Special issue on spatial moment techniques for modelling biological processes.

Over the last two decades, there has been an increasing awareness of, and interest in, the use of spatial moment techniques to provide insight into a range of biological and ecological processes. Models that incorporate spatial moments can be viewed as extensions of mean-field models. These mean-field models often consist of systems of classical ordinary differential equations and partial differential equations, whose derivation, at some point, hinges on the simplifying assumption that individuals in the underlying stochastic process encounter each other at a rate that is proportional to the average abundance of individuals. This assumption has several implications, the most striking of which is that mean-field models essentially neglect any impact of the spatial structure of individuals in the system. Moment dynamics models extend traditional mean-field descriptions by accounting for the dynamics of pairs, triples and higher n-tuples of individuals. This means that moment dynamics models can, to some extent, account for how the spatial structure affects the dynamics of the system in question. Previous applications of moment dynamics models have focused on several application areas, such as: ecological dynamics (Bolker and Pacala 1997; Law et al. 2003; Lewis and Pacala 2000); epidemics (Keeling et al. 1997; Sharkey 2008); surface chemistry reactions (Mai et al. 1993, 1994); herding behaviour (Levin 1994); and clustering of organisms (Young et al. 2001). Twoexamples of applicationswheremoment dynam-