When Does Evolution Optimise? On the relation between types of density dependence and evolutionarily stable life history parameters

In this paper we (i) put forward a simple notational device clarifying the, undeniable but generally ignored, role of density dependence in determining evolutionarily stable life histories, (ii) use this device to derive necessary and su#cient conditions for (a) the existence of an evolutionary extremisation principle, and (b) the reduction of such a principle to straight r-orR 0 -maximisation, (iii) use the latter results to analyse a simple concrete example showing that the details of the population dynamical embedding may influence our evolutionary predictions to an unexpected extent. 1 Introduction The literature is replete with statements that evolutionary predictions about behavioural, c.q. life history, parameters should be based on the maximisation of individual lifetime reproductive success, R 0 (Stearns, 1992, Ro#, 1992, Charnov, 1993, Charlesworth, 1994, provide surveys), or else the intrinsic rate of natural increase, r (Stearns, 1992, Ro#, 1992, Charlesworth, 1994, Caswe..