Spatiotemporal modelling of marine movement data using Template Model Builder (TMB)

Abstract

Tracking of marine animals has increased exponentially in the past decade, and the resulting data could lead to an in-depth understanding of the causes and consequences of movement in the ocean. However, most common marine tracking systems are associated with large measurement errors. Accounting for these errors requires the use of hierarchical models, which are often difficult to fit to data. Using 3 case studies, we demonstrate that Template Model Builder (TMB), a new R package, is an accurate, efficient and flexible framework for modelling movement data. First, to demonstrate that TMB is as accurate but 30 times faster than bsam, a popular R package used to apply state-space models to Argos data, we modelled polar bear Ursus maritimus Argos data and compared the locations estimated by the models to GPS locations of these same bears. Second, to demonstrate how TMB's gain in efficiency and frequentist framework facilitate model comparison, we developed models with different error structures and compared them to find the most effective model for light-based geolocations of rhinoceros auklets Cerorhinca monocerata. Finally, to maximize efficiency through TMB's use of the Laplace approximation of the marginal likelihood, we modelled behavioural changes with continuous rather than discrete states. This new model directly accounts for the irregular sampling intervals characteristic of Fastloc-GPS data of grey seals Halichoerus grypus. Using real and simulated data, we show that TMB is a fast and powerful tool for modelling marine movement data. We discuss how TMB's potential reaches beyond marine movement studies.

Movement responses to environment: fast inference of variation among southern elephant seals with a mixed effects model

“…Comparing Bayesian and TMB versions of a location‐filtering model, Auger‐Méthé et al. () found a 30‐fold decrease in computation time for the TMB fit with no loss of accuracy. All code for fitting these models in R is available online ,…”

Novel step selection analyses on energy landscapes reveal how linear features alter migrations of soaring birds

“…Irregular observations are often handled in the observation equation in a state-space model; however, with GPS data, we can typically assume negligible observation error and save considerable model complexity by modeling the observations directly with the movement equation (Patterson et al, 2008, 2017; Hooten et al, 2017). Notably, parameterizing a CRW in terms of displacement vectors allows for straightforward relationships with time without an observation equation (Auger-Méthé et al, 2017; Gurarie et al, 2017; Eisaguirre et al, 2019; Jonsen et al, 2019).…”

“…To account for behavioral heterogeneity, its predictors, and irregular observations, we implemented our SSF with the following movement model representing ϕ ( · ) (Auger-Méthé et al, 2017; Eisaguirre et al, 2019; Jonsen et al, 2019): Where Here, Δ t i = t i − t i− 1 represents the time interval between Cartesian coordinate vectors x i and x i− 1 for the observed locations of the animal at times t i and t i− 1 , and i = 1, 2, …, N for a track with N observations. Note that the movement parameters in equation 1 are θ i = ( γ i , Σ i ).…”

Abundance and species diversity hotspots of tracked marine predators across the North American Arctic

“…Because of large data sets for each species with ARGOS data and computational limitations restricting the fit of one large hierarchical SSM per species, we grouped ~20 individuals per species per model run. Models were run in r v. 3.3.2 (R Development Core Team, ) and jags v 4.2.0 (Plummer, ) using bsam v. 1.1.1 (Jonsen, ) for ARGOS data and in TMB v. 1.7.4 (Kristensen, Nielsen, Berg, Skaug, & Bell, ) for GLS data using modified code (Auger‐Méthé et al., ). In bsam , two Markov chain Monte Carlo chains were run for 40,000 iterations with a 20,000‐sample burn‐in and thinned every 20 samples.…”