Some of the most impressive behavioral and reproductive adaptations of organisms are in response to periodic variability of the region they reside. To capture these temporal dynamics, statistical models that estimate the spatiotemporal distribution of a species currently include categorical seasonal covariates, temporally varying parameters, polynomial terms, or smoothing splines. While these techniques provide a useful starting point, they may require many parameters to estimate, be difficult to interpret or make predictions with, and do not explicitly capture periodic trends and deviations from them. Here, we present a technique that uses Fourier series to identify periodic trends in dynamic occupancy models, and parameterize them under a Bayesian framework with data from a large-scale long-term camera trapping study of medium to large mammals in Chicago, Illinois, USA. Although Fourier series can approximate any periodic signal in terms of a possibly infinite sum of sines and cosines, we focus our attention on parameterizations that are informed by the life history of a target species. Such information can be easily collected in natural history texts and formulated as a simple Fourier series that represent an explicit and biologically reasonable formulation of a periodic pattern for a given species.
Our periodic models accounted for up to 75% of the temporal variability in species colonization rates and outperformed standard occupancy models with temporally varying parameters in 3 of the 5 species analyzed. Overall, this method is able to partition variability between periodic and non-periodic trends in a highly versatile model-based framework. It also allows ecologists to estimate the proportion of temporal variability that is attributable to a given periodic trend, is easy to interpret, make future predictions with, and uses fewer parameters. Most importantly, this method makes it simpler to incorporate prior knowledge on the natural history of a species into a statistical model. This will, in turn, create more biologically reasonable models for the conservation and management of species in temporally heterogeneous environments.