
following manner: The obvious modes were 
selected (see Eig. 1) and the three highest 
classes for each mode were averaged. This 
average was thereafter taken as the modal 
length (these modal values are shown in part 
in Table 1). Then the modal lengths as ob- 
tained from the summer samples were paired 
with the modes presumed to be the same of 
a year later. 
This relationship between length at age 
N and at age N + 1 which may be taken as 
a year or any other equal time interval later, 
as shown by Walford (1946), is usually a 
linear one. It was assumed to be linear for 
these data, and the line of best fit was com- 
puted by the method of least squares for the 
following paired values: Length at age N and 
N + 1, at age N + 1 and N + 2, and at age 
N + 2 and N + 3, if available. The equation 
of this line would permit, of course, the com- 
putation of the length at N + 1, given the 
length at N, or the length at N + 2, given 
the length at N + 1. 
The average of all the mean sampling dates 
for the summer for the period of September 
