Predator-prey interactions in Arctic Canada : a discrete-time model of lemmings, foxes and snowy owls on Bylot Island
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: Hewa Thudallage, Sanuri
issued: 2024-09-04T07:00:00Z
issued: 2024
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: Bylot Island, in the Canadian Arctic, hosts a predator-prey system that includes snowy owls, arctic foxes, and lemmings. The latter are prey for both the snowy owls and foxes. Snowy owls reside temporarily on the island, their presence or absence depending on the availability of the prey only. Hence, unlike many other predator-prey systems, the composition of the food web (one or two predators) depends on the internal system dynamics. We begin with an ordinary differential equation model, that we reduce to a simple onespecies discrete map. This simplification is possible because we assume that the fox and owl population on Bylot Island remains constant because of a fixed number of territories and nests. The simplified model allows us to prove several key aspects of solution behaviour. We investigate the asymptotic behaviour of solutions. We also fully characterise the cyclic and pseudo-cyclic dynamics in the lemming-arctic fox-snowy owl (LFO) system. Next, since arctic regions exhibit drastic seasonal changes, we extend the model to account for some behavioural changes. Specifically, sufficient lemmings are also a necessity for arctic foxes to breed. As in the previous case, we now obtain a model with two thresholds. The second threshold represents the lemming density above which arctic foxes breed. We observe and characterise more complex behaviour in pseudo-cyclic dynamics relative to our first model. We also discover bistable behaviour: long-term dynamics vary between two- or three-cycle solutions depending on the initial conditions. The availability of lemmings determines the presence or absence of snowy owls and the breeding behaviour of arctic foxes in our model. We implement these seasonal changes as thresholds. Using these threshold values and lemming growth rates, we explain the necessary conditions to observe cyclic dynamics in this predator prey system. Moreover, we demonstrate that our simple mathematical model can exhibit complex behaviour that nonethel…
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/89206
note: Predator-Prey Interactions in ArcticCanada: A Discrete-Time Model ofLemmings, Foxes and Snowy Owlson Bylot Island.bySanuri Hewa ThudallageA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe College of Graduate Studies(Mathematics)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)September 2024© Sanuri Hewa Thudallage, 2024The following individuals certify that they have read, and recommend to the College ofGraduate Studies for acceptance, a thesis entitled:Predator-Prey Interactions in Arctic Canada: A Discrete-Time Model ofLemmings, Foxes and Snowy Owls on Bylot Island.submitted by Sanuri Hewa Thudallage in partial fulfilment of the requirements of thedegree of Master of ScienceDr. Rebecca C. Tyson, Irving K. Barber Faculty of ScienceSupervisorDr. Frithjof Lutscher, Faculty of Science, University of OttawaCo-SupervisorDr. Eric Foxall, Irving K. Barber Faculty of ScienceSupervisory Committee MemberDr. Wayne Broughton, Irving K. Barber Faculty of ScienceSupervisory Committee MemberDr. Sarah P. Otto, Department of ZoologyUniversity ExamineriiAbstractBylot Island, in the Canadian Arctic, hosts a predator-prey system that includes snowyowls, arctic foxes, and lemmings. The latter are prey for both the snowy owls and foxes.Snowy owls reside temporarily on the island, their presence or absence depending on theavailability of the prey only. Hence, unlike many other predator-prey systems, the compo-sition of the food web (one or two predators) depends on the internal system dynamics.We begin with an ordinary differential equation model, that we reduce to a simple one-species discrete map. This simplification is possible because we assume that the fox and owlpopulation on Bylot Island remains constant because of a fixed number of territories andnests. The simplified model allows us to prove several key aspects of solution behaviour.We investigate the asymptotic behaviour of solutions. We also fully characterise the cyclicand pseudo-…
has type: Thesis/Dissertation
date issued: 2024-11
is shown at: 10.14288/1.0445352
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: Tyson, Rebecca
contributor: Lutscher, Frithjof
type: Text
identifier URI: http://hdl.handle.net/2429/89206