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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Biomathematics Seminar: Spiralling patterns in models inspired by bacterial games with cyclic competition

Presented by Mauro Mobilia, Leeds University

20 January 2015 14:00 in CM105

Evolutionary game theory, where the success of one species depends on what the others are doing, provides a promising framework
to investigate the mechanisms allowing the maintenance of biodiversity. Experiments on microbial populations have shown that cyclic
local interactions promote species coexistence. In this context, rock-paper-scissors games are used to model populations in cyclic
competition. After a brief overview of some inspiring experiments, I will discuss the subtle interplay between the individuals'
mobility and local interactions in two-dimensional rock-paper-scissors systems. This leads to the loss of biodiversity above a
certain mobility threshold, and to the formation of spiralling patterns below that threshold. I will then discuss a generic
rock-paper-scissors metapopulation model formulated on a two-dimensional grid of patches. When these have a large carrying capacity,
the model's dynamics is faithfully described in terms of the system's complex Ginzburg-Landau equation suitably derived from a
multiscale asymptotic expansion. The properties of the ensuing complex Ginzburg-Landau equation are exploited to derive the
system's phase diagram and to characterize the spatio-temporal properties of the spiralling patterns in each phase. This enables
us to analyse the spiral waves stability, the influence of linear and nonlinear diffusion, and the far-field breakup of the
spiralling patterns.

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