Figure 6.1 Population growth in two genotypes with clonal reproduction, starting out with equal numbers of individuals and therefore equal proportions in the total population. Genotype A grows 3% per generation (X = 1.03) and genotype B grows 1% per generation (X = 1.01). (a) Individuals of both genotypes increase in number over time. (b) Because the genotypes grow at different rates, their relative proportions in the total population change over time. The solid line shows the initial equal proportions. Eventually, genotype A will approach 100% and genotype B 0% of the total population. Values are plotted for every third generation.

where NA + NB is the total population size. Figure 6.1a shows numbers of individuals over time for an example where genotype A grows faster than genotype B. In absolute numbers of individuals, the population sizes of both genotypes increase over time. However, the proportion of the population made up of individuals with A and B genotypes changes over time in the population (Fig. 6.1b). Since the A genotype grows faster, A individuals represent an increasing proportion of the individuals in the total population. This is equivalent to saying that p increases over time while q decreases over time. Thus, Fig. 6.1 shows a case of natural selection favoring the A genotype since it has a higher level of absolute fitness.

An alternative way to represent the changing proportions of the two genotypes in the population is to follow the ratio of the number of A and B individuals, Na/Nb, over time. The value of the ratio at any point in time will depend on the initial numbers of A and B individuals (call them NA(0) and NB(0)), the growth rates of the two genotypes, and the number of generations that have elapsed. The ratio Nb/Na after one generation of population growth is given by

which is akin to dividing a version of equation 6.1 for genotype A by a version of equation 6.1 for genotype B. In general, we can predict the ratio of NA/NB at any time t using

by assuming that genotype-specific growth rates (XA and XB) remain constant through time.

The ratio of genotype-specific growth rates is called the relative fitness and is represented by the symbol w in models of natural selection with discrete generations. Substituting the relative fitness for the ratio of the genotype-specific growth rates in equation 6.5 gives

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