Abstract
The steady state distribution of age structure is studied for populations with two age classes and stochastic vital rates. For a serially uncorrelated dichotomic vital rate the distribution of age structure is found analytically to be a singular steplike function; outside a specific region of vital rate values the singular function crosses a threshold to a smooth function. For a vital rate following a correlated two state Markov process the joint distributions of age structure and environment are found analytically to be singular steplike functions; again a threshold marks a transition to a smooth function. For fecundities which are serially uncorrelated but continuously distributed the age structure distribution is obtained as a smooth analytic function for all parameter values. These explicit results have applications to studies of age structure and average growth rate.
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Tuljapurkar, S. Demography in stochastic environments. I. Exact distributions of age structure. J. Math. Biology 19, 335–350 (1984). https://doi.org/10.1007/BF00277104
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DOI: https://doi.org/10.1007/BF00277104