Clustering Nonstationary Circadian Rhythms using Locally Stationary Wavelet Representations

Abstract

Rhythmic processes are found at all biological and ecological scales, and are fundamental to the efficient functioning of living systems in changing environments. The biochemical mechanisms underpinning these rhythms are therefore of importance, especially in the context of anthropogenic challenges such as pollution or changes in climate and land use. Here we develop and test a new method for clustering rhythmic biological data with a focus on circadian oscillations. The method combines locally stationary wavelet time series modelling with functional principal components analysis and thus extracts the time-scale patterns arising in a range of rhythmic data. We demonstrate the advantages of our methodology over alternative approaches, by means of a simulation study and real data applications, using both a published circadian dataset and a newly generated one. The new dataset records plant response to various levels of stress induced by a soil pollutant, a biological system where existing methods which assume stationarity are shown to be inappropriate. Our method successfully clusters the circadian data in an interesting way, thereby facilitating wider ranging analyses of the response of biological rhythms to environmental changes.