Qualitative Stability and Digraphs in Model Ecosystems

Roughly speaking, an ecosystem is called q ualitatively stable" when one may conclude solely on the basis of the qualitative effects of member species on each other, that the system is stable. The conditions for qualitative stability are rather severe, particularly for ecosystems with great species diversity. Nonetheless, qualitative stability conditions may be met in nature by very simple ecosystems. In a recent paper, R. M. May (1973) presented necessary but insufficient conditions for qualitative stability. In this report, sufficient conditions are expressed in terms of the food web design viewed as a s igned digraph."