A New Perspective to Fish Trajectory Imputation: A Methodology for Spatiotemporal Modeling of Acoustically Tagged Fish Data

The focus of this paper is a key component of a methodology for understanding, interpolating, and predicting fish movement patterns based on spatiotemporal data recorded by spatially static acoustic receivers. Unlike GPS trackers which emit satellite signals from the animal’s location, acoustic receivers are akin to stationary motion sensors that record movements within their detection range. Thus, for periods of time, fish may be far from the receivers, resulting in the absence of observations. The lack of information on the fish’s location for extended time periods poses challenges to the understanding of fish movement patterns, and hence, the identification of proper statistical inference frameworks for modeling the trajectories. As the initial step in our methodology, in this paper, we devise and implement a simulation-based imputation strategy that relies on both Markov chain and random-walk principles to enhance our dataset over time. This methodology will be generalizable and applicable to all fish species with similar migration patterns or data with similar structures due to the use of static acoustic receivers.

💡 Research Summary

This paper addresses a critical gap in the analysis of fish movement data collected via static underwater acoustic receivers, which unlike GPS tags provide only intermittent, spatially sparse detections. The authors propose a simulation‑based imputation framework that blends Markov chain principles with random‑walk dynamics to reconstruct full daily trajectories for acoustically tagged fish. The methodology is built around two distinct probabilistic components. First, when a fish is detected within a receiver’s effective radius (≈500 m), its exact location is treated as a draw from a bivariate normal distribution centered at the receiver’s coordinates with isotropic variance σ_R², reflecting the decreasing detection probability with distance. Second, for periods when the fish is outside any detection zone, the model generates a sequence of intermediate positions by iteratively updating direction and distance. The remaining distance to the next observed point is denoted d_{jt} and serves as the mean of a normal distribution for the step length D_{jt}, whose variance decays according to a power‑law parameter φ as the fish approaches the target. Directional uncertainty ψ_{jt} is modeled with an initial variance γ that decays exponentially with rate α for short gaps (n_j ≤ β) and switches to a uniform distribution for longer gaps (n_j > β), thereby capturing both purposeful movement toward the endpoint and exploratory “curiosity” behavior.

Mathematically, the authors derive the joint likelihood for a single observation segment by multiplying the density of the observed endpoints (P₀) with the product over unobserved steps of the conditional densities for position updates (P₁) and step‑length draws (P₂). A second‑order Taylor expansion approximates the distribution of the directional unit vector, enabling a closed‑form expression for P₁. Extending this to all K segments of a fish’s trajectory yields a full joint distribution that can be evaluated for any simulated path.

The empirical component uses a dataset of cobia (Rachycentron canadum) tagged between 2014 and 2020 along the U.S. East Coast, focusing on 48 receivers deployed in the Chesapeake Bay region. Daily time steps are adopted to reduce sparsity, and the model is calibrated to the known detection radius and receiver locations. Through Monte‑Carlo simulation, the authors generate many plausible daily trajectories for each fish, then construct a 90 % heat‑map of the most likely paths. The visualizations demonstrate that the imputed routes fill the gaps between detections in a biologically reasonable manner, especially in areas where receivers are widely spaced.

The paper concludes by highlighting the novelty of a dedicated probabilistic imputation scheme for static acoustic telemetry, noting its potential extensions: Bayesian inference for parameter uncertainty, incorporation of environmental covariates (e.g., temperature, currents), and real‑time trajectory updating. Limitations are acknowledged, including the assumption of identical detection variance across receivers, the simplistic distance‑only mean for step lengths, and the need for sensitivity analyses of the behavioral parameters (γ, α, β, φ). Overall, the study provides a solid statistical foundation for reconstructing fish movement from highly irregular acoustic data, paving the way for more accurate ecological inference and management decisions.