Explaining the U-Shape of Age-Specific Mortality

Cyrus Chu, Academia Sinica
Ronald Lee, University of California, Berkeley

The age-shape of mortality is U-shaped for many species, declining from birth to sexual maturity, and then rising in adulthood (Finch, 1990; for mammals, see Caughley, 1966). Although there are exceptions, the U-shape is sufficiently common to invite explanation. Here we show why the optimal life history of a species with determinate growth is likely to have this shape, building on a literature which showed these optimal patterns through numerical simulation (Cichon, 1997; Cichon and Kozlowski, 2000). Our approach assumes a physiological technology characterized by a linear budget constraint for energy at each age. We also incorporate intergenerational transfers, so that a young organism can allocate more energy than it produces. Using dynamic programming to solve the optimization problem, we find the forces shaping the optimal age-shape of mortality, and show the conditions under which it will be U-shaped.