Life History, Evolution of 635 Static Environments combined population This conclusion does not depend on the two clones beginning with the same population size: differences in starting condition simply accelerate or retard the rate at which clone increases in frequency relative to clone For these two clones, an appropriate measure of fitness is r, since the frequency of the clone with the highest value of r will increase toward unity Thus any mutation in a set of clones that increases r by changing rates of birth or death will increase in frequency in the population There are no difficulties in assigning r as a measure of fitness in the preceding circumstances Difficulties arise, however, when sexual reproduction and age structure are introduced Suppose we have a random mating population in which a mutation arises that increases birthrate or decreases death rate Since the mutant will initially be rare in the population, its fate can be ascertained by considering the birthrates and death rates of the heterozygote alone If the heterozygote’s rate of increase is enhanced, the mutation will increase in frequency in the population, but its ultimate fate depends on the relative birthrates and death rates of the homozygotes and heterozygotes bearing the mutant allele If the homozygote carrying both mutant alleles has a higher birthrate or a lower death rate than the heterozygote, the mutant allele will eventually be fixed in the population; otherwise the population will reach a stable polymorphism The general assumption, stemming from the work of Fisher, has been that r can be associated with genotypes that follow particular life histories and that selection will favor that genotype with the highest value of r In an age-structured population, the rate of increase is obtained by solving the characteristic equation Z N erx lxịmxịdx ẳ ð9Þ A population growing in an unlimited, homogeneous, and constant environment follows the simple exponential growth function where l(x) is the probability of surviving to age x and m(x) is the number of female births at age x The discrete time equivalent of this is Figure Distributions of the genetic correlation between Morphological traits (M Â M) and Life History traits L Â L history components, the best example being Fisher’s Malthusian parameter r Local measures assume that maximization of a fitness component will also maximize the overall fitness of the organism: for example, a common local measure used in foraging theory is the net rate of energy intake This is an appropriate measure if it can be shown that maximizing this rate does not detrimentally affect other components of fitness, in which case maximizing net rate of energy intake will also increase global fitness Local measures are generally tailored for the particular analysis under consideration, but there now exists a general consensus, and more important sound theoretical rationale, of what global measures are likely maximized by natural selection dNtị ẳ rNtị dt N X erx lxịmxị ¼ ð10Þ x¼1 NðtÞ ¼ Nð0Þert ð6Þ where N(t) is population size at time t and r is the intrinsic rate of increase, comprising the difference between instantaneous rates of birth and death Equation can also be written as Ntị ẳ N0ịer ịt ẳ N0ịlt 7ị The symbol l is called the finite rate of increase and is sometimes used instead of r Suppose there are two clones with population sizes, N1(t) and N2(t), respectively, the first with an intrinsic rate of increase of r1 and the second with r2, with r14r2 The ratio of population sizes after some time t, given that both clones start with the same population size is, N1 tị ẳ er1 r2 ịt N2 ðtÞ ð8Þ It is clear that as time progresses this ratio will increase, clone becoming numerically more and more dominant in the Note that in the discrete version the initial age is subscripted as not The important issue to be considered is the fate of a mutant that increases r Charlesworth demonstrated that to a rough approximation the rate of progress of a rare gene eventually becomes directly proportional to its heterozygous effect on r In this case, the probability of survival of a mutant gene of small effect in a near-stationary population is largely determined by its effect on r Following a more detailed analysis, Charlesworth (1994) concluded that for the case of weak selection and random mating with respect to age, the intrinsic rate of increase of a genotype or, more generally, the mean of the male and female intrinsic rates, provides an adequate measure of fitness in a density-independent and constant environment Lande tackled the problem of applying quantitative genetic theory to the evolution of r in a population Assuming weak selection, large population size, and a constant genetic