Empirical Dynamic Model Research Articles

Medium-term prediction of key chemical process parameter trend with small data

Accidents might happen in chemical factories when less experienced operators unreasonably react to emergencies. It is therefore desirable to predict key process parameters early enough to help plant management easily and readily assess the coming risks and take proper actions to avoid them. Some of the predictions are in the time scale of days, if not months. However, such tools are rarely available in the chemical process industry, and often require a large amount of data for modeling. With inspiration from ecological researches, we propose a novel integrated causal analysis multiview embedding(ICAME) algorithm to predict medium-term trends of key chemical process parameters with small datasets. The proposed ICAME is mainly based on empirical dynamic modeling(EDM), a group of time series analysis approaches. Its application in a simulated dataset and a real industrial process demonstrated its advantages on small data over other methods for medium-term trend predictions of chemical process parameters.

The Relationship between Environmental Factors and Catch Abundance of Hairtail in the East China Sea Using Empirical Dynamic Modeling

The East China Sea population of hairtail (Trichiurus lepturus, also known as T. japonicus) is a commercially important element of Chinese fisheries. Hairtail has long been widely exploited. Due to overfishing, however, its production declined over the years. One of solutions to this dilemma is to institute reasonable fishery policies. Generally, skillful short-term and long-term prediction of fish catch is a central tool for guiding the development of fishery policy. Accurate predictions require a comprehensive understanding of the relationship between fluctuations in fish catch and variability in both fishing effort and marine environmental conditions. To investigate the combined impact of fishing effort and marine environments on hairtail catch and to develop models to predict hairtail catch, we applied empirical dynamic modeling (EDM) to data on East China Sea fisheries, including hairtail catch, fishing effort, and marine environmental factors. EDM is an equation-free approach that enables the investigation of various complex systems. We constructed all possible multivariate EDM models to investigate the potential mechanisms affecting hairtail catch. Our analysis demonstrates that all key environmental factors (salinity, summer monsoon, sea surface temperature, precipitation, and power dissipation index of tropical cyclones) have an impact on nutrient supply, which we suggest is the central factor influencing hairtail catch. Finally, our comparison of EDM models with parametric models demonstrates that EDM models overwhelmingly outperform parametric models in analysis of these complex interactions.

Digging out intersexual and meteorological effects on cicada emergence using 10‐year citizen monitoring

Abstract Understanding the mechanisms determining the emergence timing of herbivorous insects is ecologically important. However, little is known about the effect of climatic factors and the presence of conspecific individuals on their emergence in the field. In particular, it is challenging to investigate the seasonal emergence of cicadas because these insects have a long life‐cycle and subterranean larval stages. We assembled a time‐series dataset that consists of daily counts of emerging cicadas together with meteorological factors, using long‐term collection of cicada exuviae by elementary and junior‐high‐school students. We then performed a non‐linear time‐series analysis, empirical dynamic modelling, to identify factors behind the timing of cicada emergence. Our findings are three‐fold: (1) emergence of individuals of the opposite sex constitute a major driver of the number of individuals emerging per day, and this effect is stronger in males than in females, (2) as in other insect species, air temperature consistently affects cicada emergence, but its effects are relatively weak and (3) precipitation and humidity were causally related to emergence. These results are consistent with the theory of sexual selection as well as the fact that it is hard for the subterranean cicada larvae to use information about air temperature. Significantly, the findings are based on long‐term field data collected by non‐expert citizens.

An Empirical Dynamic Model of Trade with Consumer Accumulation

This paper develops a dynamic structural model of trade in which firms slowly accumulate consumers in foreign markets. Estimating the model using export data from individual firms and a particle Markov chain Monte Carlo estimator, the model predicts lower survival rates for new exporters and estimates low entry costs of exporting—less than half of those estimated in the absence of consumer accumulation. Using simulations and out-of-sample predictions, I show that the introduction of such frictions and the reduction in estimated entry costs allow the model to match important facts regarding the aggregate response of international trade to shocks. (JEL D22, F12, F14, L66)

Nonlinear causal analysis reveals an effective water level regulation approach for phytoplankton blooms controlling in reservoirs

