ArticleAbstract. Rhythmic processes are found at all biological and ecological scales, and are fun-5 damental to the efficient functioning of living systems in changing environments. The biochemical 6 mechanisms underpinning these rhythms are therefore of importance, especially in the context of 7 anthropogenic challenges such as pollution or changes in climate and land use. Here we develop and 8 test a new method for clustering rhythmic biological data with a focus on circadian oscillations. The 9 method combines locally stationary wavelet time series modelling with functional principal compo-10 nents analysis and thus extracts the time-scale patterns arising in a range of rhythmic data. We 11 demonstrate the advantages of our methodology over alternative approaches, by means of a simula-12 tion study and real data applications, using both a published circadian dataset and a newly generated 13 one. The new dataset records plant response to various levels of stress induced by a soil pollutant, a 14 biological system where existing methods which assume stationarity are shown to be inappropriate. 15Our method successfully clusters the circadian data in an interesting way, thereby facilitating wider 16 ranging analyses of the response of biological rhythms to environmental changes. 17Key words. evolutionary wavelet spectrum, nondecimated wavelet transform, nonstationary 18 processes, unsupervised learning, plant circadian clock 19

Rhythmic data are ubiquitous in the life sciences. Biologists need reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal. When these signals display nonstationary behaviour, as is common in many biological systems, the established methodologies may be misleading. Therefore, there is a real need for new methodology that enables the formal comparison of nonstationary processes. As circadian behaviour is best understood in the spectral domain, here we develop novel hypothesis testing procedures in the (wavelet) spectral domain, embedding replicate information when available. The data are modelled as realisations of locally stationary wavelet processes, allowing us to define and rigorously estimate their evolutionary wavelet spectra. Motivated by three complementary applications in circadian biology, our new methodology allows the identification of three specific types of spectral difference. We demonstrate the advantages of our methodology over alternative approaches, by means of a comprehensive simulation study and real data applications, using both published and newly generated circadian datasets. In contrast to the current standard methodologies, our method successfully identifies differences within the motivating circadian datasets, and facilitates wider ranging analyses of rhythmic biological data in general.MSC 2010 subject classifications: Primary 62M10, 60G18; secondary 60-08.

Negative father-son relationships may play a role in fostering young men's perpetration of MMARA in the barroom context.

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