Environmental variability and fish stock dynamics: a stochastic model of Mahi Mahi abundance

Erika Johanna Martínez-Salinas; Andrés Ríos-Gutiérrez; Viswanathan Arunachalam; John Josephraj Selvaraj; Erika Johanna Martínez-Salinas; Andrés Ríos-Gutiérrez; Viswanathan Arunachalam; John Josephraj Selvaraj

doi:10.3934/mbe.2025115

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 12: 3107-3129. doi: 10.3934/mbe.2025115

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Environmental variability and fish stock dynamics: a stochastic model of Mahi Mahi abundance

1.
Department of Statistics, Universidad Nacional de Colombia, Sede Bogotá, Colombia
2.
School of Mathematics, Universidad Industrial de Santander, Bucaramanga, Colombia
3.
Faculty of Engineering and Administration, Universidad Nacional de Colombia, Sede Palmira, Colombia

Received: 25 July 2025 Revised: 13 October 2025 Accepted: 16 October 2025 Published: 24 October 2025

Climatic factors exert a substantial influence on both biotic and abiotic components of marine ecosystems, significantly affecting the abundance and spatial distribution of fish species. In this study, we introduced a stochastic modeling framework, grounded in stochastic differential equations (SDEs), to analyze the temporal dynamics of sea surface temperature and its relationship with the abundance of Mahi Mahi (Coryphaena hippurus) in a region of the Colombian Pacific coast. Model parameters such as sea surface temperature, fish stock, and catch per unit effort for the period 2000 to 2012 were estimated using the maximum likelihood method, implemented via the Euler–Maruyama numerical scheme. The model's performance was assessed using empirical data through numerical simulation, cross-validation, and sensitivity analysis, demonstrating its applicability and robustness in capturing key ecological dynamics.
- stochastic differential equations,
- Ornstein-Uhlenbeck process,
- catch per unit of effort,
- maximum likelihood estimation,
- Euler-Maruyama method
Citation: Erika Johanna Martínez-Salinas, Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, John Josephraj Selvaraj. Environmental variability and fish stock dynamics: a stochastic model of Mahi Mahi abundance[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 3107-3129. doi: 10.3934/mbe.2025115

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Abstract

Climatic factors exert a substantial influence on both biotic and abiotic components of marine ecosystems, significantly affecting the abundance and spatial distribution of fish species. In this study, we introduced a stochastic modeling framework, grounded in stochastic differential equations (SDEs), to analyze the temporal dynamics of sea surface temperature and its relationship with the abundance of Mahi Mahi (Coryphaena hippurus) in a region of the Colombian Pacific coast. Model parameters such as sea surface temperature, fish stock, and catch per unit effort for the period 2000 to 2012 were estimated using the maximum likelihood method, implemented via the Euler–Maruyama numerical scheme. The model's performance was assessed using empirical data through numerical simulation, cross-validation, and sensitivity analysis, demonstrating its applicability and robustness in capturing key ecological dynamics.

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