A probability problem arising out of an entomological experiment

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Virginia Polytechnic Institute


The female of Spalangia drosophilae, Ashm, attack the puparia of Drosophila melanogaster, laying eggs between the puparial case and the pupa. The procedure is as follows: the parasite makes a careful examination of the puparia, tapping it with its antennae; then it stings the pupa to immobility and lays an egg.

In a series of observations carried at the Imperial Institute of Entomology, Canada, using Spalangia as parasite and Drosophila as host, it was noted that the ovipositing female seemed to avoid superparasitism -- that is, laying eggs in already parasitized puparia. Naturally, if the number of non-parasitized insects still available was relatively small, the restraint exercised by the female tended to break down, and several eggs would be laid in some of the hosts.

In order to determine the number of times the female Spalangia could exercise restraint before she was compelled to lay an egg, a series of three hundred and sixty separate experiments were performed. These involved the exposure of groups of five, ten and twenty-five Drosophila puparia to different numbers of parasites for various lengths of time, so that considerable variation in the number of eggs laid occurred. The observational results were expressed in terms of the number of puparia containing zero, one, two, etc., eggs.

As the probability theory involved in this type of situation does not seem to be available, it is proposed to develop it in such a manner that experimental results may be analyzed to estimate the number of times the parasite could withhold an egg. The aspect of the experimental data which is of primary interest is the number of cases of superparasitism occurring for any given number of eggs laid and hosts exposed.