Open Collections

Bansal, Neha

University of British Columbia

Reproductive value is the relative expected number of offspring produced by an individual in its remaining lifetime. For time-homogeneous population models, there are two existing meth- ods for obtaining the reproductive value function: Perron-Frobenius (PF) method and renewal method. The PF method proceeds by looking for an invariant function or an eigenvector and the renewal method proceeds by fixing a type (state of an individual) and counting the number of offspring collected there. Both methods fail for time inhomogeneous population models (those with time dependent parameters), therefore other methods are needed to compute the reproductive value in that case. Towards that goal, we present two new characterizations of this function: for a general class of critical age-structured population models, we show that the asymptotic ratio of the survival probabilities, from different initial states, is equal to the initial ratio of reproductive values, and that in relation to a specific coupling of the size-biased model, both are equal to the limit of the inverse ratio of total reproductive values. To provide context and background, we also discuss two defining properties of reproductive value, namely time-invariance in deterministic models and the martingale property in stochastic models, for some commonly used models. These findings contribute to a deeper understanding of reproductive value functions and their implications in critical population models.

Text

2023-08-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/85626

Mathematics

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/4.0/