  A fissioning organism may purge unrepairable damage by bequeathing it
preferentially to one of its daughters. Using the mathematical formalism of
superprocesses, we propose a flexible class of analytically tractable models
that allow quite general effects of damage on death rates and splitting rates
and similarly general damage segregation mechanisms. We show that, in a
suitable regime, the effects of randomness in damage segregation at fissioning
are indistinguishable from those of randomness in the mechanism of damage
accumulation during the organism's lifetime. Moreover, the optimal population
growth is achieved for a particular finite, non-zero level of combined
randomness from these two sources. In particular, when damage accumulates
deterministically, optimal population growth is achieved by a moderately
unequal division of damage between the daughters. Too little or too much
division is sub-optimal. Connections are drawn both to recent experimental
results on inheritance of damage in protozoans, to theories of the evolution of
aging, and to models of resource division between siblings.
