Scale-insensitive estimation of speed and distance traveled from animal tracking data

Abstract

BackgroundSpeed and distance traveled provide quantifiable links between behavior and energetics, and are among the metrics most routinely estimated from animal tracking data. Researchers typically sum over the straight-line displacements (SLDs) between sampled locations to quantify distance traveled, while speed is estimated by dividing these displacements by time. Problematically, this approach is highly sensitive to the measurement scale, with biases subject to the sampling frequency, the tortuosity of the animal’s movement, and the amount of measurement error. Compounding the issue of scale-sensitivity, SLD estimates do not come equipped with confidence intervals to quantify their uncertainty.MethodsTo overcome the limitations of SLD estimation, we outline a continuous-time speed and distance (CTSD) estimation method. An inherent property of working in continuous-time is the ability to separate the underlying continuous-time movement process from the discrete-time sampling process, making these models less sensitive to the sampling schedule when estimating parameters. The first step of CTSD is to estimate the device’s error parameters to calibrate the measurement error. Once the errors have been calibrated, model selection techniques are employed to identify the best fit continuous-time movement model for the data. A simulation-based approach is then employed to sample from the distribution of trajectories conditional on the data, from which the mean speed estimate and its confidence intervals can be extracted.ResultsUsing simulated data, we demonstrate how CTSD provides accurate, scale-insensitive estimates with reliable confidence intervals. When applied to empirical GPS data, we found that SLD estimates varied substantially with sampling frequency, whereas CTSD provided relatively consistent estimates, with often dramatic improvements over SLD.ConclusionsThe methods described in this study allow for the computationally efficient, scale-insensitive estimation of speed and distance traveled, without biases due to the sampling frequency, the tortuosity of the animal’s movement, or the amount of measurement error. In addition to being robust to the sampling schedule, the point estimates come equipped with confidence intervals, permitting formal statistical inference. All the methods developed in this study are now freely available in the ctmmR package or the ctmmweb point-and-click web based graphical user interface.

A Guide to Pre-Processing High-Throughput Animal Tracking Data

“…Users must first define plausible upper limits for speed and turning angle for the study species (Calenge et al, 2009;Seidel et al, 2018). Here, it is important to remember that speed estimates are scale-dependent; high-throughput tracking typically overestimates the speed between positions where the animal is stationary or moving slowly due to smallscale location errors (Noonan et al, 2019;Ranacher et al, 2016). Even after data with large location errors have been removed by filters, it is advisable to begin with a liberal (high) speed threshold that excludes only the most unlikely of speeds.…”

“…The aggregation method is less sensitive to selecting point outliers by chance than resampling. When users want to account for location error with methods such as state-space models (Johnson et al, 2008;Jonsen et al, 2005Jonsen et al, , 2003, or continuous time movement models (Calabrese et al, 2016;Fleming et al, 2014Fleming et al, , 2020Gurarie et al, 2017;Noonan et al, 2019), correctly propagating the location error when thinning is important. In ATLAS systems the location error (SD; see F P C ) is calculated from the variance-covariance matrix of the coordinates of candidate positions considered by the location solver (Weiser et al, 2016); this is equivalent to GPS systems' HDOP (Ranacher et al, 2016).…”

“…Even after removing large location errors and evidently unrealistic movement, a track may comprise of positions that are distributed around the true animal location. Discarding these positions as 'untrue' would lead to excessive data loss, but treating them as 'real' locations would lead to unrealistic estimates of metrics such as speed (Noonan et al, 2019). The large data-volumes of highthroughput tracking allow for a neat solution: tracks can be 'smoothed' to reduce small location errors that have remained undetected.…”

“…For instance, smoothing breaks the relationship between a coordinate and the location error estimate around it (VARX, VARY, and SD in ATLAS systems, or HDOP in GPS tracking). This makes subsequent filtering on covariates of data quality unreliable, and smoothed data are unsuitable for use with methods that model location uncertainty (Calabrese et al, 2016;Fleming et al, 2014Fleming et al, , 2020Noonan et al, 2019). Furthermore, while larger K may result in smoother tracks (Fig.…”

Animal movement models for multiple individuals

“…However, if uncertainty about the true location is comparable to the scale of the individual pixels in the grid on which covariates are measured, there will be uncertainty about what type of landscape individuals actually move through, and inference can be strongly affected by ignoring measurement error. Variation in animal ecology and behavior, monitoring technology, sampling interval, and desired inference make it difficult to provide general guidance for when one cannot ignore measurement error, but see Brost, Hooten, Hanks, and Small (2015), Frair et al (2010), Hurford (2009), Noonan et al (2019) for some specific applications that incorporate measurement error.…”