Reservoirs are a rapidly increasing water body providing water supply, irrigation, and many other benefits for human societies globally. However, due to changes in hydrological conditions, building reservoirs tends to bring adverse effects such as eutrophication and phytoplankton blooms, reducing the ecosystem service values. This study focuses on using the empirical dynamic modeling (EDM), an emerging approach for nonlinear analysis, to investigate the nonlinear causal relationship of water level fluctuation (WLF) on phytoplankton biomass and then develop a quantitative model guiding effective phytoplankton blooms controlling based on water level regulations in reservoirs. Specifically, with 9-year continued daily observed data in the Three Gorges Reservoir, we examined the causal effects of different WLF parameters on the dynamics of phytoplankton blooms for the first time. We found that the water level change in the past 24 h (ΔWL) has the strongest causal effect on the daily dynamics of phytoplankton biomass among all WLF parameters (ΔWL, |ΔWL|, and the water level), with a time lag of 2 days. Moreover, EDM revealed a nonlinear relationship between ΔWL and daily dynamics of phytoplankton biomass and achieved a successful prediction for the chlorophyll a concentration 2-day ahead. Further scenario analyses found that both the rise and fall of water level will significantly reduce the chlorophyll a concentration when phytoplankton blooms occur. Nevertheless, on the whole, the rising water level has a more substantial effect on phytoplankton blooms than falling the water level. This result reveals that regulating ΔWL is a simple and effective approach in controlling phytoplankton blooms in reservoirs. Our study reported the nonlinear causal effect of ΔWL on the dynamics of chlorophyll a and provided a quantitative approach guiding effective phytoplankton blooms controlling based on the water level regulation, which might have a broad application in algal blooms controlling in reservoirs and similar waterbodies.

Changes in energy and livestock systems largely explain the forest transition in Austria (1830–1910)

Achieving a global forest transition, that is a shift from deforestation to reforestation, is important for climate-change mitigation. Forest transitions are enabled by socioecological processes, including land displacement, agricultural intensification and woodfuel substitution for other energy, but their respective contributions remain poorly understood. Here, by means of a scenario approach we quantify the importance of enabling conditions of the forest transition in Austria between 1830 and 1910 and their overall emissions implications, including the forest carbon sink potential in the hypothetical absence of wood use. We combine historical databases on land use, biomass production and energy use and an empirical dynamic forest growth model to develop five hypothetical counterfactual scenarios. The scenarios assume food and energy consumption in the absence of woodfuel substitution, food imports and three variations of agricultural intensification and assess effects on forest change and carbon balances. We find that the absence of any of the enabling conditions would have completely depleted forest biomass by 1910. Livestock efficiency gains and woodfuel substitution, two rarely discussed drivers of forest change, were equally important as yield increase and land displacement. The cumulative forest sink potential in the absence of any wood extraction throughout the period was found to be about twice the forest carbon stock in 1830. All counterfactual scenarios led to increasing overall emissions, “no woodfuel substitution” being closest to the historical trend. Our work lays the ground for a new typology of forest transitions according to the socioecological processes that enable them.

Tracking changes in behavioural dynamics using prediction error.

Automated analysis of video can now generate extensive time series of pose and motion in freely-moving organisms. This requires new quantitative tools to characterise behavioural dynamics. For the model roundworm Caenorhabditis elegans, body pose can be accurately quantified from video as coordinates in a single low-dimensional space. We focus on this well-established case as an illustrative example and propose a method to reveal subtle variations in behaviour at high time resolution. Our data-driven method, based on empirical dynamic modeling, quantifies behavioural change as prediction error with respect to a time-delay-embedded ‘attractor’ of behavioural dynamics. Because this attractor is constructed from a user-specified reference data set, the approach can be tailored to specific behaviours of interest at the individual or group level. We validate the approach by detecting small changes in the movement dynamics of C. elegans at the initiation and completion of delta turns. We then examine an escape response initiated by an aversive stimulus and find that the method can track return to baseline behaviour in individual worms and reveal variations in the escape response between worms. We suggest that this general approach—defining dynamic behaviours using reference attractors and quantifying dynamic changes using prediction error—may be of broad interest and relevance to behavioural researchers working with video-derived time series.

