Chapters 5 and 6 deal with the questions which arise when the strategies brought forth by evolution, which we define in terms of non-invasibility, are searched by means of maximizing simple optimization criteria. In other words, when is the fittest (in the environment set by itself) also the best (in a more general sense)?

In chapter 5, I concentrate on monomorphic populations in demographic
steady state, and present three different conditions under which the
evolutionarily stable life-history strategy can be characterized as
the life-history strategy at which a relatively simple function is
maximal. Depending on the way density dependence shapes the
environmental feedback loop, this function can be the individual
lifetime reproductive success (*R*_{0}), the intrinsic rate of natural
increase (*r*), or another quantity from a large range of possible
optimization criteria. I illustrate this by examining the optimal age
at maturity for a hypothetical example organism, showing that the
details of the population dynamical embedding may influence our
evolutionary predictions to an unexpected extent. This analysis is
extended in chapter 6, where I derive necessary and sufficient
conditions for the equivalence between non-invasible strategies and
maxima of optimization functions.

These results show that optimization functions should be
*derived*, using all information available about the precise
way in which density dependence limits population growth, instead of
*assumed*, as is common practice in evolutionary ecology and
life-history theory. If we want to assess the validity of prevalent
optimization functions, more empirical research on mechanisms of
density dependence is of crucial importance.

Taken together, the six chapters demonstrate that it pays to incorporate detailed information concerning individual life-history or population dynamics in an early stage of evolutionary model building. By taking biologically validated approximations, one can still end up with simple models, but with qualitatively different results than from models arrived at in more phenomenological ways.

Tue Aug 10 12:25:42 MET DST 1999