The elements of food web stability

One of the most pressing issues in ecology lies in the identification of structures within food webs that are associated with stability.  Numerous mechanisms have been proposed through empirical, experimental, and theoretical studies (e.g. weak interactions, loop weight, compartmentation, vertical energy flux, and diversity).  Here, we propose a simplified geometrical categorization of these stabilizing mechanisms.  By plotting the graphical representation of the potential range of eigen values (such as the Gershgorin circles), the stabilizing properties of given mechanisms can be readily interpreted. For example, both decreased maximum loop weight and decreased vertical energy flux have both been associated with increased food web stability.  Both of these food web properties can also be geometrically represented as decreasing the potential range of eigen values in the complex plane.  The strength of this approach is that it allows for a consistent framework in addressing the influence of significant food web characteristics such as omnivory, mutualism and diversity on food web stability.  Harnessing similar geometrical rules, we reinterpret previous theory from a unified perspective.