Coupling of dissolved organic carbon, sulfur and iron cycling in Black Sea sediments over the Holocene and the late Pleistocene: Insights from an empirical dynamic model

An understanding of how the coupled cycles of carbon, iron and sulfur in sediments respond to environmental change throughout Earth history requires the reconstruction of biogeochemical processes over a range of spatial and temporal scales. In this study, sediment cores from the southwestern Black Sea were analyzed to gain insight into past changes in biogeochemical processes with particular focus on the cycling of dissolved organic carbon (DOC). The sediment consists of Late Pleistocene deposits of iron oxide-rich and organic-poor lacustrine sediments, a Holocene sapropel layer deposited after the inflow of saline Mediterranean seawater about 9300 yr BP, and overlying recent marine sediments. The porewaters displayed high concentrations of DOC, acetate, dissolved iron and an extended depth interval over which sulfate and methane were both present. The historical fluctuations of the fluxes of carbon, sulfur and iron species at the seafloor that led to these present-day geochemical profiles, and which cannot be easily interpreted from the measured data alone, were hindcasted with a reaction-transport model. The model suggests that the inflow of Mediterranean seawater impacted the rain rate and reactivity of organic matter reaching the sediments, which shifted the sedimentary redox regimes throughout the Holocene that now are reflected on different lithology units. Organic matter in the sapropel layer is apparently the main source of modern-day accumulations of DOC and acetate, both of which probably sustained subsurface microbial activity throughout the post-glacial period. The ratio between DOC and dissolved inorganic carbon (DIC) flux to the bottom water decreased from ∼40% before the inflow of Mediterranean water to ∼2% at the present day. We suggest that the coexistence of methanogenesis and sulfate reduction was associated with sulfate-reducing bacteria and methanogens sharing common substrates of acetate and lactate and utilizing non-competitive substrates such as methylated compounds in the sapropel layer and in the bottom of modern marine deposits. Intense sulfur and iron cycling mainly took place in the organic-poor freshwater deposits, today characterized by high concentrations of dissolved iron and methane. In contrast to previous studies in similar environments, anaerobic oxidation of methane coupled to the reduction of ferric iron was negligible. The results have broad implications for coastal environments that are currently experiencing deoxygenation and seawater intrusion and also for understanding the role of DOC in the sedimentary carbon cycle.

Dynamic Compressive Strength Tests of Corroded SFRC Exposed to Drying-Wetting Cycles with a 37 mm Diameter SHPB.

This study focuses on the dynamic compression performance of corroded steel fiber-reinforced concrete (SFRC) exposed to drying–wetting chloride cycles by a 37 mm diameter split Hopkinson pressure bar (SHPB) system. Three steel fiber contents (0.5%, 1.0%, 2.0%, by volume) were incorporated into concrete, and samples were subjected to drying–wetting cycles for different corrosion durations (30 days, 60 days, 90 days) after 28 days age. The sample damage mode, stress–strain curve and the dynamic compression performance of corroded SFRC were compared with plain concrete. Through the experimental data, strain-rate effect, fiber reinforcement effect and the corrosion duration influence on the impact compression property of SFRC were identified. The dynamic increase factor results of these samples were compared with the existing models in previous published literature. An empirical dynamic increase factor profile characterization model considering fiber content, corrosion duration and strain-rate is proposed.

Empirical Dynamic Modeling for Low-Altitude UAV Propagation Channels

During the last few years, with the decrease of their sizes and costs, Unmanned Aerial Vehicles (UAVs) became more feasible for their use in general-purpose applications. As an important basis for UAV applications, the Air-to-Ground (A2G) radio propagation channel has gained attention in the channel modeling literature. However, whereas the A2G propagation channel is inherently dynamic (time-varying), the majority of the available models do not consider such a time-variability. This paper proposes a channel multi-path component (MPC) tracking algorithm and shows its ability to analyze the data collected by a real A2G measurement campaign in a suburban environment. Based on the obtained results, a time-varying statistical channel model for A2G communications in realistic suburban scenarios is proposed. The model is able to stochastically characterize parameters related to the birth and time-of-life of the multi-path components (MPCs), as well as their evolution in terms of delay, Doppler frequency or magnitude. Correlation coefficients to relate different channel characteristics are also obtained. Our work shows that the MPCs evolution over time for the UAV A2G channel can be described by simple regular patterns.

