A life history model of indeterminate growth, somatic maintenance, and negative senescence

Some organisms exhibit declining mortality and increasing fecundity following sexual maturity, a demographic pattern known as negative senescence. According to life history theory, ageing occurs because resources are preferentially allocated to reproduction over somatic maintenance. Models connecting indeterminate growth to negative senescence exist, but none integrate somatic maintenance as a competing allocation decision alongside growth and reproduction. We formulate a life history model in which an individual allocates energy among reproduction, somatic growth, and somatic maintenance and mortality rate depends on both body size and somatic damage. We show that negative actuarial senescence, whereby mortality declines with age, occurs when the proportional change in reproductive value exceeds the proportional change in fitness returns from current investments into reproduction and soma. We derive the necessary conditions for an uninvadable allocation strategy using invasion analysis and Pontryagin's maximum principle, and examine biologically relevant cases numerically. We show that both negative senescence and indeterminate growth arise together as uninvadable outcomes even when maintenance competes for the same resources as growth and reproduction. We show that both diminishing returns to reproduction and diminishing returns to growth can give rise to negative senescence. These results extend the disposable soma theory to organisms with indeterminate growth, in which mortality decreases with size, and identify key mechanisms for the empirically observed association between indeterminate growth and non-senescent demographic trajectories.