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Preface
1.  AGIM Laboratory, FRE 3405 UJFCNRS, TIMB Team, University J. Fourier of Grenoble (UJF), Faculty of Medicine, 38700 La Tronche 
2.  Laboratoire de Mathématiques, CNRS et Université de ParisSud XI, F91405 Orsay Cedex 
3.  Graduate school of Mathematical Sciences, University of Tokyo, Komaba 381, Tokyo 1538914 
4.  Department of Mathematics, School of Science and Technology, Meiji University, 111 Higashimita, Tamaku, Kawasaki 2148571 
In order to understand the problems occurring in these areas of application, one should not only apply known methods, but also develop novel mathematical tools. Because of this, many results corresponding to new approaches are given in the main topics of this CPAA Special Volume, including demography and travelling waves in epidemics modelling, structured populations growth, propagation in inhomogeneous media, ecology and dry land vegetation, formation of stationary spatiotemporal patterns in reactiondiffusion systems both from a mathematical and an experimental view point, spatiotemporal dynamics of cooperation, cell migration and bacterial suspensions. This issue also includes more mathematically oriented topics such as interface dynamics, stability of nonconstant stationary solutions, heterogeneityinduced spot dynamics, boundary spikes, appearance of anomalous singularities in parabolic equations, finite time blowup, a multiparameter inverse problem, and the numerical approximation of parabolic equations and chemotactic systems. We hope these advanced results will be useful to the community of researchers working in the domain of partial differential equations, and that they will serve as examples of mathematical modelling to those working in the different areas of application mentioned above.
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