Evolutionary demographic models for mortality plateaus.

Plateaus in the age pattern of hazard functions at extreme ages have been discovered in large populations of medflies, Drosophila, nematodes, and people. Mueller and Rose [(1996) Proc. Natl. Acad. Sci. USA 93, 15249-15253] have proposed several age-structured demographic models to represent effects of mutation accumulation and antagonistic pleiotropy on randomly evolving schedules of demographic rates. They assert that "evolutionary theory [as embodied in their models] predicts late-life mortality plateaus." This paper defines a class of Markovian models that includes those of Mueller and Rose and obtains a characterization of the possible limiting states. For the basic model, the result implies that schedules with late-life mortality plateaus above a minimal threshold are not limiting states. The models fail, but not for reasons previously conjectured. Transient states, visited early by the process, do display mortality plateaus. Other models from this class may have a role to play in reconciling observed plateaus with evolutionary theory.