Beyond linearity, stability, and equilibrium: The edm package for empirical dynamic modeling and convergent cross-mapping in Stata

How can social and health researchers study complex dynamic systems that function in nonlinear and even chaotic ways? Common methods, such as experiments and equation-based models, may be ill-suited to this task. To address the limitations of existing methods and offer nonparametric tools for characterizing and testing causality in nonlinear dynamic systems, we introduce the edm command in Stata. This command implements three key empirical dynamic modeling (EDM) methods for time series and panel data: 1) simplex projection, which characterizes the dimensionality of a system and the degree to which it appears to function deterministically; 2) S-maps, which quantify the degree of nonlinearity in a system; and 3) convergent cross-mapping, which offers a nonparametric approach to modeling causal effects. We illustrate these methods using simulated data on daily Chicago temperature and crime, showing an effect of temperature on crime but not the reverse. We conclude by discussing how EDM allows checking the assumptions of traditional model-based methods, such as residual autocorrelation tests, and we advocate for EDM because it does not assume linearity, stability, or equilibrium.

Illuminating the intrinsic and extrinsic drivers of ecological stability across scales

AbstractOur knowledge of ecological stability is built on assumptions of scale. These assumptions limit our ability to reach a generalizable and mechanistic understanding of stability under global environmental change. Moving towards a multiscale approach—across space, time and environment—will allow us to better understand the intrinsic (e.g., demographic) and extrinsic (environmental) drivers of ecological stability. In this perspective, we review multiple sources of variation responsible for shaping ecological dynamics, and how scale affects our observation of these dynamics through its confounding effect on drivers of variation in ecosystems. We discuss the effect of temporal scale when combining empirical dynamic modeling with high‐resolution population time series to consider the time‐varying nature of multispecies interaction networks, highlighting interspecific interactions as an intrinsic driver of community dynamics. Next, we examine energy landscape analysis as a method for inferring stability and transience during community assembly and its interaction with spatial scale, emphasizing the intrinsic role of compositional variability in assembly dynamics. We then examine population dynamics at species' range margins and show how considering the interaction between spatial and temporal environmental heterogeneity, an extrinsic driver of population dynamics, can facilitate a nuanced understanding of population expansions, range shifts, and species invasions. Finally, we discuss broadly how the sources of intrinsic and extrinsic variation interact with each other and with spatiotemporal scale to shape ecological dynamics. Better recognition of the scale‐dependent nature of the relationship between drivers of variation and ecological dynamics will be invaluable to illuminate the dynamics influencing ecological stability across scales.

A Visual Analytics Approach for Ecosystem Dynamics based on Empirical Dynamic Modeling.

An important approach for scientific inquiry across many disciplines involves using observational time series data to understand the relationships between key variables to gain mechanistic insights into the underlying rules that govern the given system. In real systems, such as those found in ecology, the relationships between time series variables are generally not static; instead, these relationships are dynamical and change in a nonlinear or state-dependent manner. To further understand such systems, we investigate integrating methods that appropriately characterize these dynamics (i.e., methods that measure interactions as they change with time-varying system states) with visualization techniques that can help analyze the behavior of the system. Here, we focus on empirical dynamic modeling (EDM) as a state-of-the-art method that specifically identifies causal variables and measures changing state-dependent relationships between time series variables. Instead of using approaches centered on parametric equations, EDM is an equation-free approach that studies systems based on their dynamic attractors. We propose a visual analytics system to support the identification and mechanistic interpretation of system states using an EDM-constructed dynamic graph. This work, as detailed in four analysis tasks and demonstrated with a GUI, provides a novel synthesis of EDM and visualization techniques such as brush-link visualization and visual summarization to interpret dynamic graphs representing ecosystem dynamics. We applied our proposed system to ecological simulation data and real data from a marine mesocosm study as two key use cases. Our case studies show that our visual analytics tools support the identification and interpretation of the system state by the user, and enable us to discover both confirmatory and new findings in ecosystem dynamics. Overall, we demonstrated that our system can facilitate an understanding of how systems function beyond the intuitive analysis of high-dimensional information based on specific domain knowledge.

Susceptible host availability modulates climate effects on dengue dynamics.

