Wednesday, August 8, 2007 - 8:20 AM

OOS 27-2: Age from stage and stochasticity

Carol Horvitz, University of Miami and Shripad Tuljapurkar, Stanford University.

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<>  <>The study of stage-structured populations sheds light on the fundamental question of why mortality rate at age x, μ(x) = - log  [ l(x+1)/l(x)], does NOT always increase monotonically with age as predicted by theory.  As previously known, in organisms where demographic rates are recorded for observable, discrete stages, stage-structured matrix projection models of population dynamics contain information about age-specific rates.  Here we provide new insights by tracking dynamic stage structure and one-period stage-specific survival across ages for both constant and variable environments.  The underlying process constitutes a “killed” Markov process, where the mass of the system changes state as it decreases over time.  At each age, the stage structure may change and total cohort survival to the next age is given by a weighted average of stage-specific survivals.  Some stages may eventually drop out; at later ages individuals are reshuffled among the remaining stage classes.  For a cohort, this means that at early ages, transient dynamics rule and anything can happen, meaning that the age pattern of mortality can rise, fall or rise and fall before reaching the asymptotic dynamics as the stage structure approaches a quasi-stationary distribution.  Over the lifetime, mortality may start out higher or lower than the late age plateau and it may overshoot the plateau.  Later, asymptotic dynamics rule and a constant rate of mortality, a plateau, is approached.  We find that in variable environments, an expected long run stochastic sequence of environments has a long run stochastic mortality rate which has not previously been described.  We illustrate these points employing examples of a pine tree, two African grasses and a temperate forest herb using constant environment models and an understory shrub inhabiting forests characterized by hurricane-driven canopy dynamics using a variable environment model. <>


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