AbstractEnvironmental factors interact with internal rules of population regulation, sometimes perturbing systems to alternate dynamics though changes in parameter values. Yet, pinpointing when such changes occur in naturally fluctuating populations is difficult. An algorithmic approach that can identify the timing and magnitude of parameter shifts would facilitate understanding of abrupt ecological transitions with potential to inform conservation and management of species.The “Dynamic Shift Detector” is an algorithm to identify changes in parameter values governing temporal fluctuations in populations with nonlinear dynamics. The algorithm examines population time series data for the presence, location, and magnitude of parameter shifts. It uses an iterative approach to fitting subsets of time series data, then ranks the fit of break point combinations using model selection, assigning a relative weight to each break. We examined the performance of the Dynamic Shift Detector with simulations and two case studies. Under low environmental/sampling noise, the break point sets selected by the Dynamic Shift Detector contained the true simulated breaks with 70-100% accuracy. The weighting tool generally assigned breaks intentionally placed in simulated data (i.e., true breaks) with weights averaging >0.8 and those due to sampling error (i.e., erroneous breaks) with weights averaging <0.2. In our case study examining an invasion process, the algorithm identified shifts in population cycling associated with variations in resource availability. The shifts identified for the conservation case study highlight a decline process that generally coincided with changing management practices affecting the availability of hostplant resources.When interpreted in the context of species biology, the Dynamic Shift Detector algorithm can aid management decisions and identify critical time periods related to species’ dynamics. In an era of rapid global change, such tools can provide key insights into the conditions under which population parameters, and their corresponding dynamics, can shift.Author SummaryPopulations naturally fluctuate in abundance, and the rules governing these fluctuations are a result of both internal (density dependent) and external (environmental) processes. For these reasons, pinpointing when changes in populations occur is difficult. In this study, we develop a novel break-point analysis tool for population time series data. Using a density dependent model to describe a population’s underlying dynamic process, our tool iterates through all possible break point combinations (i.e., abrupt changes in parameter values) and applies information-theoretic decision tools (i.e. Akaike’s Information Criterion corrected for small sample sizes) to determine best fits. Here, we develop the approach, simulate data under a variety of conditions to demonstrate its utility, and apply the tool to two case studies: an invasion of multicolored Asian ladybeetle and declining monarch butterflies. The Dynamic Shift Detector algorithm identified parameter changes that correspond to known environmental change events in both case studies.
Mathematical Model for Small Size Time Series Data of Bacterial Secondary Metabolic Pathways
