  Mathematical theory of selection is developed within the frameworks of
general models of inhomogeneous populations with continuous time. Methods that
allow us to study the distribution dynamics under natural selection and to
construct explicit solutions of the models are developed. All statistical
characteristics of interest, such as the mean values of the fitness or any
trait can be computed effectively, and the results depend in a crucial way on
the initial distribution. The developed theory provides an effective method for
solving selection systems; it reduces the initial complex model to a special
system of ordinary differential equations (the escort system). Applications of
the method to the Price equations are given; the solutions of some particular
inhomogeneous Malthusian, Ricker and logistic-like models used but not solved
in the literature are derived in explicit form.
