54 
PACIFIC SCIENCE, VoL VI, January, 1952 
graduated to !4 inch and read to the nearest 
Vs inch. For convenience in calculating, 
inches were later converted to centimeters and 
pounds to kilograms. These converted mea- 
surements are listed in Table 1. It may be 
added here that measurements made with a 
tape are not completely satisfactory. As a 
result of this experience, we suggest the use 
of large calipers, which can be laid parallel 
to the long axis of the body and the arms of 
which are long enough to encompass the 
greatest depth of the animal. In this way, 
accuracy will be greatly enhanced. 
Throughout this study, use has been made 
of the logarithmic growth equation, Y = 
bX*^, or log Y = log b+k log X, where 
Y = length of body part, X = standard length, 
b = initial growth index, k = equilibrium con- 
stant (Huxley, 1932: 4-8; Huxley and Teissier, 
1936: 780). In the use of this equation, k=l 
indicates isometry, with the portion under 
consideration increasing in size at the same 
rate as the standard length. Similarly, k greater 
or less than 1 indicates positive or negative 
allometry, with the body parts increasing at 
a greater or lesser rate than the standard 
length. Note also that the units of the body 
parts are not necessarily equal to the units of 
the standard length, but are related to them 
through a factor represented by the constant 
b. Thus, if X changes by 1 meter and Y 
changes by only 1 centimeter, then k = 1.0 
and b = 0.01. 
With respect to the length-weight relation- 
ship, it should be noted that weight is equal 
to density times volume. Since volume is the 
resultant of three dimensions, length, breadth 
and depth, the length-weight relationship is 
thus a cubic rather than a linear one. Isometry 
of length and weight, therefore, must be 
indicated by k = 3. In the same way as before, 
k greater or less than 3 indicates that weight 
is increasing more or less rapidly than the 
cube of length, and also shows that the three 
linear components of weight do not vary at 
the same rate. 
Each set of measurements was plotted on a 
double logarithmic scale and regression 
equations were fitted by the method of least 
squares. The significance of deviations from 
isometry was tested by methods outlined by 
Snedecor (1948: 103-168) and Simpson and 
Roe (1939: 186-284). Comparisons of k 
values followed the methods of Snedecor 
(1948: 318-339) and Simpson and Roe 
(1939: 277-280). The standard length was 
always measured along the central axis of the 
body from the tip of the sword to the center 
of the notch on the caudal peduncle. Other 
measurements are described in the appro- 
priate sections. 
There appears to be but little data in the 
literature on allometry in the striped marlin. 
Gregory and Conrad (1939: Table 1) give 
detailed measurements of 17 specimens 
(standard lengths from 250.8 to 284.0 cm.) 
from Cape Brett, N. Z., and nine specimens 
(standard lengths from 203.0 to 286.0 cm.) 
from Mayor Island, N. Z. Shapiro (1938: 
1-20) has examined growth patterns in the 
blue marlin {Makaira nigricans ampla) of the 
Atlantic from 195.0 to 304.0 centimeters in 
standard length. Where appropriate, we have 
compared the patterns shown by our sample 
with the data given by these authors. 
GROWTH PATTERNS 
The Length-Weight Relationship 
In the vast majority of fishes which have 
been examined from this standpoint, the 
equilibrium constant of weight on length is 
approximately 3. However, wide variations 
have been recorded, from as low as 1.4 (Hile, 
1936: 243) to over 3.9 (Shapiro, 1938: 5 ), in 
various species. Indeed, comparable variations 
are to be found between different populations 
of the same species (e.g., the cisco, Leucich- 
thys artedi, according to Hile, varies approxi- 
mately from 1.4 to 3.7. Although sampling 
errors may often account for a large portion 
of the deviations in this relationship (Mor- 
row, 1951: 20-22), real differences in the 
length-weight relationship undoubtedly in- 
