Fitness in Age-structured Populations

A population that contains individuals of different ages will quickly settle into a stable age distribution. This greatly simplifies their description and leads to a simple measure of fitness. We illustrate this principle with data from a Drosophila population.

Adult females are almost certain to survive for 25 days, but they are almost all dead after 50 days (green line in Fig. WN17.1A). Egg production shows a similar pattern (Fig. WN17.1B). An adult female is expected to produce 1500 eggs over her whole lifetime. Thus, if the population is to remain at a steady size, the chance of survival from egg to newly emerged adult must be 2/1500 = 0.13%. (The factor of 2 arises because only half of all eggs will be females.) We assume that development from egg to adult takes 10 days.

Now, suppose that the populations starts with 10,000 eggs. The population size will decline as larvae die (Fig. WN17.1C, left). However, once adult females emerge and lay eggs themselves, numbers increase rapidly. After a few months of fluctuations, the population settles to an equilibrium with approximately 1150 individuals. Figure WN17.1D shows how the distribution of ages of adult flies changes through time. For the first 50 days, the cohort that founded the population survives and is seen as a spike in the top three panels (t = 0, 20, and 40 days). The smooth distribution that emerges from the left represents their offspring; after about 100 days, this settles to a steady age distribution (Fig. WN17.1D, bottom row, t = 120, 140, and 160 days).

Now, suppose that a new allele invades the population at low frequency (purple line in Figure WN17.1C). Females that are heterozygous for this allele survive less well but produce more eggs when young (purple lines in Fig. WN17.1A,B). Over their lifetime, they produce 13% more eggs. As long as the new allele is rare, we can follow its increase as if it were a separate population evolving in the environment determined by the common genotype. Again, numbers fluctuate erratically as the age distribution settles down to a steady state. Eventually, however, the numbers of the rare allele increase exponentially at 0.5% per day. (On the logarithmic scale of Fig. WN17.1C, this appears as a straight line increasing with a slope of 0.005 per day.) This long-term rate of increase of 0.5% per day is the best measure of the fitness of the new genotype.