2005 ), also require the relationships of traits to fitness and of trade-offs among
traits used in optimality modelling. However, adaptive dynamics can be distin-
guished from classical life-history theory by its different fitness concept, regard-
ing it as the ability of a phenotypic strategy to invade and persist in a population
with realistic dynamics, i.e. frequency and density dependence. For instance,
the optimal life history can change as population size varies, depending on
which life-history phase (juveniles, adults) and which processes (growth, mortal-
ity) are most affected by density. Adaptive dynamics theory typically assumes an
initially very rare mutation that codes for a trait value that is different from that
in the initial population of ‘residents’. Fitness then refers to the ability of the
mutation to ‘invade’ the population. Metz, Nisbet and Geritz ( 1992 ) formulated
this as the average exponential growth rate of the invader, growing in the
environment set by the resident. The models thus identify the evolutionarily
unbeatable strategy, which is able to invade the population, taking account of
the extent to which the fitness function, termed the invasion fitness, is depend-
ent on trait frequencies and population densities (Mylius & Diekmann, 1995 ;
Waxman & Gavrilets, 2005 ).Methodological issues
Determining trade-offs
In trade-offs, investment in a trait can affect more than one other trait (Sibly &
Calow, 1983 ): egg size, for example, can affect fecundity rates, mortality and
growth rate of young, and development time of egg and juvenile. However,
optimality models of life-history evolution usually deal with one trade-off at a
time, presumably because this is both mathematically more tractable and more
manageable for conducting empirical tests (though possibly at the expense of
rigour). Knowing the shape of trade-offs is important for identifying life histo-
ries that are best adapted to particular environments. However, we still await
accurate quantification of trade-offs, which has proved difficult because they
should ideally be measured among individuals provided with the same resour-
ces, and which differ only in genes coding for one trait (e.g. offspring size). An
alternative is to manipulate a trait and observe its consequences although this,
too, is challenging, as it can be difficult to simulate alternative genotypes by
manipulating the phenotype. When manipulating traits it is important, for
instance, to ensure that the amount of resources provided to the organism is
not adjusted (Lessells, 1991 ; Atkinson & Thorndyke, 2001 ).Frequency and density dependence
Mylius and Diekmann ( 1995 ) advocated more effort towards accounting for
adaptive dynamics, and argued that ‘the unpleasant fact that we usually know
little about the way density dependence operates in real populations should
not seduce us to pursue an ostrich-policy’. However, measuring selection in36 D. ATKINSON AND A. G. HIRST