An Application of Stochastic Processes to Experimental Studies on Flour Beetles

Abstract

This study is concerned with a gener al stochastic model of population growth in experimental studies on flour beetles. The population under consideration is that of eggs of flour beetles and the statistical investigation was initiated in a series of lectures by Professor J. Neyman. Consider an experiment which starts with a known number of eggs of flour beetles and a knowni number of pairs of flour beetles of a certain species contained in a vial with a definite amount of medium. Beetles used at the initiation of the experiment are those just emerged from pupae. Neither pupae nor larvae are present at any time in the course of the experimenit. Experimenital conditions are kept constant with respect to temperature, relative humidity, conditioning of medium, etc. At regular time intervals, observations are made on the number of eggs. To avoid hatching, after each observation the eggs are replaced by fresh eggs and the same beetles are returned to the vial. The experiment is carried out through the entire life span of the female beetles. Depending on the number of fresh eggs replacing the old ones, the experiment may be classified into two types. In the first type of experiment, the number of fresh eggs replacing the old ones is equal to the number of old eggs removed. In this case, the number of eggs observed at any time depends on the previous observations. In the second type of experiment, the number of fresh eggs is predetermined by the experimenter. For example, the nlumber of fresh eggs may be constant. The objective of the experiment is to determine, on the basis of the observed numbers of eggs, the female beetles' ability to lay eggs (that is,