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A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is non-zero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI. This article will appear in Bulletin of Mathematical Biology (Springer), 26 pages

Darwinian fitness with respect to the age of maturity (α) in stationary populations can be written as the product of two functions: pre-α survival times the Fisherian reproductive value of an age α (a just mature) individual. This reduces normalizing selection on α to the maximization of a simple product,a twodimensional problem (Charnov in press). I apply this products theorem to α in Pandalid shrimp and compare the results to previous analysis (Roff, 1986) of α in fish.