This work presents an abstract approach of a mathematical analysis of the evolution of a species. A mathematical model is proposed as well that characterizes the natural evolutive phenomena. On the basis of this model, and setting the adequate constraints, it is developed an proved the convergency of a new computational evolutionary algorithm, applied to minimizing (or maximizing) a costs function that meets certain requirements. Simulation studies are carried out in order to validate the theoretical aspects and to evaluate the performance of the evolutionary algorithm.