Reproductive value for branching population models
department or school: Science, Irving K. Barber Faculty of (Okanagan)
department or school: Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
data provider: DSpace
degree campus: UBCO
creator: Bansal, Neha
issued: 2023-08-24T22:54:43Z
issued: 2023
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: 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.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/85626
note: Reproductive Value for Branching Population ModelsbyNeha BansalB.Tech., Indian Institute of Technology Roorkee, 2015A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE COLLEGE OF GRADUATE STUDIES(Mathematics)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)August 2023© Neha Bansal, 2023The following individuals certify that they have read, and recommend to the College ofGraduate Studies for acceptance, the thesis titled:Reproductive Value for Branching Population Modelssubmitted by Neha Bansal in partial fulfilment of the requirements of the degree ofMaster of Science in MathematicsExamining Committee:Dr. Eric Foxall, Assistant Professor, I. K. Barber Faculty of SciencesSupervisorDr. Rebecca Tyson, Professor, I. K. Barber Faculty of SciencesSupervisory Committee MemberDr. Michael Noonan, Assistant Professor, I. K. Barber Faculty of SciencesSupervisory Committee MemberDr. Loic Markley, Associate Professor, School of EngineeringUniversity ExamineriiAbstractReproductive value is the relative expected number of offspring produced by an individual inits remaining lifetime. For time-homogeneous population models, there are two existing meth-ods for obtaining the reproductive value function: Perron-Frobenius (PF) method and renewalmethod. The PF method proceeds by looking for an invariant function or an eigenvector andthe renewal method proceeds by fixing a type (state of an individual) and counting the num-ber of offspring collected there. Both methods fail for time inhomogeneous population models(those with time dependent parameters), therefore other methods are needed to compute thereproductive value in that case. Towards that goal, we present two new characterizations ofthis function: for a general class of critical age-structured population models, we show that theasymptotic ratio of the survival probabilities, from different initial states, is equal to the initialratio of reproductive values, and that in relation to a specif…
has type: Thesis/Dissertation
date issued: 2023-09
is shown at: 10.14288/1.0435572
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Foxall, Eric
type: Text
identifier URI: http://hdl.handle.net/2429/85626