Strengths and limitations of period estimation methods for circadian data

A key step in the analysis of circadian data is to make an accurate estimate of the underlying period. There are many different techniques and algorithms for determining period, all with different assumptions and with differing levels of complexity. Choosing which algorithm, which implementation and which measures of accuracy to use can offer many pitfalls, especially for the non-expert. We have developed the BioDare system, an online service allowing data-sharing (including public dissemination), data-processing and analysis. Circadian experiments are the main focus of BioDare hence performing period analysis is a major feature of the system. Six methods have been incorporated into BioDare: Enright and Lomb-Scargle periodograms, FFT-NLLS, mFourfit, MESA and Spectrum Resampling. Here we review those six techniques, explain the principles behind each algorithm and evaluate their performance. In order to quantify the methods' accuracy, we examine the algorithms against artificial mathematical test signals and model-generated mRNA data. Our re-implementation of each method in Java allows meaningful comparisons of the computational complexity and computing time associated with each algorithm. Finally, we provide guidelines on which algorithms are most appropriate for which data types, and recommendations on experimental design to extract optimal data for analysis.