A guide to state–space modeling of ecological time series

Auger‐Méthé, Marie; Newman, Ken; Cole, Diana J.; Empacher, Fanny; Gryba, Rowenna; King, Aaron A.; Leos-Barajas, Vianney; Flemming, Joanna Mills; Nielsen, Anders; Petris, Giovanni De; Thomas, Len

doi:10.1002/ecm.1470

Cited by 130 publications

(149 citation statements)

References 208 publications

(502 reference statements)

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“…First, natural systems are driven by networks of interacting biotic and abiotic processes (Levin 1998, Choler et al 2001, Massoud et al 2018). These dynamic natural processes are the products of multiple sources of variation including long-term trends, seasonal and other cyclic oscillations, environmental forcing, temporal dependence or species interactions (Choler et al 2001, Dietze 2017, Auger-Méthé et al 2021). Second, ecological time series tend to be integer-valued variables such as observations of species presence or abundance that exhibit complex features including observation error, zero-inflation, over-dispersion, bounds, missing values and uneven sampling frequency (Lindén and Mäntyniemi 2011, Simpson 2018, Warton 2018, Kowal and Canale 2020).…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Generalised Additive Models (DGAM) for forecasting discrete ecological time series

Clark

Wells

2022

Preprint

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Generalised Additive Models (GAMs) are increasingly popular for describing smooth nonlinear relationships between predictors and response variables. GAMs are particularly relevant in ecology for representing hierarchical functions for discrete responses that encompass complex features including zero-inflation, bounding and uneven sampling. However, GAMs are less useful for producing forecasts as their smooth functions provide unstable predictions outside the range of training data. We introduce Dynamic Generalised Additive Models (DGAMs), where the GAM linear predictor is jointly estimated with unobserved dynamic components to model time series that evolve as a function of nonlinear predictor associations and latent temporal processes. These models are particularly useful for multivariate series, as they can estimate hierarchical smooths while learning complex temporal associations via dimension-reduced latent factor processes. We implement our models in the mvgam R package, which uses the mgcv and rjags packages to construct smoothing splines and estimate unobserved parameters in a probabilistic framework. Using simulations, we illustrate how our models outperform competing formulations in realistic ecological forecasting tasks while identifying important smooth predictor functions. We use a real-world case study to highlight some of mvgam's key features, which include functions for: calculating correlations among series' latent trends, performing model selection using rolling window forecasts, online data augmentation via a recursive particle filter, and visualising probabilistic uncertainties for smooths and predictions. Dynamic GAMs (DGAM) offer a solution to the challenge of forecasting discrete time series while estimating ecologically relevant nonlinear predictor associations. Our Bayesian latent factor approach will be particularly useful for exploring competing dynamic ecological models that encompass hierarchical smoothing structures while providing forecasts with robust uncertainties, tasks that are becoming increasingly important in applied ecology.

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Section: Introductionmentioning

confidence: 99%

“…Moreover, ecological observations are almost always multivariate when contextual information is considered. These features make it difficult to analyse ecological time series while sufficiently accounting for the various systematic time series components and possible multivariate relationships (Auger-Méthé et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Dynamic Generalised Additive Models (DGAM) for forecasting discrete ecological time series

Clark

Wells

2022

Preprint

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“…Finally, in addition to differences in how location error can be modeled and estimated, there are also differences in how these error models are propagated through movement analyses. The most convenient and approximate correction is to “smooth” the data (Auger-Méthé et al, 2021)—which involves calculating predictions of the true locations, conditional on the entire track—before feeding the smoothed data into movement analyses that assume no location error. However, as smoothing does not fully resolve the true locations, there will be a degree of bias and unpropagated uncertainty in the smoothed analysis (for some comparisons, see Noonan et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

