  We introduce a methodology to study the possible matter flows of an ecosystem
defined by observational biomass data and realistic biological constraints. The
flows belong to a polyhedron in a multi dimensional space making statistical
exploration difficult in practice; instead, we propose to solve a convex
optimization problem. Five criteria corresponding to ecological network indices
have been selected to be used as convex goal functions. Numerical results show
that the method is fast and can be used for large systems. Minimum flow
solutions are analyzed using flow decomposition in paths and circuits. Their
consistency is also tested by introducing a system of differential equations
for the biomasses and examining the stability of the biomass fixed point. The
method is illustrated and explained throughout the text on an ecosystem toy
model. It is also applied to realistic food models.
