Wavelet Analysis of Nonstationary Circadian Time Series

Rhythmic data are ubiquitous in the life sciences, with biologists needing reliable statistical tools for the analysis of such data. When these signals display rhythmic yet nonstationary behaviour, common in many biological systems, the established methodologies
are often misleading.
Chapter 2 develops and tests a new method for clustering nonstationary rhythmic biological data. The method combines locally stationary wavelet time series modelling with
functional principal components analysis and thus extracts time—scale patterns useful for
identifying common characteristics. We demonstrate the advantages of our methodology
over alternative approaches by means of a simulation study and for real circadian data applications.
Motivated by three complementary applications in circadian biology, Chapter 3 develops new reliable statistical tests to identify whether a particular experimental treatment
has caused a significant change in a rhythmic signal that displays nonstationary characteristics. As circadian behaviour is best understood in the spectral domain, we develop
novel hypothesis testing procedures in the (wavelet) spectral domain, which facilitate 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 for real data applications, involving both plant and animal signals.
Chapter 4 investigates the effect of industrial and agricultural pollutants on the plant
circadian clock. We examine the impact of exposure to a comprehensive range of environmentally relevant pollutants by utilising the methodologies developed in Chapters 2 and 3.
Our findings indicate that many of the tested chemicals have an effect on the plant circadian clock, most of which would have remained undetected by classical methods overlooking nonstationarity. The results of Chapter 4 demonstrate the additional insight gained by
using the appropriate methodologies, as developed in Chapters 2 and 3, and also have important implications for understanding environmental ramifications associated with soil
pollution.