Empirical Dynamic Modeling of Fish Population Dynamics

Empirical Dynamic Modeling (EDM) has emerged as a powerful, equation-free framework for understanding and forecasting fish population dynamics in complex and nonlinear ecosystems. Unlike traditional parametric approaches that rely on pre-specified functional relationships, EDM reconstructs the underlying dynamics directly from observational time series by embedding data in a multidimensional state space. In this reconstructed attractor manifold, each point represents a system state defined by past observations of fish abundance, age structure, environmental drivers and other relevant variables. Techniques such as Simplex Projection and S-map then exploit local neighbourhoods on this manifold to predict future states, capture state-dependent interactions and quantify causal influences. Convergent Cross Mapping extends this toolbox by testing for direct causal links among variables, revealing how fishing pressure, temperature fluctuations and trophic interactions drive population trajectories. The approach accommodates non-stationarity, regime shifts and stochastic perturbations, offering robust short-term forecasts and mechanistic insights into bifurcations, resilience and tipping points. Applied globally from temperate to tropical fisheries, EDM has informed adaptive management by identifying early-warning signals of declines, quantifying the benefits of age-diverse stock structures and integrating environmental variability into harvest control rules. Its capacity to synthesise multiple interacting drivers underpins more resilient policy design, contributing to sustainable exploitation and conservation of marine resources.

Research from Nature Portfolio

Recent studies have quantified how demographic and environmental factors causally shape spatial variability in marine fish populations. Using 25 years of survey data for North Sea species, researchers applied attractor reconstruction to disentangle the effects of age structure, abundance and ocean temperature on distributional heterogeneity. Findings reveal that truncated age distributions increase spatial patchiness, while warming and spatially uneven temperature fields further amplify variability. Fishing emerges as a dual threat, directly depleting biomass and indirectly altering spatial stability via shifts in age composition. This empirical dynamic analysis underscores the need to incorporate spatial and demographic dimensions into stock assessments and management strategies to safeguard population resilience under climate change.

Empirical Dynamic Modeling of Fish Population Dynamics publication trend

The graph below shows the total number of articles in empirical dynamic modeling of fish population dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Attractor manifold: Geometric reconstruction of a system’s possible states in a multidimensional phase space.

Simplex Projection: Forecasting technique that predicts future states by averaging outcomes of nearest neighbours on the attractor.

S-map: Locally weighted linear mapping method that captures state-dependent relationships and nonlinearities.

Convergent Cross Mapping (CCM): Causal inference tool that assesses whether one variable’s state-space reconstruction can reliably predict another.

State-space reconstruction: Embedding of time series data into multiple lagged coordinates to recover the dynamics of the underlying system.

References

1. Effects of embedded distance measurements interacting with modeling approaches on empirical dynamical model predictions. Ecological Indicators (2023).
2. Causal effects of population dynamics and environmental changes on spatial variability of marine fishes. Nature Communications (2020).
3. Empirical dynamic modeling for beginners. Ecological Research (2017).
4. Environmental variability and fishing effects on the Pacific sardine fisheries in the Gulf of California. Canadian Journal of Fisheries and Aquatic Sciences (2021).
5. The Relationship between Environmental Factors and Catch Abundance of Hairtail in the East China Sea Using Empirical Dynamic Modeling. Fishes (2021).