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ABSTRACT Estimates of movement costs are essential for understanding energetic and life-history trade-offs. Although overall dynamic body acceleration (ODBA) derived from accelerometer data is widely used as a proxy for energy expenditure (EE) in free-ranging animals, its utility has not been tested in species that predominately use body rotations or exploit environmental energy for movement. We tested a suite of sensor-derived movement metrics as proxies for EE in two species of albatrosses, which routinely use dynamic soaring to extract energy from the wind to reduce movement costs. Birds were fitted with a combined heart-rate, accelerometer, magnetometer and GPS logger, and relationships between movement metrics and heart rate-derived V̇O2, an indirect measure of EE, were analyzed during different flight and activity modes. When birds were exclusively soaring, a metric derived from angular velocity on the yaw axis provided a useful proxy of EE. Thus, body rotations involved in dynamic soaring have clear energetic costs, albeit considerably lower than those of the muscle contractions required for flapping flight. We found that ODBA was not a useful proxy for EE in albatrosses when birds were exclusively soaring. As albatrosses spend much of their foraging trips soaring, ODBA alone was a poor predictor of EE in albatrosses. Despite the lower percentage of time flapping, the number of flaps was a useful metric when comparing EE across foraging trips. Our findings highlight that alternative metrics, beyond ODBA, may be required to estimate energy expenditure from inertial sensors in animals whose movements involve extensive body rotations. 

In machine learning applications, data are often high-dimensional and intricately related. It is often of interest to find the underlying structure and Granger causal relationships among the data and represent these relationships with directed graphs. In this paper, we study multivariate time series, where each series is associated with a node of a graph, and where the objective is to estimate the topology of a sparse graph that reflects how the nodes of the graph affect each other, if at all. We propose a novel fully Bayesian approach that employs a sparsity-encouraging prior on the hyperparameters. The proposed method allows for nonlinear and multiple lag relationships among the time series. The method is based on Gaussian processes, and it treats the entries of the graph adjacency matrix as hyperparameters. It utilizes a modified automatic relevance determination (ARD) kernel and allows for learning the mapping function from selected past data to current data as edges of a graph . We show that the resulting adjacency matrix provides the intrinsic structure of the graph and answers causality-related questions. Numerical tests show that the proposed method has comparable or better performance than state-of-the-art methods.