The University of Southampton
University of Southampton Institutional Repository

# Mathematical studies of conservation and extinction in inhomogeneous environments

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.

Text
V.AlonsoChavez-PhDthesis.pdf - Other

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: http://eprints.soton.ac.uk/id/eprint/341661
PURE UUID: 73ddfcc1-e95f-4199-a07e-65ef3b55dd0f
ORCID for T.J. Sluckin: orcid.org/0000-0002-9163-0061
ORCID for G.R. Richardson: orcid.org/0000-0001-6225-8590
ORCID for C.P. Doncaster: orcid.org/0000-0001-9406-0693

## Catalogue record

Date deposited: 27 Sep 2012 14:41

## Contributors

Author: Vasthi Alonso Chavez