Using Fourier series to estimate periodic patterns in dynamic occupancy models

Some of the most impressive adaptations of organisms are in response to periodic environmental variability. To capture these temporal dynamics, statistical models that estimate the spatiotemporal distribution of a species typically include categorical seasonal covariates, temporally varying parameters, or smoothing splines. While these techniques provide a useful starting point, they may require many parameters to estimate and are not well suited for making predictions. Here, we present a technique that uses Fourier series to estimate periodic signals in dynamic occupancy models, and parameterize these models with data from a large‐scale long‐term camera trapping study of medium to large mammals in Chicago, Illinois,USA. Our periodic models captured up to 75% of the temporal variability in species colonization rates and performed similar to dynamic occupancy models with temporally varying parameters. Overall, this method can partition variability between periodic and non‐periodic sources and estimate the proportion of temporal variability that is attributable to a periodic source in a model‐based framework. Further, practitioners can use this method to incorporate prior knowledge on a species' natural history (e.g., natal dispersal and migration). This will, in turn, create more biologically reasonable models for conservation and management applications.