A comprehensive framework for handling location error in animal tracking data

Fleming

Drescher‐Lehman

Noonan

et al. 2020

Preprint

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Animal tracking data are being collected more frequently, in greater detail, and on smaller taxa than ever before. These data hold the promise to increase the relevance of animal movement for understanding ecological processes, but this potential will only be fully realized if their accompanying location error is properly addressed. Historically, coarsely-sampled movement data have proved invaluable for understanding large scale processes (e.g., home range, habitat selection, etc.), but modern fine-scale data promise to unlock far more ecological information. While location error can often be ignored in coarsely sampled data, fine-scale data require much more care, and tools to do this have been lacking. Current approaches to dealing with location error largely fall into two categories—either discarding the least accurate location estimates prior to analysis or simultaneously fitting movement and error parameters in a hidden-state model. Unfortunately, both of these approaches have serious flaws. Here, we provide a general framework to account for location error in the analysis of animal tracking data, so that their potential can be unlocked. We apply our error-model-selection framework to 190 GPS, cellular, and acoustic devices representing 27 models from 14 manufacturers. Collectively, these devices are used to track a wide range of animal species comprising birds, fish, reptiles, and mammals of different sizes and with different behaviors, in urban, suburban, and wild settings. Then, using empirical data on tracked individuals from multiple species, we provide an overview of modern, error-informed movement analyses, including continuous-time path reconstruction, home-range distribution, home-range overlap, speed and distance estimation. Adding to these techniques, we introduce new error-informed estimators for outlier detection and autocorrelation visualization. We furthermore demonstrate how error-informed analyses on calibrated tracking data can be necessary to ensure that estimates are accurate and insensitive to location error, and allow researchers to use all of their data. Because error-induced biases depend on so many factors—sampling schedule, movement characteristics, tracking device, habitat, etc.—differential bias can easily confound biological inference and lead researchers to draw false conclusions.

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“…To calibrate such models using biological parameters that have uncertainty associated with them (e.g., estimated abundances, with confidence intervals or standard error), statistical tools that account for uncertainty are required to derive robust results. State Space Models (SSM) are an appropriate statistical framework for this [ 17 – 19 ]. A SSM contains two linked components: a “process model” that describes in our case how the true but unknown population sizes change over time and an “observation model” that describes how the true population sizes are linked to the observations.…”

Section: Introductionmentioning

confidence: 99%

“…Both components have model parameters: the process model parameters govern the population dynamics while the observation model parameters describe any bias and uncertainty in the observations. SSMs are often implemented in a Bayesian framework, where informative prior distributions can be specified for the model parameters, reflecting biological knowledge on their possible values [ 17 – 19 ].…”

Section: Introductionmentioning

confidence: 99%

Alternative method for assessment of southwestern Atlantic humpback whale population status

et al. 2021

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The population of humpback whales (Megaptera novaeangliae) wintering off eastern South America was exploited by commercial whaling almost to the point of extinction in the mid-twentieth century. Since cessation of whaling in the 1970s it is recovering, but the timing and level of recovery is uncertain. We implemented a Bayesian population dynamics model describing the population’s trajectory from 1901 and projecting it to 2040 to revise a previous population status assessment that used Sampling-Importance-Resampling in a Bayesian framework. Using our alternative method for model fitting (Markov chain Monte Carlo), which is more widely accessible to ecologists, we replicate a “base case scenario” to verify the effect on model results, and introduce additional data to update the status assessment. Our approach allowed us to widen the previous informative prior on carrying capacity to better reflect scientific uncertainty around historical population levels. The updated model provided more precise estimates for population sizes over the period considered (1901–2040) and suggests that carrying capacity (K: median 22,882, mean 22,948, 95% credible interval [CI] 22,711–23,545) and minimum population size (N1958: median 305, mean 319, 95% CI 271–444) might be lower than previously estimated (K: median 24,558, mean 25,110, 95% CI 22,791–31,118; N1958: median 503, mean 850, 95% CI 159–3,943). However, posterior 95% credible intervals of parameters in the updated model overlap those of the previous study. Our approach provides an accessible framework for investigating the status of depleted animal populations for which information is available on historical mortality (e.g., catches) and intermittent estimates of population size and/or trend.

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A guide to state–space modeling of ecological time series

Cited by 130 publications

References 208 publications

Dynamic Generalised Additive Models (DGAM) for forecasting discrete ecological time series

Dynamic Generalised Additive Models (DGAM) for forecasting discrete ecological time series

A comprehensive framework for handling location error in animal tracking data

Alternative method for assessment of southwestern Atlantic humpback whale population status

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