Viability conditions permit to characterize all processes compatible with given constraints,
notably of available food, so that there exists at least one possibility for the
system to perpetuate itself forever. The concept of contingent cone to a set of
constraints permits to identify two classes of corrections to apply to equations of
natural growth. Usual basic models convey those corrections only in certain regions
of the parameter space. A general model-building stemming from the constraints
is presented. Experimental populations from historical case studies highlight the
mathematical concept of viability corrections.