January 27th, 2010
Bioe 109
Winter 2010
Lecture 9
Microevolution 2 - mutation & migration
Natural selection and mean population fitness
- we can examine what happens to the mean population fitness as natural selection fixes an advantageous allele.
- rather than plotting the frequency of the selected allele over time we can plot how wbar changes.
- when we plot wbar over time as selection acts on a favorable allele we see that natural selection acts in a manner that maximizes mean population fitness (see Box 6.7 in textbook).
- in fact, it cannot do the opposite, i.e., result in a net reduction in fitness.
- what happens when selection does not cause the fixation of the allele, i.e., the case of balancing selection?
- let us now reconsider the case of overdominance.
Genotype:A1A1A1A2A2A2
Fitness (w):w11w12w22
1-s 11-t
- the equilibrium allele frequencies are: A = phat = t/(s + t)
a = qhat = s/(s + t).
- suppose the fitnesses are
Genotype:A1A1A1A2A2A2
Fitness (w):0.90 10.90
- here s and t are both = 0.10.
- the equilibrium frequency of A1 = A2 = 0.50.
- we can plot mean population fitness (wbar) as a function of the frequency of the A1 allele.
- two important conclusions can be drawn.
- first, natural selection results in a maximization of mean population fitness at some intermediate frequency of the two alleles.
- if the frequencies are perturbed from this point, then overdominant selection will return them to this equilibrium point.
- second, the population never realizes its highest possible fitness (i.e., that of the heterozygote = 1) but is maintained at a reduced level because of the maintenance of the polymorphism.
- this is a type of genetic load incurred by the population.
- it is called the segregational load because less fit homozygotes always produced by matings between the most fit heterozygote.
- we will return to the issue of genetic load later in class.
- the concept of mean population fitness has been at the center of an important controversy in evolutionary biology.
- this took place between Sewall Wright and Ronald Fisher and concerned Wright’s shifting balance theory.
- central to this theory is the concept of an adaptive landscape – a multi-dimensional representation of mean population fitness as a function of allele frequencies at multiple loci.
- according to Wright, this surface was covered by many peaks separated by valleys of reduced fitness.
- under this model, natural selection would act to push populations up to local adaptive peaks but not necessarily the highest “global” peak.
- once at a local peak, the population would be stuck – its ability to move across a saddle of lower fitness to reach a higher adaptive peak would be thwarted by selection.
- to circumvent this problem, Wright argued that random genetic drift could act to move populations off local peaks, across valleys, and on to higher adaptive peaks.
- for this process to occur, however, natural populations must be small (so the effects of drift are large) and experience little gene flow.
- in contrast, Fisher viewed natural populations as extremely large and not subdivided to any significant degree.
- according to Fisher, Wright’s model simply wouldn’t work because of the inability of random genetic drift to knock populations off local peaks.
- this controversy persists today as theoreticians continue to explore the feasibility of Wright’s model.
- a nice example where a population can get “stuck” on a lower peak when an adjacent peak of higher fitnesses is present involves sickle-cell hemoglobin.
- in a class last week, this was discussed as a nice example of overdominance.
- however, the situation is more complicated because an other allele occurs at this locus – HbC.
- here are the fitnesses of genotypes including HbC:
GenotypeFitnessPhenotype
AA0.9malarial susceptible
AS1malarial resistant
SS0.2severe anemia
AC0.9malarial susceptible
SC0.7anemia
CC1.3malarial resistant
- the highest mean population fitness would be realized by a population fixed for the C allele.
- why doesn’t this happen?
- because the C allele cannot invade a population at the stable equilibrium point for the A and S alleles because it would have to traverse a valley of reduced fitness (i.e., the AC and SC heterozygotes).
- natural selection will act to oppose any movement off the local AS peak.
- the population could get onto the higher CC peak if inbreeding results in the production of CC homozygotes in a small isolated population, or if random drift happened to cause a higher frequency of the C allele.
Mutation
- mutation is the process that fuels evolution.
- without a continuous influx of mutations into natural populations, genetic variability will eventually be lost and the population will become monomorphic.
- as a process causing evolutionary change at individual loci within natural populations, however, mutation is very inefficient.
- consider a simple case in which we have two alleles at a locus A and a, with frequencies of 0.5 each.
- suppose that the A allele mutates to a at a rate of u = 1 x 10-5.
u
Aa
- this is a typical estimate for a protein coding gene for a new allele causing an amino acid replacement.
- in each generation, the frequency of a is increased by u x p (and conversely the frequency of A is reduced by u x p).
- denoting the change in frequency of a in one generation as q:
q = u x p = u(1-q) = 0.000005.
- the frequency of q has thus increased in one generation to 0.500005.
- at this rate it would take about 70,000 to get the frequency to 0.75, and another 70,000 years to get the frequency to 0.875.
- thus, the rate of change due to mutation pressure is exceedingly small.
- despite this fact, mutation rates are sufficient to generate large pools of genetic variation in natural populations.
- this is because there are many loci capable of mutating and there are typically many individuals in a population in which these new mutations can occur.
Migration/gene flow
- gene flow can be defined as the movement of gametes or individuals among populations.
- unlike selection, drift, and mutation that occur within single populations, gene flow by definition refers to a process that occurs among populations
- gene flow, if unopposed by other factors (i.e., selection, drift, or mutation) will lead to the homogenization of different populations of a species.
- this means that allele frequency differences that existed among the populations will be eliminated by gene flow.
- gene flow is thus the most important process determining what determining population structure.
How rapidly does gene flow occur?
- the magnitude of gene flow is determined by m.
m = the proportion of genes entering a population in individuals
immigrating from other populations
- consider the simplest case of a single population receiving migrants from another population.
- let p1 be the frequency of an allele in the recipient population 1 and p2 be the frequency of the allele in the “donor” population 2.
- let m = the proportion of gene copies in population 1 that originate from population 2.
- thus a fraction 1-m of genes are non-immigrant alleles.
p1’ = p1(1-m) + p2m
= p1 - p1m + p2m
p = p1’ - p1 = m(p2 - p1)
- this tells us that the relative change in frequency in population 1 is determined by the allele frequency difference between population 1 and population 2 and by the level of gene flow.
an example:let p1 = 0.25, p2 = 0.75, and m = 0.001,
then p = 0.0005.
if p1 = 0.25, p2 = 0.75, and m = 0.1,
then p = 0.05.
- these rates of change approach those that we saw for selection.
- gene flow can thus be a very potent force in causing microevolution.
- however, given the above two examples allele frequency differences among populations would be rapidly eliminated.
- if unopposed by selection, gene flow will always result in the elimination of genetic differences between populations.