  Given a reaction (network) we are looking for minimal sets of species
starting from which all the species will have positive concentrations for all
positive times in the domain of existence of the solution of the induced
kinetic differential equation. We present three algorithms to solve the
problem. The first one essentially checks all the possible subsets of the sets
of species. This can obviously work for only a few dozen species because of
combinatorial explosion. The second one is based on an integer programming
reformulation of the problem. The third one walks around the state space of the
problem in a systematic way and produces all the minimal sets of the
advantageous initial species, and works also for large systems. All the
algorithms rely heavily on the concept of Volpert indices, used earlier for the
decomposition of overall reactions [Kov\'acs \textit{et al., Physical Chemistry
Chemical Physics} 2004, 6, 1236]. Relations to the permanence hypothesis,
possible economic or medical uses of the solution of the problem are analyzed,
and open problems are formulated at the end.
