the same organizational structure (key elements, methodological issues, eco-
logical applications).Understanding and predicting the evolution of body size
Key elements of life-history theory
Optimality models
Life-history theory attempts to predict the life histories that evolve under partic-
ular selection pressures. Optimality models have been referred to as ‘classical
life-history theory’ (summarized in Roff, 1992 ; Stearns, 1992 , 2000), which pre-
dicts those life histories that will maximize some measure of Darwinian fitness in
a population with stable age structure in particular selective environments. The
key elements are a fitness definition, a relationship of traits to fitness, and trade-
offs among traits.Fitness definition Fitness has been defined in different ways in different life-
history models (see Kozłowski, 1993 ; Mylius & Diekmann, 1995 ; Benton & Grant,
2000 ; Brommer, 2000 ; Brommer, Merila & Kokko, 2002 ; Brommeret al., 2004for
a discussion of alternatives). One widely used fitness measure in classical life-
history theory isr, known as the intrinsic rate of natural increase. This popula-
tion concept can be adopted for individuals or genotypes, such that the genotype
with the highestrwill grow more rapidly than all other genotypes. Maximization
ofris equivalent to maximization of reproductive value at birth (Brommer,
2000 ), which is the number of descendants that a female newborn is expected
to have over her lifetime, discounted by the rate at which the population is
increasing (see below). Reproductive value (V) at birth can be represented as:V¼X
lxmxerx ( 3 : 1 )wherelxis the probability of surviving to agexandmxis the number of offspring
produced at agex: their product when summed over the organism’s lifetime is
lifetime reproductive success (LRS), which can be viewed as the individual
organism analogue of the population-wide measure, net reproductive rate (or
ratio) (Brommeret al., 2002). While it is easy to see the link between LRS of a
genotype and its Darwinian fitness, a discount term is also needed because in an
expanding population offspring produced now are worth more than those
produced in the future, as they themselves can breed sooner. Thus the expo-
nential term at the right of the equation is the discount term, which disappears
in a stationary population asrbecomes zero. This leaves LRS, which is often used
as a fitness measure when no net population growth is assumed.
As the equation for reproductive value can be expanded to incorporate sepa-
rate juvenile and adult phases, with separate mortalities and durations between
life-history events (juvenile development, duration between reproductive
events), it is possible to calculate the combinations of traits that give the same34 D. ATKINSON AND A. G. HIRST