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MIR@W Day / CoSyDy meeting

Movement in Models of Mathematical Biology


Monday 15 November 2010
OrganiserS: Colm Connaughton (Warwick) Robert Mackay (Warwick) and Mauro Mobilia (Leeds)

This is a meeting of the London Mathematical Society supported network CoSyDy.

This meeting is now over but here is a link to a blog post by Alan Winfield about some of the topics which were discussed.

All talks will be in Room B3.02 Mathematics Institute, Zeeman Building

  • 12:45 Buffet Lunch in the Mathematics Institute common room
  • 13:25 Welcome from the organisers
  • 13:30-14:30 J. Pitchford (York) Optimal foraging for the stupid
  • 14:30-15:00 A.Winfield (UWE) Swarm Robotics: a short review
  • 15:00-15:30 A. Ali (Warwick) Pattern formation through genetic drift at expanding population fronts
  • 15:30-16:00 Tea in the Mathematics Institute Common Room
  • 16:00-17:00 R. Erban (Oxford) Individual-based models for collective behaviour
  • 17:00-17:30 T. House (Warwick) How germs use us to move around
  • 17:30 Wine and snacks in the Mathematics Institute Common Room


J. Pitchford (York) Optimal foraging for the stupid

"How should I move to find food efficiently?" - a simple question with some disappointingly complicated answers. I will argue that the complexities involved can be interesting, mathematically tractable, and important in setting mathematical biology within its ecological and evolutionary context. Empirical and theoretical studies argue in favour of diffusive random walks, superdiffusive Levy walks, or combinations and generalisations of the two. I will explain how such studies can be vulnerable when confronted with biological reality, both in terms of data analysis and in the interpretation of idealised toy models. The talk will be motivated by "stupid" fish larvae foraging in unpredictable seas, but the ideas apply generally to evolution constrained by uncertain trade-offs.

A.Winfield (UWE) Swarm Robotics: a short review

Swarm robotics is a new approach to multi-robot systems in which control is completely decentralised and distributed. Inspired by the self-organising collective behaviours of social insects each robot has a simple set of behaviours with local sensing and communications. The overall desired system behaviours emerge from the local interactions between robots, and between robots and their environment. The promise of swarm robotics is that it offers the potential of highly adaptable, scalable and robust systems, able to tolerate the failure of many individual robots without loss of overall system (i.e. swarm) functionality. The challenge however, is how to design the emergent, self-organising properties of the swarm, and how to assure safe and dependable operation. This talk will introduce swarm robotics, illustrating the state-of-the-art with respect to current research, both within the Bristol Robotics Lab and elsewhere.

T. House (Warwick) How germs use us to move around

The spatial spread of infectious diseases of humans used to be captured by standard diffusion-based methods: the black death spread through Europe in waves, at walking speed. Modern pandemics in an interconnected world, like the SARS outbreak or H1N1v swine influenza, take place against the background of a highly interconnected world and can cross continents in days. I will discuss how network theory can help
give insights the spatial spread of human pathogens.

R. Erban (Oxford) Individual-based models for collective behaviour

We will discuss individual-based modelling of biological systems, with a focus on locusts and bacteria. We will review mathematical approaches based on self-propelled particle models and velocity jump processes. Connections between individual-based models and macroscopic modelling approaches (based on partial differential equations) will also be discussed.

A. Ali (Warwick)

We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc. Natl. Acad. Sci., 104(50): 19926–19930 (2007)]. A well-mixed population of two fluorescently labeled microbial species is grown in a circular geometry. As the population expands, a coarsening process driven by genetic drift gives rise to sectoring patterns with fractal boundaries, which show a nontrivial asymptotic distribution. Using simplified lattice-based Monte Carlo simulations as a generic caricature of the above experiment, we present detailed numerical results to establish a model for sector boundaries as time-changed Brownian motions. This is used to derive a general one-to-one mapping of sector statistics between circular and linear geometries, which leads to a full understanding of the sectoring patterns in terms of annihilating diffusions.

poster of programme(PDF Document)