The Relationship Between Body Length and Scale Length in Five 
Year-Classes of the Pacific Pilchard or Sardine, 
Sardinops caerulea (Girard, 1854). 
Antonio Landa’ 
INTRODUCTION 
By correlating the marginal growth of 
scales (the amount of growth between the 
last ring or annulus and the margin of the 
scale) with the season of the year in which 
the scales were collected, Walford and Mosher 
(1943^: 9 and 1943^: 12) have shown for the 
Pacific pilchard or sardine, Sardinops caerulea 
(Girard) 1854, that these rings are formed 
annually and consequently can be used for 
age determination as well as for back-calcula- 
tion of the length of the fish at a given earlier 
age. The application of the scale rings to the 
problem of age determination in the pilchard 
has been thoroughly discussed in the papers 
cited above. The application of the same phe- 
nomenon to back-calculation of lengths, 
which lengths are used in several different 
types of problems, requires further considera- 
tion. The literature on this subject is volumi- 
nous and of considerable interest. Reference 
should be made to the works of Blackburn 
(1949), Buchanan-Wollaston (1934), Lea 
(1910, 1913), Lee (1912), Ottestad (1938), 
and Schuck (1949) for further information. 
The estimation of body length at a previous 
age, using length of the scale from its center 
to the ring corresponding to that age, in- 
volves the regression of body length on scale 
length. The regression of scale length on body 
length, sometimes used, will give the mean 
scale length corresponding to a given body 
length, information which is not pertinent to 
1 Biologist, Cia. Admora del Guano, Lima, Peru. 
Manuscript received December 4, 1951. 
the problem. It should be noted at once that 
different regression lines could be obtained 
from a given set of material depending on the 
manner of sampling and that this manner, in 
turn, depends on the use for which the re- 
gression values are intended. Thus, if the goal 
is to know at which body length the scales 
start growing, it should be emphasized that 
the sampling be comprehensive of the very 
small body lengths. Moreover, such sampling 
should be equally representative of all the 
body lengths if a further goal is desired, i.e., 
to know whether or not the regression of body 
length on scale length is the same throughout 
all different body lengths. 
In the particular case of the Pacific pilchard 
investigations, and, presumably, in others of 
similar commercial fisheries, the goal is to 
know the body lengths that the fish caught 
commercially had in previous years. It follows 
that the sampling should, before anything 
else, be representative of the commercial catch 
even if that requirement makes the data un- 
suitable for the attainment of goals of the 
type indicated above. Once the scope of the 
problem is thus limited, the following are 
some of the questions that arise in the back- 
calculation and use of estimated lenghts: 
(1) Are the regression constants (regres- 
sion coefficient and body intercept) of 
body length on scale length the same 
for all year-classes regardless of region 
of capture? 
(2) Are the regression constants for a given 
year-class the same regardless of region 
of capture? 
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