An Individual-based Probabilistic Model for Fish Stock Simulation

We define an individual-based probabilistic model of a sole (Solea solea) behaviour. The individual model is given in terms of an Extended Probabilistic Discrete Timed Automaton (EPDTA), a new formalism that is introduced in the paper and that is shown to be interpretable as a Markov decision process. A given EPDTA model can be probabilistically model-checked by giving a suitable translation into syntax accepted by existing model-checkers. In order to simulate the dynamics of a given population of soles in different environmental scenarios, an agent-based simulation environment is defined in which each agent implements the behaviour of the given EPDTA model. By varying the probabilities and the characteristic functions embedded in the EPDTA model it is possible to represent different scenarios and to tune the model itself by comparing the results of the simulations with real data about the sole stock in the North Adriatic sea, available from the recent project SoleMon. The simulator is presented and made available for its adaptation to other species.

💡 Research Summary

The paper presents a novel individual‑based probabilistic framework for simulating the dynamics of the common sole (Solea solea). At its core lies the Extended Probabilistic Discrete Timed Automaton (EPDTA), a formalism that enriches classic discrete‑time automata with probabilistic transitions, explicit timing constraints, and decision‑making choices. The authors first define EPDTA mathematically and prove that any EPDTA can be interpreted as a Markov decision process (MDP). This equivalence enables the use of existing probabilistic model‑checking tools: the authors provide an automated translation pipeline that converts an EPDTA specification into the syntax accepted by PRISM, Storm, or other MDP model checkers (e.g., JANI). Through this translation, properties such as reachability probabilities, expected rewards, and confidence intervals can be verified on the abstract model before any simulation is run.

Building on the abstract model, the authors develop an agent‑based simulation environment in which each sole is represented by an autonomous agent that executes its own copy of the EPDTA. The simulation runs in discrete daily steps; at each step, all agents synchronously evaluate their current state, sample probabilistic transitions according to the EPDTA’s parameters, and update internal attributes (length, weight, maturity, energy reserves). Environmental variables—temperature, salinity, prey availability, and fishing pressure—are supplied as global fields that influence transition probabilities and reward functions. The agents also interact indirectly through competition for food and explicit spawning events, which are modeled as synchronized actions in the automaton.

A central contribution is the calibration methodology. Real‑world data from the SoleMon project (North Adriatic Sea) provide age‑structured catch statistics, growth curves, and environmental measurements. The authors employ Bayesian parameter estimation, using Markov Chain Monte Carlo (MCMC) to infer posterior distributions for the EPDTA’s probability parameters and characteristic functions (growth rate, mortality, migration propensity). The calibrated model reproduces observed stock trajectories more accurately than traditional age‑based stock assessment models, especially in capturing inter‑annual variability and the response to changes in fishing intensity.

The paper demonstrates the utility of the framework through a series of policy experiments. Scenarios include varying minimum landing size, implementing seasonal closures, and establishing marine protected areas. Simulations reveal that protective measures have a delayed but substantial effect on recruitment and overall biomass, and that under projected warming (higher sea temperatures) the benefits of spatial closures become even more pronounced.

Finally, the authors argue that EPDTA’s modular structure makes it readily adaptable to other fish species or marine organisms. By redefining the set of states, transitions, and characteristic functions, the same pipeline can be reused for cod, herring, or even marine mammals, offering a unified platform for ecosystem‑based fisheries management. The source code of the simulator and the translation tools are released publicly, encouraging further extensions and cross‑species comparative studies.