Leveraging spatial information to forecast nonlinear ecological dynamics

Abstract

There has been a recent demand for forecasting in ecology, particularly in the field of ecosystem management. Empirical dynamic modelling (EDM), an equation‐free nonlinear forecasting method, is receiving growing attention, but it requires long time series to produce accurate predictions. Though most ecological time series are short, spatial replicates are often available. Here we explore how utilizing available spatial data can improve our ability to forecast ecological dynamics. There are several ways to incorporate spatial information into EDM and not all have been applied in ecology. We compare spatial EDM approaches used in ecology and physics and introduce a flexible Bayesian model that makes use of prior movement information. We test these methods on simulated data generated with three population dynamics models with varying levels of complexity, time series length, spatial symmetry and heterogeneity. Adding spatial data generally improves accuracy, though the best method depends on the spatial process. We applied the methods to empirical fisheries data, highlighting the complexity of real population dynamics. Leveraging spatial data is an effective way to overcome the problem of short ecological time series. Since the best forecasting method depends on the underlying dynamics, we suggest that users apply several in concert and that this may be useful in identifying spatial heterogeneity in dynamics.

Age structure augments the predictive power of time series for fisheries and conservation

“…We found that, in most cases, using age structure in a hierarchical or mixed age modeling approach improved predictive skill of models, both in empirical and simulated data. Our results are consistent with theory, which suggests that lags of additional age classes can stand in for unknown state variables (Munch et al 2017) analogously to incorporating spatial information (Johnson et al 2021) or information from additional species (Ye and Sugihara 2016).…”

“…In reality, if maturation, survival, and growth are not constant (Gulland 1965;Hutchings 1993;Van der Veer et al 2000;Secor 2007;White et al 2014), then the time series of abundance from different ages will not maintain constant proportionality. Previous attempts to use additional information to improve prediction skill of short time series have emphasized that replicate groups (in this case age classes), must be similar enough so that their dynamics are mutually informative, but different enough to provide new information (Ye and Sugihara 2016;Munch et al 2017;Johnson et al 2021). We hypothesized that age-structured time series, in a sufficiently complex system, would contribute new information which will improve forecast skill relative to time series of a single age or total abundance.…”

“…Data-driven approaches like EDM can outperform even correctly specified mechanistic models (Perretti et al 2013). Though only a single time series is needed, EDM has the flexibility to incorporate additional observations from the system, including environmental covariates (Deyle et al 2013;Ye et al 2015;Wasserman et al 2022), additional species (Liu et al 2012;Deyle et al 2016Deyle et al , 2018Ye and Sugihara 2016;Brias and Munch 2021), and spatial information (McNamara et al 2019;Wang et al 2020;Johnson et al 2021).…”

“…There are a few solutions to the challenge of short time series, many of which make use of additional, contemporaneously collected data. For example, data from other species in the ecosystem can be included as predictors (Hsieh et al 2008;Ye and Sugihara 2016;Deyle et al 2018;Kuriyama et al 2020), or data from multiple populations in space can be leveraged (Glaser et al 2014b;Johnson et al 2021). Many population surveys collect information on age-structure in addition to abundance.…”

Southern Ocean Food Web Modelling: Progress, Prognoses, and Future Priorities for Research and Policy Makers

“…Previously, this approach has been limited by requiring longtime series. Recent work shows that integrating an equation free non-linear approach with a Bayesian model can overcome the problem of short ecological time series (Johnson et al, 2020). To many in marine management, this concept is challenging despite recent work demonstrating the utility of this approach to a wide range of topics in marine ecology (Griffith, 2020).…”