Evolutionary Optimality in Structured Systems and its Applications to Biological and Medical Problems

The well known to specialist in the field of mathematical biology principle of evolutionary optimality, rising to darvinian concept of natural selection, which is based upon mechanisms of survival of the most strong is formulated. Expressed in term of stability of established equilibria in model system, this principle allows to generalize it to the systems, which can be described by mathematical models, including both integro-and partial differential equations. In the presented article the ways to use the author’s evolutionary optimality theory, which initially was constructed for the dynamical systems in Banach spaces, for to find the selection functional, which are to be optimized, for several structured biological systems are indicated. Particularly it is shown that in the case of communities with age and with spatial structure the constructed functionals have a real biological interpretation. As a practical application of the constructed theory the central result of the theory of correlation adaptometry is formulated.

evolutionary optimality, stability, selection functionals, correlation adaptometry