Damia Gomila
Damia Gomila

Pattern formation in marine clonal plant meadows

Damia Gomila
damia@ifisc.uib-csic.es
IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca

Competition for water or nutrients or interactions with herbivores drive spatial instabilities in landscapes of terrestrial plants, resulting in pattern formation phenomena that have been a subject of intense research in the last years. Observations from aerial images and side -scan sonar data have recently revealed analogous pattern forming phenomena in submerged vegetation in the Mediterranean Sea, mainly in meadows of seagrasses such as Posidonia oceanica and Cymodocea nodosa. Starting from growth rules of these clonal plants, we have derived a macroscopic model for the plant density able to provide an explanation to the observed submarine hexagonal patterns or isolated ‘fairy circles’, and landscapes of spots and stripes. The essential ingredient is a competitive interaction at a distance of 20-30m. Beyond a qualitative description of the observed patterns, and their prevalence under different meadow conditions, the model fits well measurements of the population density of Posidonia, which show great variability close to the coast, where patterns typically appear.

Andrew Krause
Andrew Krause

Reaction-Diffusion Systems on Structured and Evolving Manifolds

Andrew Krause
krause@maths.ox.ac.uk
University of Oxford, Oxford OX1 2JD, United Kingdom
I will discuss recent work with biologists related to understanding particular structural characteristics in the whiskers of mice, and in synthetic quorum-sensing mechanisms of bacteria. These scientific problems are typically modelled using reaction-diffusion systems, and one is often interested in emergent spatial and spatiotemporal patterns from instabilities of a homogeneous equilibrium. I will use these scientific questions to motivate fundamentally mathematical questions regarding instabilities and the emergence of patterns in complex domains. First I will discuss the well-known effects of how manifold structure impacts the modes which may become unstable in reaction diffusion systems, and hence how the kinds of patterns we may observe on manifolds can change due to geometry directly. More strikingly, I will discuss recent work where coupling between two different simple planar geometries leads to highly non-intuitive results regarding the role of geometry. Finally I will discuss results on instabilities on a large class of time-evolving manifolds, and show that one can derive a meaningful notion of instability of the homogeneous state even in this explicitly time-dependent setting. The technical Theorems in this last part may also have application far beyond the realm of developmental biology, as they generalize notions of instability to a large class of non-autonomous systems.