Adaptation and Stability Analysis of the May–Holling–Tanner Model Applied to the Anchovy–Pelican System in the Humboldt Current

Abstract

This work adapts a non-linear model with a ratio-dependent functional response to analyze the trophic interaction between the Peruvian anchoveta (Engraulis ringens) and the Peruvian pelican (Pelecanus thagus) in the Humboldt Current ecosystem. Beyond classifying local stability, the study introduces the estimation of the characteristic recovery time τ≈1/ λdom based on the dominant eigenvalue, allowing for the quantification of the system's dynamic resilience. Under baseline conditions, a stable node is obtained with approx λdom ≈-0.10, implying a recovery time of nearly 10 years. Under a severe El Niño scenario (r = 0.15, c = 2.0), the dominant eigenvalue approaches 0.02, extending the recovery time to approximately 50 years and reducing the Jacobian determinant by 89%. Although formal stability is maintained, a significant degradation of the dynamic margin is evident. This study allows for the detection of structural fragility before an observable collapse occurs, providing an additional quantitative criterion for ecological resilience assessment.