Movement toward stability as a fundamental principle of population dynamics

Although convergence to stability is typically a complex and irregular process, the Kullback distance provides a measure that moves consistently to 0 as a population becomes stable. The roots of the Kullback distance are in information theory, but it is a meaningful demographic quantity. It reflects a population's log momentum, or the amount of growth built into a population's nonstable age distribution. The rate at which the Kullback distance moves toward 0 is neither constant nor monotonic. At any point in time, however, it decreases by the covariance between a population's age-specific growth rates and its log momentum. Although the present findings are couched in terms of movement toward stability, they are generally applicable because they relate to the behavior of any population at any instant. It is a fundamental principle of population dynamics that a population is always moving toward the stable population implied by its prevailing fertility and mortality rates, and that the extent of its movement is determined by the covariance between its age-specific growth and its log momentum.