HAMILTON RULE MEETS THE HAMILTONIAN - KIN SELECTION ON DYNAMIC CHARACTERS

Many biological characters of interest are temporal sequences of decis ions. The evolution of such characters is often modelled using dynamic optimization methods such as the maximum principle. A quantity centra l to these analyses is the 'Hamiltonian' function, named after the mat hematician William R. Hamilton. On the other hand, evolutionary models in which individuals interact with relatives are usually based on Ham ilton's rule, named after the evolutionary biologist William D. Hamilt on. In this article we present a generalized maximum principle that in cludes the effects of interactions among relatives and we show that a time-dependent (dynamic) version of Hamilton's rule holds involving th e Hamiltonian. This result brings together the power and generality of both the maximum principle and Hamilton's rule thereby providing a na tural framework for understanding the evolution of 'dynamic' character s under kin selection.