Sensitivity of stochastic growth rate and lifetime reproductive output to kin effects: A nonlinear feedback model

Humans exhibit a coevolutionary relationship between the trajectory of social evolution and senescence. A focal individual's kinship network is a function of his/her life history, while that network in turn shapes the focal individual's life history through kin effects on reproduction, generating a dynamic, nonlinear feedback loop across the population. Assessing directional selection on kin effects, therefore, requires explicitly modelling the feedback between the kinship network and life history. Here, we develop such a framework and apply it to examine selection pressures on the cooperative behaviour of closely related kin, including mothers, grandmothers, and older sisters. We hypothesise that the negative association of grandmothers, mothers, and older sisters (>10 years) with child mortality are under positive selection because increasing the absolute values of these kin effects would increase the stochastic growth rate. Furthermore, we hypothesise that the positive association of older sisters with child mortality is subject to negative selection, as increasing this effect would reduce the stochastic growth rate. We estimate kin-specific slope coefficients for child mortality using a Bayesian hierarchical model and solve a system of nonlinear equations linking kinship structure and survival to account for the nonlinear feedback between kinship and child survival. Thereafter, we compute stochastic sensitivities of both the stochastic growth rate and the mean lifetime reproductive output to these slope coefficients. Consistent with our hypotheses, all slope coefficients for kin presence on child mortality are negatively sensitive to both fitness metrics. We discuss the applications of our framework to examine the coevolution of social behaviours and senescence in age-structured populations.