Dynamic generalised additive models (DGAMs) for forecasting discrete ecological time series

Abstract

1. 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.2. 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.3. 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. 4. 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..

Synthesizing forecasts to inform decision‐making and advance ecological theory

“…Examples include modelling non‐linearities in response variables, modelling unobserved variables, and quantifying uncertainty. Many of the papers in this special feature deal with these ubiquitous challenges of forecasting, but address them with a range of modelling approaches from machine learning (Clark & Wells, 2023; Lapeyrolerie & Boettiger, 2022) to process‐based models (Cameron et al, 2022). To illustrate this, we consider how some of the papers in this special feature approach estimates of unobserved variables or uncertainty with myriad approaches.…”

“…linear extrapolations) or fail to capture temporal dependence (Zurell et al, 2012). To overcome these shortcomings of GAMs for forecasting, Clark and Wells (2023) An alternative approach to compensating for unobserved variables with process noise is empirical dynamic modelling (EDM) that stems from dynamical systems theory and employs time delays as surrogates for missing data in a non-parametric framework.…”

“…Given this complexity, it is seldom possible to acquire data on all relevant variables needed for an ecological forecast. Clark and Wells (2023) forecast abundances of single and multiple species beyond the range of observed data by modelling unobserved dynamic components in an extension of generalized additive models (GAMs). GAMs are a popular choice for modelling time series because of their ability to describe smooth, nonlinear relationships between predictor and response variables.…”

“…linear extrapolations) or fail to capture temporal dependence (Zurell et al, 2012). To overcome these shortcomings of GAMs for forecasting, Clark and Wells (2023) present dynamic generalized additive models (DGAMs) that jointly estimate the GAM linear predictor and unobserved dynamic components to model an evolving time series for the cases of both univariate and multivariate response variables. Examples with simulations and empirical data on ticks from the EFI NEON forecasting challenge illustrate the utility of DGAMs for forecasting discrete ecological time series, and an r package mvgam with worked examples makes the use of this approach accessible.…”

“…Given this complexity, it is seldom possible to acquire data on all relevant variables needed for an ecological forecast. Clark and Wells (2023) forecast abundances of single and multiple species beyond the range of observed data by modelling unobserved dynamic components in an extension of generalized additive models (GAMs).…”