Introduction
Understanding behavior of fish in aquaculture relies on semi-continuous monitoring, yet obtained data are discrete and often irregular. This study investigates the fish acoustic telemetry RMS acceleration measurements as a stochastic stationary process. Unlike in the wild conditions, where fish behavior is highly variable and nonstationary, captive aquaculture environments should offer stability and predictability. The stability is valid under the assumption of weak stationarity, where the mean and variance of the process remain constant over time. Such conditions is justifying the use of probabilistic model which preserves the statistical characteristics during interpolation to reconstruct the continuous behavior from discrete samples.
Dataset and Methods
The dataset analyzed in this study comprises root mean square (RMS) acceleration values recorded via acoustic telemetry of Atlantic salmon held in captive. The data covers the period of 148 days, with approximately 92,500 values for a single fish. The measurements were taken in non-equidistant intervals ranging from 220 to 380 seconds. The acceleration values range from 0 to 255, with each unit increment corresponding to 0.014 m/s². The acceleration time series is modeled as a causal stochastic system using discrete Markov transition matrices to estimate conditional probabilities between acceleration states. The data passed the tests for weak stationarity (Augmented Dickey-Fuller test), for Markov property (Chapman-Kolmogorov Equation), and for practical differentiability of the autocorrelation function. A Wiener-Levy process was then applied to perform high-resolution interpolation of transition probabilities while preserving the mean and standard deviation of the original distributions.
Results and Discussion
Two levels of continuation tests were performed: one on reduced transitions matrix, and one witht 100× finer resolution. The results demonstrated that the RMS acceleration data from captive Atlantic salmon exhibited weak stationarity and practical differentiability, validating its suitability for modeling as a diffusion system. Transition matrices revealed dominant self-transitions, indicating behavioral stability. The application of the Wiener-Levy process, repeated 1,000 times for each transition, enabled fine-resolution interpolation that preserved statistical properties.
These tests confirmed that the system exhibits the necessary smoothness and continuity properties, validating the use of Wiener-Levy diffusion as a tool to simulate realistic interpolated behavior in fish activity.
Acknowledgment
The study was _supported by the Ministry of Education, Youth and Sports of the Czech Republic - project CENAKVA (LM2018099), the CENAKVA Centre Development (No:CZ:1:05/2:1:00/19:0380) This project also received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement N° 871108 (AQUAEXCEL3.0). This output reflects only the author’s view and the European Union cannot be held responsible for any use that may be made of the information contained therein
References
Urban, J., Lastovka, D. 2025. Fish acoustic telemetry as a diffusion system. Lecture Notes in Bioinformatics, Springer, Cham.