What question did this study set out to answer?

This research aims to develop a mathematical model for assessing fish populations under uncertain conditions.

February 21, 2026

A Multi‐Factor Uncertain Model for Fishery Stock Assessment With Application to Pacific Halibut

Key Points

This research aims to develop a mathematical model for assessing fish populations under uncertain conditions.
Articulated a mathematical framework for fish population dynamics.
Derived a multi-factor uncertain fishing equation considering fluctuating mortality and growth rates.
Provided applications for first hitting time, supremum, and infimum analysis.
Utilized a residual-based approach for parameter inference.
Established that the fish population size exists uniquely under the new framework.
Provided an explicit expression of the inverse uncertainty distribution.
Demonstrated applications show how the model can assess various aspects of fish population dynamics.

Abstract

ABSTRACT A mathematical framework for multi‐factor uncertain fishing is first articulated to model fish population dynamics. Assuming that both the additional mortality rate and natural growth rate fluctuate, we derive a multi‐factor uncertain fishing equation. Then we prove that the fish population size exists and is unique. The explicit expression of the inverse uncertainty distribution is given. Furthermore, we provide three applications of the solution, namely, the first hitting time, the supremum, and the infimum. Finally, the method of moments, a residual‐based approach, is utilized for parameter inference.

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