This work presents the analysis of species evolution properties which are considered to design a new evolutionary algorithm for evolvable hardware. These properties reduce the risk of malfunctions in a physical system when it is evolving. A mathematical model, that characterises the natural evolution phenomena of a species, is proposed. A new evolutionary algorithm based on this model is proposed as well. This algorithm is designed to evolve hardware, e.g., to obtain the optimal control parameters of a real control system, while it is executing a repetitive task. The convergence of the proposed algorithm was proven by means of new theorems. Simulations and experimentation studies were carried out in order to validate the theoretical aspects and to evaluate the performance of the evolutionary algorithm. Copyright © 2009 Inderscience Enterprises Ltd.