Crossovers that link populations with the same vital rates*

Abstract

This paper looks at relationships that exist among an observed population and its associated model populations by examining “crossover”; points. Crossovers are mean ages where proportional distributions from two populations with the same vital rates intersect, for example curves representing the age distributions of an observed population and its stable counterpart. Crossovers conceptually unify a number of diverse threads in mathematical demography, including generation length, population momentum, and the relationship between a population's stable growth rate and its observed age‐specific growth rates. More specifically, Lotka's length of generation T is the stable‐stationary birth crossover age, and intrinsic growth rate r is equal to the average growth rate of an observed population up to the observed‐stable birth crossover age. The momentum of a population is the ratio of observed to stationary population proportions at the reproductive value function crossover age. Crossovers thus provide useful insights into demographic relationships.

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