Demography, class-structure and kin selection in continuous-time models

The Wright-Fisher infinite island model and the neighbour-modulated approach to kin selection have enabled major advances in the understanding of social evolution in a demographic context. Due to structural assumptions, however, some important evolutionary problems are difficult to solve within the Wright-Fisher discrete-time framework. Although these major constraints are relaxed in the Moran continuous-time framework, a formal treatment of the mathematics of kin selection in continuous-time class-structured populations is still lacking. Here, I employ the neighbour-modulated approach to formalise key features of the kin selection theory in continuous-time infinite-island models. Next, I derive a general form of Hamiltons rule to enable an inclusive fitness interpretation of social behaviours. I consider class-structure at the group and individual level, and I focus on conditional and unconditional phenotypes. I illustrate how the general theory can be applied to solve a wide range of biological problems. Finally, I show how a simple extension of the framework allows for the study of problems pertaining to the transmission of parental quality. I show that while inheritance of parental quality may either promote or inhibit selection on conditional helping behaviours, unconditional behaviours are invariant with respect to the fidelity of inheritance.