Ecosystem Stability: Admissibility and Persistence in Ecological Systems

Ecosystems consist of interacting biological organisms, environmental conditions, and resource flows that together form dynamic ecological systems. This paper interprets ecosystem stability within the Paton System framework as a condition governed by admissibility constraints. Ecological systems remain stable when the interactions between species, resources, and environmental conditions remain within structural limits that allow continued system persistence. When ecological pressures exceed these limits, instability may appear in the form of population collapse, trophic imbalance, or ecosystem failure. Ecosystem stability therefore depends on maintaining compatibility between biological populations and the environmental constraints that support them. Biological populations must remain within the resource limits of their environments, while ecological interaction networks must remain compatible with environmental conditions such as climate, habitat capacity, and nutrient availability. Disruptions including biodiversity loss, invasive species, habitat degradation, or environmental change may push ecological systems beyond admissible stability thresholds. When these limits are exceeded, ecosystems may experience cascading instability or collapse. By interpreting ecological systems through admissibility boundaries, the Paton System clarifies how ecosystems maintain persistence under environmental variability and why collapse occurs when ecological limits are exceeded.