On a statistical approach to mate choices in reproduction

TL;DR

This paper introduces a probabilistic Markov chain model with exponential survival times to analyze the movement and choice behavior of female turkeys in selecting mates, providing estimation methods and hypothesis testing tools.

Contribution

It presents a novel statistical framework for modeling multi-stage reproductive choices using conditional Markov chains and maximum likelihood estimation.

Findings

Model effectively captures stage transitions and survival times.

Provides methods for estimating the probability of reaching the final stage.

Enables hypothesis testing on mate choice behaviors.

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.