LDSG Workshop on "Dynamical Systems and Mathematical Biology"
You
are invited to attend an afternoon meeting on "Dynamical Systems and Mathematical Biology",
to be held at University College London on Wednesday, 3 May 2006.
Invited Speakers:
Sebastian Schreiber (College of William and Mary)
Vincent Jansen (Royal Holloway)
Stephen Gourley (Univ of Surrey)
Program
13:30 Sebastian Schreiber: Living in the variable world: Tales from ecology, evolution, and epidemiology
Abstract:
Plants, animals, and viruses exhibit phenotypic variation and live in heterogenous landscapes where environmental conditions vary in space and time. Understanding how these heterogeneities in isolation or how mixtures of these heterogeneities influence population persistence, the evolution of dispersal, or the spread of diseases lead to many challenging questions in matrix theory and dynamical system theory. I will discuss some progress on these questions and suggest avenues for future research.
14:30 Vincent Jansen:
The evolution of altruism through beard chromodynamics
Abstract:
It was already proposed by Hamilton that kin recognition would favour
the evolution of altruism and cooperation. Surprisingly, the theoretical
basis has until recently not been strongly developed. We have modeled,
arguably the simplest recognition system, consisting of conspicuous,
heritable tags, that elicit altruistic behaviour if the donor and the
recipient of the altruistic act have matching tags. The maintenance of
altruism through this form of recognition is known as green beard
effect. Although such tags, or green beard genes, have been reported,
the green beard effect has often been dismissed because it is deemed
unlikely that a single gene can code for altruism and a recognizable tag.
Our model for the green beard effect and showed that if recognition and
altruism are always inherited together, the dynamics are highly
unstable, and indeed lead to the loss of altruism.
In contrast, if the effect is
caused by loosely coupled separate genes, altruism is facilitated
through beard chromodynamics in which many beard colours co-occur.
This allows altruism to persist even in weakly structured
populations and implies that the green beard effect, in the form of
a fluid association of altruistic traits with a recognition tag, can be
much more prevalent than hitherto assumed.
15:30 - 16:00 Coffee Break
16:00 Stephen Gourley:
The mathematics of mosquito borne diseases
Abstract:
I will discuss the effectiveness of `larvicide' and ‘adulticide’ in controlling mosquito borne diseases such as West Nile virus. Mathematical models take the form of autonomous delay differential equations with impulses (if the adult insects are culled) or a system of nonautonomous delay differential equations where the time-varying coefficients are determined by the culling times and rates (in the case where the insect larvae are culled). Sufficient conditions are derived to ensure eradication of the disease, and simulations are provided to compare the effectiveness of larvicides and insecticide sprays for the control of West Nile virus. Eradication of vector-born diseases is possible by culling the vector at either the immature or the mature phase.
Location:
Department of Mathematics, University College London, Gordon Street 25, floor 5, room 505
Contact:
Josef Hofbauer
We will have lunch at an Indian restaurant in Drummond Street. Meeting point:
in front of the UCL math building, corner Gordon Street/Gower Place at 12:00.
This workshop is part of a series organized by the London Dynamical Systems Group and supported by the London Mathematical Society.
Previous meetings in the series:
- Imperial College, November 16, 2005 details
- University of Surrey, January 27, 2006 details
- Queen Mary, University of London, February 24, 2006 details
For future events please see the webpage of the London Dynamical Systems Group.
Additional support for this event from the Department of Mathematics, University College London, is gratefully acknowledged.