Here are the figures I used in lecture on Friday, March 27, to talk about the statistical predictions for the outcomes of genetic drift.
Figure 1 shows the changes in allele frequency due to drift in 24 different populations, each of size N = 9 (2N = 18). The graphs show the changes in allele frequency (the changes in the number of A alleles) over time. Each graph is a separate trial. The graph in your lab (Figure 1.) will be essentially like this, except that you will graph all three trials on the same grid. In the lab manual, the y axis is FREQUENCY of A allele, not NUMBER of A alleles as in the figure below.
What is the take-home message? Populations diverge from one another as a result of genetic drift.
The following figure shows the effect of population size (N) on the divergence and the rate of fixation of populations. In this figure, multiple trials with the same N are plotted on top of one another on the same graph grid. The differences shown here (top graph has N = 9; lower graph has N = 50) would be analogous to the differences you saw in your lab between Experiment 1 (where N=2) and Experiment 2 (N = 8). Where N is larger, divergence occurs more slowly, and average time to fixation is slower. However, no matter WHAT N is, if the population is finite in size and no other factors (mutation, selection, etc) are operating on the population, sooner or later every population goes to fixation. This means that, over evolutionary time, mutation is crucial to keep generating new variation on which evolution can work. Without mutation, variation would blink out of populations as a result of genetic drift.
This process of population divergence due to drift is shown in another way in the next figure. Here, a total of 107 populations of Drosophila, all starting with p = q = 0.5, undergo genetic drift for 19 generations. The height of the bar in each graph (each graph being a generation) indicates the number of populations with that allele frequency. The allele is bw75, which produces brown eye color. From the progeny in each generation, 8 males and 8 females were chosen at random to be the parents of the next generation. The x axis shows the number of bw75 alleles in the population. Population size is N=16, so the x axis goes from 0 to 32 bw alleles. Graph from Hartl, 1980; data from Buri, 1956).
So over all, genetic variability is lost randomly over time through genetic drift. The equation derived by Sewell Wright gives the loss of genetic variation per generation as a function of population size (N, or Ne). That equation is:
change in F (heterozygosity) per generation = 1 / 2 Ne.
The figure below (from Primack, 1997) shows this relationship. The graph
shows the average percentage of genetic variability remaining over 10 generations
in theoretical populations of various population sizes (Ne). After 10 generations,
there is a loss of genetic variation of about 40% with a population size
of 10, 65% with a population size of 5, and 95% with a population size of
2.
Another way of describing the effect of drift is to ask, what is the average
time to fixation or loss of an allele in a drifting population? This time,
in generations, depends on two parameters: the population size N, and the
initial allele frequencies p and q. When p = q = 0.5, there is an equal
chance of going to fixation for either allele. Where allele frequencies
are asymmetrical, the chance of fixation for the common allele is higher
than that for the rare allele. One way to say this is to ask about the "average
persistence of a neutral allele (one which is not under selection) in a
population." As the following figure shows, the average persistance
(the average time till loss) varies with allele frequency, and is measured
(on the y axis) as time in units of N generations until fixation or loss.
The x axis is the initial allele frequency, ranging from 0 to 1.0 When p
= .5 (the middle of the curve) average time to fixation or loss is the highest,
and it is 2.8 N generations.
Finally, you can show this "time to fixation" in another way by
graphing the distribution of population allele frequencies after various
times, where different graphs show the trajectories of a set of populations
with different initial allele frequencies. In the figure below, the graph
on the left is for p = q = .5, and the one on the right is for p =0.1, q=0.9.
The different curves on each graph show the shape of the distribution of
population allele frequencies (like the 107 populations in figure 3 above)
after different numbers of generations. However, populations which have
gone to fixation are dropped from the graph. So as time progresses, a set
of populations which started out genetically identical come to take very
different allele frequencies (they diverge), and the pattern of divergence
depends in part on initial genetic conditions. At t = N/10 in both graphs,
the populations are still clumped around the starting points. By time t
= N, many populations are fixed (the area under the curve is getting smaller)
and the unfixed populations are spread out with a whole spectrum of genetic
states. But when p is rare, even after N generations, few populations have
drifted to where p is now common.
