Applied Maths Seminar: Merrifield -- Statistical analysis of directed movement of groups: swarms of honeybees and cell invasions

Mathematical models of honeybee swarms and neural crest cells migrating into the
developing gut system in embryos result in behaviours and trajectories that can be
quantified.  The outcomes of these models are samples of directions of travel of the
individuals.  The use of conventional linear statistical techniques is inappropriate in
this context.  Spherical probability theory has been developed for the study of
directional data and this theory best reflects the physical situation being modelled.  

I shall discuss some relevant spherical theory and introduce a suite of statistical
tools that researchers in directional animal movement may find useful.  I shall
illustrate by applying these tools to a model of guidance of honeybee swarms.  I shall
also discuss applications of these ideas to cell migrations (the mathematical modelling
of these same cell migrations will be discussed by Kerry Landman next week).