Experiments and models suggest that climate affects mosquito-borne disease transmission. However, disease transmission involves complex nonlinear interactions between climate and population dynamics, which makes detecting climate drivers at the population level challenging. By analysing incidence data, estimated susceptible population size, and climate data with methods based on nonlinear time series analysis (collectively referred to as empirical dynamic modelling), we identified drivers and their interactive effects on dengue dynamics in San Juan, Puerto Rico. Climatic forcing arose only when susceptible availability was high: temperature and rainfall had net positive and negative effects respectively. By capturing mechanistic, nonlinear and context-dependent effects of population susceptibility, temperature and rainfall on dengue transmission empirically, our model improves forecast skill over recent, state-of-the-art models for dengue incidence. Together, these results provide empirical evidence that the interdependence of host population susceptibility and climate drives dengue dynamics in a nonlinear and complex, yet predictable way.

Empirical dynamic modeling reveals climatic drivers in dynamics of bacillary dysentery epidemics in China

At present, there is still a lack of studies to address the dynamics underlying epidemics of bacillary dysentery (BD), with particular concern on the role of climatic drivers across different regions of a country or the world. The variability of climate domains, non-linear interactions, and covariations of climatic variables pose challenges for explaining the correlation between environment and BD and identifying causal climatic drivers. In this nationwide study involving 31 provincial capital cities in China, we used the empirical dynamic modeling (EDM), which is a framework for nonlinear time series analysis, to explore climate-driven patterns of BD. We first identified possible temperature (i.e. mostly via its seasonality) and relative humidity driving BD dynamics nationally. Then, we used the EDM to estimate the causal intensity of temperature and relative humidity in different latitudes. The results reveal that the combined nonlinear effect of them on BD may be nationwide, but this effect is concealed due to their high correlation in northern regions. We also found an approximately S-shaped relationship between temperature and BD at the population level; while the effects of relative humidity on BD are strongly dependent on environmental details, especially at temperatures above 0 °C. Temperature may potentially mediate and affect the effects of relative humidity on BD. This nationwide study provides a unified explanation for causal climate drivers of BD, regardless of the different climatic domains and epidemic patterns of BD in diverse cities.

Dynamic effects of insect herbivory and climate on tundra shrub growth: Roles of browsing and ramet age

Abstract To predict shrub responses under climate change in tundra, we need to understand how thermal conditions and herbivory contribute to growth. We hypothesise that shrub growth increases with thermal conditions and precipitation, but that this increase is counteracted by insect herbivory, and that these climate–insect herbivory relationships are modified by both browsing and plant age. We use empirical dynamic modelling (EDM) to analyse a 20‐year time series on willow Salix phylicifolia shoot growth, growing degree days, summer precipitation and herbivory from an experiment at forest–tundra ecotone. The experiment includes manipulations of avian and mammal browsing (fences) and ramet age (pruning to rejuvenate willows). Negative effects of insect herbivory on willow shoot growth were intensified during warmer years, whereas increasing precipitation led to reduced effects. Moreover, the effect of insect herbivores on shoot growth varied with ramet age and vertebrate browsing: younger ramets generally experienced less negative insect herbivore effects, whereas ptarmigan browsing was associated with more positive temperature effects on shoot growth, and reindeer browsing with more negative effects of insect herbivory and precipitation. Synthesis. Our findings show that the negative effects of insect herbivory on shoot growth likely intensify under warmer thermal conditions, but that increasing precipitation can counteract these effects. Moreover, changes in thermal conditions, precipitation and vertebrate browsers all have predictable, albeit complex and nonlinear, effects on shrub growth, highlighting the importance of long‐term experimental data and flexible analytical methods such as EDM for characterising climate and community interactions in artic systems.

Temperature is a regulator of leaf production in the family Dipterocarpaceae of equatorial Southeast Asia.

PremiseLeaf phenology is an essential developmental process in trees and an important component in understanding climate change. However, little is known about the regulation of leaf phenology in tropical trees.MethodsTo understand the regulation by temperature of leaf phenology in tropical trees, we performed daily observations of leaf production under rainfall‐independent conditions using saplings of Shorea leprosula and Neobalanocarpus heimii, both species of Dipterocarpaceae, a dominant tree family of Southeast Asia. We analyzed the time‐series data obtained using empirical dynamic modeling (EDM) and conducted growth chamber experiments.ResultsLeaf production by dipterocarps fluctuated in the absence of fluctuation in rainfall, and the peaks of leaf production were more frequent than those of day length, suggesting that leaf production cannot be fully explained by these environmental factors, although they have been proposed as regulators of leaf phenology in dipterocarps. Instead, EDM suggested a causal relationship between temperature and leaf production in dipterocarps. Leaf production by N. heimii saplings in chambers significantly increased when temperature was increased after long‐term low‐temperature treatment. This increase in leaf production was observed even when only nighttime temperature was elevated, suggesting that the effect of temperature on development is not mediated by photosynthesis.ConclusionsBecause seasonal variation in temperature in the tropics is small, effects on leaf phenology have been overlooked. However, our results suggest that temperature is a regulator of leaf phenology in dipterocarps. This information will contribute to better understanding of the effects of climate change in the tropics.

