We discuss two special cases of population dynamics with changing vital rates subject to the constraint NRR = I and consider the specifics of ergodicity and stationarity. By restricting the number of age groups to two, we can make explicit the way weak ergodicity works. When mortality is constant and the period NRR = I, a life-table stationary population eventually results; everything of demographic interest (except age-specific fertility and the cohort NRR) is asymptotically constant. With changing mortality, but both period and cohort NRR = 1, only weak ergodicity holds, and everything changes over time.

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