Let’s Do the Time Warp Again: Dynamic time warping as a tool for temporally structured ecological data

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Jens Hegg, Fish and Wildife Sciences, University of Idaho, Moscow, ID and Brian P. Kennedy, Department of Fish and Wildlife Sciences, and Departments of Biological and Geological Sciences, University of Idaho, Moscow, ID

Background/Question/Methods
Many sources of ecological data, across all levels of ecological organization, are fundamentally temporal. However, these data are frequently compressed or stretched in ways that make direct comparison difficult. Ecologists often isolate point estimates from longer time series to facilitate statistical comparison (e.g. - peak stream flow or maximum daily temperature). This abstraction risks overlooking important patterns contained in the shape of the time series itself. Dynamic Time Warping (DTW) is a time series comparison method used extensively in data mining and machine learning which accounts for temporal stretching and compression. Despite the temporal nature of ecological data, DTW has rarely been applied in the ecological literature. Our study introduces the DTW method through analysis of temporally structured migration data contained in fish otoliths. Otoliths accrete daily rings of calcium carbonate which record the unique chemical signatures (87Sr/86Sr and Element/Ca ratios) of the water a fish inhabits, resulting in a multivariate time-series of migratory movement. Standard techniques to classify salmon natal origin from otolith data extract an average signature during the natal period and use discriminate function analysis (DFA) to classify fish to location. Using data from 376 juvenile Chinook salmon, our study asks the question; can DTW utilize the entire otolith time-series to determine natal origin? Further, can DTW glean additional information from the raw time series which standard methods cannot?
Results/Conclusions
Traditional multivariate DFA identified each known natal location and both hatcheries in the watershed with an error rate below 13% in the training and test sets. However, two important spawning areas, the Upper and Lower Snake River, were indistinguishable and had to be combined. Multivariate DTW identified each of the known natal locations and hatcheries with remarkable precision, in some cases with 80-100% accuracy. Further, DTW convincingly separated the combined Upper and Lower Snake River group and identified specific migratory life-histories within each natal location. These results indicate that DTW is capable of comparing time series data with remarkable sensitivity. Further, our data indicate that DTW is capable of discerning information from time series shape which is lost when the data is abstracted to point estimates. As technology provides ever-increasing richness in the data we can collect, methods that extract meaning from that information richness are increasingly important. Since many ecological datasets are temporal, the flexibility and efficiency of DTW methods may be a useful tool to answer questions that more traditional techniques cannot.