Inclusive fitness forces of selection in an age-structured population

Hamilton's force of selection acting against age-specific mortality is constant and maximal prior to the age of first reproduction, before declining to zero at the age of last reproduction. The force of selection acting on age-specific reproduction declines monotonically from birth in a growing or stationary population. Central to these results is the assumption that individuals do not interact with one another. This assumption is violated in social organisms, where an individual's survival and/or reproduction may shape the inclusive fitness of other group members. Yet, it remains unclear how the forces of selection might be modified when inclusive fitness, rather than population growth rate, is considered the appropriate metric for fitness. Here, we derive such inclusive fitness forces of selection, and show that selection on age-specific survival is not always constant before maturity, and can remain above zero in post-reproductive age classes. We also show how the force of selection on age-specific reproduction does not always decline monotonically from birth, but instead depends on the balance of costs and benefits of increasing reproduction to both direct and indirect fitness. Our theoretical framework provides an opportunity to expand our understanding of senescence across social species.