L1

15th Biennial OXFORD / CAMBRIDGE MEETING

PROGRAMME FOR THE

‘WOOLLY OWL TROPHY’

Invited Judges

John Harper

(Victoria University of Wellington, NZ)

Arash Yavari

(Georgia Tech, Atlanta, USA)

Sharon Stephen

(University of Birmingham, UK)

10:45 Morning Coffee The Maths Inst Common Room

Coarse geometry provides a very useful organising point of view on the study
of geometry and analysis of discrete metric spaces, and has been very
successful in the context of geometric group theory and its applications. On
the other hand, the work of Carlsson, Ghrist and others on persistent
homology has paved the way for applications of topological methods to the
study of broadly understood data sets. This talk will provide an
introduction to this fascinating topic and will give an overview of possible
interactions between the two.

The timing of developmental milestones such as egg hatch or bud break

can be important predictors of population success and survival. Many

insect species rely directly on temperature as a cue for their

developmental timing. With environments constantly under presure to

change, developmental timing has become highly adaptive in order to

maintain seasonal synchrony. However, climatic change is threatening

this synchrony.

Our model couples existing models of developmental timing to a

quatitative genetics framework which descibes the evolution of

developmental parameters. We use this approach to examine the ability of a

population to adapt to an enviroment that it is highly maladapted to.

Through a combination of numerical and analtyical approaches we explore

the dynamics of the infinite dimensional system of

integrodifference equations. The model indicates that developmental timing

is surprisingly robust in its ability to maitain synchrony even under

climatic change which works constantly to maintain maladaptivity.

Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on extensions of simple random walk processes. In this talk I will review some of the basic ideas behind the theory of random walks and diffusion processes and discuss how these models are used in the context of modelling animal movement. I will present several case studies, each of which is an extension or application of some of the simple random walk ideas discussed previously. Specifically, I will consider problems related to biased and correlated movements, path analysis of movement data, sampling and processing issues and the problem of determining movement processes from observed patterns. I will also discuss some biological examples of how these models can be used, including chemosensory movements and interactions between zooplankton and the movements of fish.