Thesis Defence: Reproductive Value for Branching Population Models

Neha Bansal, supervised by Dr. Eric Foxall, will defend their thesis titled “Reproductive Value for Branching Population Models” in partial fulfillment of the requirements for the degree of Master of Science in Mathematics.

An abstract for Neha Bansal’s thesis is included below.

Defences are open to all members of the campus community as well as the general public. Registration is not required for in person defences.

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ABSTRACT

Reproductive value is the relative expected number of offspring produced by an individual in its remaining lifetime. In this study, we provide an overview of reproductive value functions in various models and explore existing methods for obtaining these functions in time-homogeneous population models. Specifically, the Perron-Frobenius (PF) method and the renewal method are thoroughly investigated in this context. However, for time inhomogeneous population models, obtaining reproductive value functions using the mentioned methods becomes challenging.

The main properties of reproductive value functions, namely time-invariance in deterministic models and the martingale property in stochastic models, are demonstrated. Furthermore, we present new results concerning critical population models. It is shown that the ratio of the asymptotic survival probability ratio exists and is equal to the ratio of initial reproductive values. Additionally, in relation to a specific coupling of the size-biased model, the inverse weight of martingale values converges to the ratio of initial reproductive values. These findings contribute to a deeper understanding of reproductive value functions and their implications in critical population models.