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.