Finding regulation among seemingly unregulated populations: a practical framework for analyzing multivariate population time series for their interactions

The structure of ecological communities is often thought to be strongly influenced by population interactions. The interactions are often labeled as bottom-up and top-down control. Previous approaches to identify these processes often assume each population in the community is itself regulated. Therefore, each time series follows a stationary process. However, complex community structure and a lack of regulation in an individual population can result in inappropriate inferences based on traditional statistical approaches. Here, we introduce a statistical framework to analyze potentially non-stationary time series that are collectively regulated. We demonstrate the method with catch-per-unit-effort time series data of selected populations in the Gulf of Mexico. In the Gulf, we found that most of the time series data, which span 26 years, were non-stationary, thus individually unregulated. Species interaction patterns were location-dependent, but where brown shrimp interacted significantly with other species, we identified significant bottom-up forcing. On the other hand, we find almost no evidence of top-down forcing throughout the study areas.