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Mathematical studies of conservation and extinction in inhomogeneous environments

Mathematical studies of conservation and extinction in inhomogeneous environments
Mathematical studies of conservation and extinction in inhomogeneous environments
A fragmented ecosystem contains communities of organisms that live in fragmented habitats. Understanding the way biological processes such as reproduction and dispersal over the fragmented habitats take place constitutes a major challenge in spatial ecology. In this thesis we discuss a number of mathematical models of density-dependent populations in inhomogeneous environments presenting growth, decay and diffusion amongst woodland patches of variable potential for reproductive success. These models include one- and two-dimensional analyses of single population systems in fragmented environments. We investigate and compute effective properties for single patch systems in one dimension, linking ecological features with landscape structure and size. A mathematical analysis of potential impacts on spread rates due to the behaviour of individuals in the population is then developed. For the analysis of the population dispersal between areas of plentiful resources and areas of scarce resources, we introduce a novel development that models individuals hazard sensitivity when outside plentiful regions. This sensitivity is modelled by introducing a term called endrotaxis that generates a dispersal gradient, resulting in realistically low migration between regions of plentiful resources. Numerical methods and semi-analytic results yield maximum patch separations for one and two dimensional systems and show that the velocity of spread depends on inter-patch distances and patch geometries. By introducing Allee effects (i.e., inverse density-dependent responses to the difficulty of finding mates at low density) over the population growth function, we find that dispersal is slowed down when combined with hazard sensitivity. In the final Chapter we sumarise the results of the previous chapters, concluding that the work performed in this thesis complements and enriches the current mathematical models of movement behaviour.
Alonso Chavez, Vasthi
7609e905-ac07-4200-b94e-64de4f46483c
Alonso Chavez, Vasthi
7609e905-ac07-4200-b94e-64de4f46483c
Sluckin, Timothy
8dbb6b08-7034-4ae2-aa65-6b80072202f6
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Doncaster, Charles
0eff2f42-fa0a-4e35-b6ac-475ad3482047

Alonso Chavez, Vasthi (2011) Mathematical studies of conservation and extinction in inhomogeneous environments. University of Southampton, School of Mathematics, Doctoral Thesis, 237pp.

Record type: Thesis (Doctoral)

Abstract

A fragmented ecosystem contains communities of organisms that live in fragmented habitats. Understanding the way biological processes such as reproduction and dispersal over the fragmented habitats take place constitutes a major challenge in spatial ecology. In this thesis we discuss a number of mathematical models of density-dependent populations in inhomogeneous environments presenting growth, decay and diffusion amongst woodland patches of variable potential for reproductive success. These models include one- and two-dimensional analyses of single population systems in fragmented environments. We investigate and compute effective properties for single patch systems in one dimension, linking ecological features with landscape structure and size. A mathematical analysis of potential impacts on spread rates due to the behaviour of individuals in the population is then developed. For the analysis of the population dispersal between areas of plentiful resources and areas of scarce resources, we introduce a novel development that models individuals hazard sensitivity when outside plentiful regions. This sensitivity is modelled by introducing a term called endrotaxis that generates a dispersal gradient, resulting in realistically low migration between regions of plentiful resources. Numerical methods and semi-analytic results yield maximum patch separations for one and two dimensional systems and show that the velocity of spread depends on inter-patch distances and patch geometries. By introducing Allee effects (i.e., inverse density-dependent responses to the difficulty of finding mates at low density) over the population growth function, we find that dispersal is slowed down when combined with hazard sensitivity. In the final Chapter we sumarise the results of the previous chapters, concluding that the work performed in this thesis complements and enriches the current mathematical models of movement behaviour.

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More information

Published date: 14 October 2011
Additional Information: Awarded by the School of Mathematics, University of Southampton
Organisations: University of Southampton, Mathematical Sciences

Identifiers

Local EPrints ID: 341661
URI: https://eprints.soton.ac.uk/id/eprint/341661
PURE UUID: 73ddfcc1-e95f-4199-a07e-65ef3b55dd0f
ORCID for Timothy Sluckin: ORCID iD orcid.org/0000-0002-9163-0061
ORCID for Charles Doncaster: ORCID iD orcid.org/0000-0001-9406-0693

Catalogue record

Date deposited: 27 Sep 2012 14:41
Last modified: 06 Jun 2018 13:20

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