  The dynamic theory of inhomogeneous populations developed during the last
decade predicts several essential new dynamic regimes applicable even to the
well-known, simple population models. We show that, in an inhomogeneous
population with a distributed reproduction coefficient, the entire initial
distribution of the coefficient should be used to investigate real population
dynamics. In the general case, neither the average rate of growth nor the
variance or any finite number of moments of the initial distribution is
sufficient to predict the overall population growth. We developed methods for
solving the heterogeneous models and explored the dynamics of the total
population size together with the reproduction coefficient distribution. We
show that, typically, there exists a phase of hyper-exponential growth that
precedes the well-known exponential phase of population growth in a free
regime. The developed formalism is applied to models of global demography and
the problem of population explosion predicted by the known hyperbolic formula
of world population growth. We prove here that the hyperbolic formula presents
an exact solution to the Malthus model with an exponentially distributed
reproduction coefficient and that population explosion is a corollary of
certain implicit unrealistic assumptions. Alternative models of world
population growth are derived; they show a notable phenomenon, a transition
from protracted hyperbolical growth (the phase of hyper-exponential
development) to the brief transitional phase of exponential growth and,
subsequently, to stabilization. The model solutions are consistent with real
data and produce relatively accurate forecasts.
