Past Mathematical Biology and Ecology Seminar

Eukaryotic systems migrate in response to gradients in external signal concentrations, a process referred to as chemotaxis. This chemotactic behaviour may of either a chemoattractive or a chemorepulsive nature.

Understanding such behaviour at the single cell level in terms of the underlying signal transduction networks is highly challenging for various reasons, including the strong non-linearity of the signal processing as well as other complicating factors.

In this talk we will discuss modelling approaches which are aimed at trying to understand how signal transduction in the networks of eukaryotic cells can lead to appropriate internal signals to guide the cell motion either up-gradient or down-gradient. One part of the talk will focus on system-specific mechanistic modelling. This will be complemented by simplified models to address how signal transduction is organized in cells so that they may exhibit both attractive and repulsive gradient sensing.

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.