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

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.