  Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks
in which the total biomass is conserved is of vital importance for the
characterization of long-term dynamics of ecological communities. Here, we
introduce a classification scheme for coexistence scenarios in these
conservative LV models and quantify the extinction process by employing the
Pfaffian of the network's interaction matrix. We illustrate our findings on
global stability properties for general systems of four and five species and
find a generalized scaling law for the extinction time.
