Applications of Circular Statistics in Plant Phenology: a Case Studies Approach

Phenology is the study of recurring biological events and its relationship to climate. Circular statistics is an area of statistics not very much used by ecologists nor by other researchers from the biological sciences, and indeed not much visited, till recently in statistical science. Nevertheless, the connection between the evaluation of temporal, recurring events and the analysis of directional data have converged in several papers, and show circular statistics to be an outstanding tool by which to better understand plant phenology. The aim of this chapter is to assess applications for circular statistics in plant phenology and its potential for phenological data analysis in general. We do not discuss the mathematics of circular statistics, but discuss its actual and potential applications to plant phenology. We provide several examples at various levels of application: from generating circular phenological variables to the actual testing of hypotheses, say, for the existence of certain a priori seasonal patterns. Circular statistics has particular value and application when flowering onset (or fruiting) occurs almost continuously in an annual cycle and importantly in southern climates, where flowering time may not have a logical starting point, such as mid-winter dormancy. We conclude circular statistics applies well to phenological research where we want to test for relationships between flowering time and other phenological traits (e.g. shoot growth), or with functional traits such as plant height. It also allows us to group species into annual, supra-annual, irregular and continuous reproducers; to study seasonality in reproduction and growth; and to assess synchronization of species.