On a statistical approach to mate choices in reproduction

Abstract: We provide a probabilistic approach to modeling the movements of subjects through multiple stages, with "stays" or survival at each stage for a random length of time, and ending at a desired final stage. We use conditional Markov chains with exponential survival times to model the movement of each subject. This is motivated by a study to learn about of the choices that different types of female turkeys make in choosing a male turkey, and in particular, the differences in male choices between groups of females. In this paper, we propose a model for the subjects' movements toward the final stage, and provide maximum likelihood estimation of the model parameters. We also provide results relating to certain questions of interest, such as the distribution of the number of subjects reaching a stage and the probability that a subject reaches the final stage, and develop methods for estimating these quantities and testing statistical hypotheses of interest.