Synchronization of life cycles by collective transport and emergence of supercycles

A model of physiological age, accompanied by nonlinear diffusion in space, is studied analytically and numerically, and is shown to develop nonstationary traveling population waves. A window of intermediate growth rates is found where collective supercycles are formed from individual (stochastic) life cycles. Supercycle periods can be considerably different (larger or smaller) than the average longevities of contributing individuals, while the time-averaged spatial expansion rate has a local maximum in the supercycling mode. A method of adiabatic similarity solutions is used to derive dependencies of the solution parameters on source and sink inhomogeneities, and obtain closed coupled dynamic equations for the age structure and leading and trailing fronts. Analytical results are compared with numerically computed similarity and full solutions for several types of population waves. We discuss possible model applications to development of lichen thallus, multiyear patterns of agricultural crop yields, and autocorrelation of locust swarming.