Fourier analysis to detect phenological cycles using long-term tropical field data and simulations

Changes in phenology are an inevitable result of climate change, and will have wide-reaching impacts on species, ecosystems, human society and even feedback onto climate. Accurate understanding of phenology is important to adapt to and mitigate such changes. However, analysis of phenology globally has been constrained by lack of data, dependence on geographically limited, non-circular indicators and lack of power in statistical analyses. To address these challenges, especially for the study of tropical phenology, we developed a flexible and robust analytical approach - using Fourier analysis with confidence intervals - to objectively and quantitatively describe long-term observational phenology data even when data may be noisy. We then tested the power of this approach to detect regular cycles under different scenarios of data noise and length using both simulated and field data. We use Fourier analysis to quantify flowering phenology from newly available data for 856 individual plants of 70 species observed monthly since 1986 at Lope National Park, Gabon. After applying a confidence test, we find that 59% of the individuals have regular flowering cycles, and 88% species flower annually. We find time-series length to be a significant predictor of the likelihood of confidently detecting a regular cycle from the data. Using simulated data we find that cycle regularity has a greater impact on detecting phenology than event detectability. Power analysis of the Lope field data shows that at least 6years of data are needed for confident detection of the least noisy species, but this varies and is often >20years for the most noisy species. There are now a number of large phenology datasets from the tropics, from which insights into current regional and global changes may be gained, if flexible and quantitative analytical approaches are used. However, consistent long-term data collection is costly and requires much effort. We provide support for the importance of such research and give suggestions as to how to avoid erroneous interpretation of shorter length datasets and maximise returns from long-term observational studies.