A Recursive Algebraic Model for Predicting Tipping Points in Ecosystems

This paper presents an iterative algebraic model aimed at identifying tipping points in ecological and biological systems, accounting for their threshold-based nature which is incompatible with continuous differential equations. The mathematical structure of the model is grounded in Malthusian growth insights, Liebig’s Law of the Minimum, Shelford’s Law of Tolerance, and Holling’s ecological threshold paralleling Bowditch’s Law in bio-systems (the All-or- None principle). Furthermore, the model integrates Vierordt’s concept within ecological immunity and the Fechner-Weber law of stimulus intensity. The model is characterized by its ability to generate complete, instantaneous scenarios for each new data point through automated updates, enabling the determination of the temporal distance to a collapse point should the variable continue to accumulate at a specific rate.