How To BE FiT 279
Fitness in age-structured populations
In Chapter 3 we defined fitness for the simple case in which individuals reproduce
once and then die (a semelparous life history). Fitness was defined as number of
offspring produced by an individual (taking into account the probability of sur-
viving to reproductive age). For iteroparous species—those in which individuals
reproduce more than once—the lifetime reproductive success is found by adding
up the reproduction over all the ages at which individuals reproduce.
To make the ideas concrete, take the example of an asexual lizard that starts to
reproduce at age 2 and never lives longer than 3 years. We form a life table that
shows the probability that a newborn will live to age x, symbolized as lx, and the
average fecundity for a female at that age, symbolized as mx:x lx mx lx mx
0 1 0 0 .0
1 0.75 0 0 .0
2 0.5 1 0.5
3 0.25 2 0.5
4 0 0 0 .0
R: 1.0The last column of the table gives the product of the survival probability and the
fecundity for the given age, lx mx. By adding those values over all ages, we find the
expected lifetime reproductive success, symbolized as R:R = l 0 m 0 + l 1 m 1 + ... = x∑= 0 lxmx (11.1)In the life table shown above, R = 1. That means each female leaves on average one
descendant, and the population is exactly replacing itself. If R is greater than 1, each
female leaves more than one offspring, and the population size increases. Lifetime
reproductive success is related to the intrinsic rate of increase, symbolized as r, which
is widely used in ecology. If R is near 1 and time is measured in generations, lifetime
reproductive success can be translated into the intrinsic rate of increase by the for-
mula r ≈ ln(R). In a population that is stable in size, R = 1 and r = 0.
Lifetime reproductive success also is closely related to absolute fitness. For val-
ues of R that are near 1, as in this example, lifetime reproductive success is an accu-
rate measure of fitness. But if R is much different than 1, a correction is needed that
gives different weights to offspring born at different ages. We will not go into the
details of the correction (because the math is complicated), but a simple example
illustrates the main point. Consider two asexual lizards that both have a lifetime
reproductive success of R = 2. The first lizard lives 2 years, produces two offspring,
and then dies. The second lizard matures after just 1 year, produces two offspring,
and then dies. Its offspring do the same: each matures after 1 year and has two off-
spring of its own. After 2 years, the first lizard has two descendants, but the second
lizard has four. The genes of the second lizard are spreading more quickly in the
population. It has higher fitness, even though its lifetime reproductive success is
the same as that of the first lizard.
This example illustrates a general principle: in growing populations, natural
selection favors earlier reproduction. No species can have a growing population for
very long because (as Malthus pointed out) it will exhaust the resources it needs.
But some species do spend much of their evolutionary histories in growing popu-
lations. For example, weedy plants specialize on colonizing patches of disturbed
habitat. A new population increases in size rapidly and disperses seeds to other11_EVOL4E_CH11.indd 279 3/22/17 1:11 PM