Mathematical Modeling to Estimate the Effect of Probiotics on the Growth of Andinoacara rivulatus in a Biofloc System

Andinoacara rivulatus, known as vieja azul, is a species native to Ecuador with great ecological and productive relevance. However, its population has declined due to overexploitation and habitat degradation. The incorporation of probiotics in fish farming is an important advancement, with multiple potential benefits, since it favors both fish growth and the stability of the aquatic ecosystem. The present study evaluated the influence of probiotics on the growth of Andinoacara rivulatus and water quality in a Biofloc system, using mathematical modeling to analyze biometric relationships. An experiment with five treatments (T1-T5) was developed in a biofloc system, under a triplicate factorial design, where fish were kept for 30 days. Probiotics with different compositions were applied, and biometric and physicochemical parameters of the water were monitored. The results indicated that the T5 treatment promoted the greatest growth of the fish, with a median height of 3.4cm, compared to 1.1cm in the control (T1). Likewise, the weight-length and weight-perimeter opercular relationship was higher in T5, coinciding with better feed conversion. In contrast, the T3 treatment optimized water quality, registered lower concentrations of TAN (0.99 ± 0.11mg/ L) and BOD (9.12 ± 0.20mg/ L), compared to the control treatment, whose TAN was 1.38 ± 0.08mg/ L and BOD (12.43 ± 0.95mg/ L). In addition, T3 presented the highest electrical conductivity (175.62 ± 0.81μS/ cm), suggesting higher microbial activity in the system. Mathematical modeling allowed characterizing growth using allometric equations, determining that T5 favored positive growth, while T3 contributed to the sustainability of the ecosystem. It is concluded that, although T5 optimizes zootechnical performance, T3 is more efficient in maintaining adequate physicochemical parameters. Therefore, probiotic selection should consider both fish development and the stability of the aquatic environment.