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1953
The Lepidopterists' News
47
CORRELATIONS BETWEEN "PUPAL VOLUME" AND WING-RADIUS AND WEIGHT IN BUTTERFLIES
by P. H. H. Gray
In a previous article the author (1951) described an experiment made to test the effects of different relative humidities on the pupae and imagines of Papilio polyxenes Fab., reared together from eggs laid in 1950 by one female. It is well known that females generally have larger wings or are of larger "build" than males. It was noted, however, that the wild males caught in 1950 were larger than the females of that year. It is also known that the future sex of the butterfly, or moth, can, in some species, be detected structurally in the pupal stage.
During the incubation of the pupae in the experiment mentioned above, 28 of the pupae were measured for length and for breadth to the nearest millimeter. The product of those two measurements has been called the "pupal volume index" for use in the analyses reported below. It was observed that these values had a very wide range, and it seemed possible that they might be of some use in predicting the sex of the future butterfly, on the assumption that the larger pupae would yield females.
The emerged insects, consisting of 15 males and 13 females, were mounted in the usual manner; when dry, the right fore wing was measured from the base to the farthest extent of the apex, also to the nearest millimeter; this value was doubled for use in the analyses. Each butterfly was then weighed, to the nearest milligram, on a beam balance; the weight of the pin, derived from weighing 100 pins of the same gauge, was subtracted to obtain the weight of each butterfly.
The range and average values for each of the variates were as follows:
RANGE AVERAGE
Pupal volume index................ 182-288 226
Wing-radius, mm................... 68-80 76
Weight, mgm....................... 76-160 109
A series of analyses was made to ascertain if there was a correlation between any two of the variates. It is useful, before proceeding with a mathematical analysis, to prepare a "correlation diagram" on graph or co-ordinate paper, on which one variate, e. g. weight, is plotted against another, assumed to be in some way related to or even controlling or being controlled by it; e. g., volume or wing-area. Fisher (1941) explains the purpose of this preliminary operation thus: " When this is done as a dot diagram, a number of dots are obtained each representing a . . . pair of observations, and it is usually clear from such a diagram whether or not any close connexion exists between the variables". Since in the present case there appeared to be a close connexion between the variates in each pair, an analysis was made to determine the correlation coefficient, r, for each of the three paired variates. The following results were obtained:
48
GRAY: Measurement Correlations
Vol.7, no.2
CHARACTERS COMPARED r VALUE
Pupal volume index vs. weight ........ 0.988 Significant
Pupal volume index vs. radius........ 0.995 Significant
Weight vs. wing-radius .............. 0.982 Significant
As each of the three paired variates showed positive correlations of a high order of significance, and as in each correlation diagram the dots representing the values for the females occupied an array distinctly removed from those for the males, in that the values for the former were higher, further analyses were made to ascertain if the mean values for the two sexes were significantly different in each set. The values obtained for the statistic / (see Fisher, 1941) for the three characters are given below:
MALES FEMALES t
Pupal volume index...... 204 230 3314
Wing-radius, mm......... 73 80 6.825
Weight, mgm........... 93 131 5.767
The t values indicate that the mean values are significantly different. It would be of interest to ascertain, by means of a much larger number of observations, if the measurement "pupal volume index" could be used to determine the sex of the future butterfly, either in this species or in others.
The same measurements and analyses have been made of pupae and imagines reared from eggs of Pieris rapae L. in 1951. The larvae were reared on Bar bar ea vulgaris L. (Winter Cress) or on a species of Arabis. The pupae were measured for length and breadth to the nearest 0.025 inch, and the product converted to the millimeter values. The butterflies were not spread before being dried. Since weighing such light objects on a beam balance is tedious work, a "wire balance" was devised, suitable for weighing objects up to about 60 milligrams; the device has been described in a separate article.
The ranges and average values are given below for each of the variates in two populations, consisting of 28 specimens reared from eggs collected at random and 34 reared from eggs laid by one 9 (averages in parentheses):
POPULATION PUPAL VOLUME WING-RADIUS WEIGHT
INDEX (MM.j (MGMj
28 random 58-109 (80.4) 36-52 (46) 8.4-27.5 (19-8)
34** single? 63-94 (79.3) 44-50 (46) 15.0-26.3 (20.5)
It will be seen that the specimens from the random set are much more variable than those of the one 9 . The following correlations were found:
CHARACTERS COMPARED RANDOM 28 SINGLE 34
Pupal volume vs. weight .......... 0.994.......... 0.981
Pupal volume vs. radius............ 0.995.......... 0.994
Weight vs. radius ................ 0.991.......... 0.966
The r values are all of a high order of significance. Ii: was not possible, however, to distinguish between the sexes in any one of the variates.
References Fisher, R. A., 1941. Statistical Methods for Research Workers, 8th ed. Edinburgh. Gray, P. H. H., 1951. Results of humidity tests with Papilio pupae. Lepid. News, vol. 5: p. 67.
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