Identification of Shared Spatial Dynamics in Temperature, Salinity, and Ichthyoplankton Community Diversity in the California Current System With Empirical Dynamic Modeling

Identifying spatially shared dynamics is a key component of community ecology studies as they provide evidence of common responses to environmental factors. We apply co-prediction, an empirical dynamic modeling method (EDM), where values in one time series are predicted from another to quantify shared dynamics in the California Cooperative Fishery Oceanographic Investigation (CalCOFI) dataset composed of spatially explicit physical and biological measurements. Co-prediction can arise in the absence of correlation between two time series. The survey dates to 1951 and consists of a semi-regular, fixed-station design off the west coast of the USA. While the California Current is a dynamic system with multiple identified regimes, we found evidence of coherence measured in terms of spatially shared dynamics in salinity, temperature, Shannon index of ichthyoplankton abundance, and single-species ichthyoplankton abundance throughout the CalCOFI survey area. Leave-one-out hindcast skill, without including any knowledge of shared dynamics was significant in 27 stations for salinity data, 36 for temperature data, and 33 for Shannon index (out of 81 total stations). We then constructed composite libraries, in which correlated or co-predicted time series are concatenated to produce denser attractors), to measure the hindcast skill when including knowledge of shared dynamics. While the number of correlated stations was generally higher than the number of co-predicted stations, hindcast skill from composite libraries of correlated stations did not improve much. On the other hand, composite libraries of co-predicted stations had significant leave-one-out hindcast skill in 60 stations for salinity data, 60 for temperature, and 72 for Shannon index. While there were high levels of correlation among stations, co-prediction proved a more robust method of identifying shared dynamics. Shared dynamics were largely concentrated south of Point Conception, considered an oceanographic and biological breakpoint, although in some cases shared dynamics spanned this boundary. Taken together, these results provide a view of the realized spatial structure occurring in the physical and biological dynamics of the California Current.

Ambient temperature and stroke hospitalization: causal analysis with empirical dynamic modelling

Background: In the climate change context, the role of ambient temperature in stroke attack has drawn much research interest. However, prior epidemiologic evidence from mechanistic model-based regressions remains mixed. Inferring causation on these findings is a big challenge. Methods: Here we applied a novel approach, empirical dynamic modeling (EDM), to explore the causality between air temperature and stroke onset in Hong Kong from 2004-2011. EDM, a data-driven analysis scheme using convergent cross mapping (CCM) to detect causal pairs and multivariate S-map to quantify effect strength, is based on state space reconstruction for nonlinear dynamical systems where climate-health relations may accommodate.Results: By comparing with surrogate data to exclude seasonality, CCM determined that daily mean temperature and its deviation from previous week were potential drivers for hemorrhagic stroke (HS) hospitalization. Yet, no significant causal signal was identified for ischemic stroke (IS). S-map further found that daily mean temperatures ranging from 8.8°C to 31.8°C drove HS counts in a negative manner with the protective effect being stronger on warmer days. By contrast, temperature swings within a week showed a positive forcing in HS and a cooling trend may be more adverse than warming scenario. Also, we traced that mean temperature drove HS with delayed effects of 2 to 17 lagged days, while the impact of short-run temperature swings on HS could persist over the lagged period from 6 to 15 days. The strength of temperature-HS link peaked on the closest lag day of exposure. The effect strengths varied through time and by exposure levels, implying the nonlinearities internal to the system.Conclusion and Significance: Our analyses support that HS attack may be more sensitive to temperature condition than IS. We envision this EDM method could offer insights for epidemiologic studies to move beyond correlation when assessing health effects of climatic exposure.

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.