The Dynamic Shift Detector: An algorithm to identify changes in parameter values governing populations

Abstract

Environmental 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.

Fig 1. Performance of the Dynamic Shift Detector (DSD) algorithm under varying parameter values.

Proportion of simulation results in which the true break scenario was detected within the top break point combinations as identified by the DSD implemented with an underlying Ricker model with varied A) noise (in the form of normally distributed error), B) starting values of the r parameter, C) percent changes in the K parameter, D) percent changes in r, and E) simulated time series length. Sets of 0, 1, 2 and 3 break points were randomly generated from within the set of possible values, and 250 datasets were simulated for each scenario. In each panel, other variables (that were not being varied) were held constant at their base values (i.e., noise = 2%; starting value of r = 2; change in r = ±25%; change in K = ±75%; time series length = 20 years). Trends within a set of scenarios (grey lines) are illustrated with a third-order GAM smoothing line.

Fig 2. Average break weight of break points detected under varying parameterization conditions.

Average weights of break points identified by the Dynamic Shift Detector algorithm reflecting true parameterization conditions (diamonds) or erroneous breaks suggested by the algorithm (triangles) under varied A) noise (in the form of normally distributed error), B) starting values of the r parameter, C) percent changes in the K parameter, D) percent changes in r, and E) simulated time series length. Sets of 0, 1, 2 and 3 break points were randomly generated from within the set of possible values, and 250 datasets were simulated for each scenario. In each panel, other variables (that were not being varied) were held constant at their base values (i.e., noise = 2%; starting value of r = 2; change in r = ±25%; change in K = ±75%; time series length = 20 years). Trends within a set of scenarios (grey lines) are illustrated with a third-order GAM smoothing line.

Fig 3. Dynamic Shift Detector breaks and Ricker model fits for an invasive species.

Population data documenting the invasion of multicolored Asian ladybeetle in Michigan, USA from 1994–2017. A) Time series data showing the average number of adults captured, per trap, per year. Vertical blue lines indicate years in which dynamic shifts occurred, as estimated by the Dynamic Shift Detector algorithm. B) Ricker fits of time series data segments. Ladybeetle art by M. Broussard, used under a CC-BY 3.0 license.

Fig 4. Dynamic Shift Detector breaks and Ricker model fits for a species of conservation concern.

Population data documenting the area occupied by monarch butterflies in their winter habitat in central Mexico from 1995–2017. A) Time series data showing the total area occupied by overwintering monarchs each year in December. Vertical blue lines indicate years in which dynamic shifts occurred, as estimated by the Dynamic Shift Detector algorithm. B) Ricker fits of time series data segments. Butterfly art by D. Descouens and T.M. Seesey, used under a CC-BY 3.0 license.