Selection leads to an increase in the average fitness of the population. Illustrated by the following example. Recall that the average fitness ("w bar") = wAA p2 + wAa 2pq + waa q2. Now consider the case where p=.2, q= .8 so f(AA)=0.04, f(Aa)=0.32 and f(aa)=0.64. If their respective fitnesses are 1.0, 0.2 and 0.1, then w bar = .04(1)+.32(.2)+.64(.1) = .132. If selection were to continue for a number of generations q would decrease and p would increase. Lets say that we recalculated the average fitness when p=0.8 and q=0.2: thus f(AA)=.64, f(Aa)=.32 and f(aa)=.04 so w bar = .64(1)+.32(.2)+.04(.1)=.708. When will the average fitness reach a maximum? when the deleterious allele (a) is selected out of the population so the only genotype is AA, the most fit genotype. (How would this differ if there was dominance?)

The sickle cell story with a new twist. There are actually more than just two alleles relevant to the sickle cell story. The normal allele (A) and the sickle allele (S) produce the genotypes traditionally considered: AA is normal but susceptible to malaria, AS individuals are not severely debilitated, but they are resistant to malaria, SS individuals are severely affected and rarely survive to reproduce. A third allele (C) results in the following genotypes and phenotypes: AC is normal but susceptible, SC has mild anemia and CC is normal and resistant to malaria. The following approximate fitnesses have been assigned to these genotypes:

Genotype w phenotype
AA 0.9 malarial susceptibility
AS 1.0 malarial resistance
SS 0.2 anemia
AC 0.9 malarial susceptibility
SC 0.7 anemia
CC 1.3 malarial resistance

Bantu speaking people moved into central and western Africa. A slash and burn agriculture opened up habitat for mosquitoes and along with them came Plasmodium the malarial agent. Consider a large population with the above fitness exposed to malaria for the first time. f(A) ~ 1.0 f(S) and f(C) very low, thus all S and C alleles will be in heterozygous states as AC or SC. Virtually No SS or CC genotypes will be present (the product of two very small numbers). Selection will lead to an increase of the S allele due to its higher fitness as a AS heterozygote. Expect no change in the C allele because heterozygotes have equal or lower fitness than other common genotypes. Can't "pass through" the heterozygote stage.

Selection is "short-sighted" cannot "see" the best solution, i.e., the highest fitness state where C goes to fixation. How do we get to the "best" condition?

Consider the effects of population structure: Bantu people establish local breeding groups of small effective population size. This necessarily will bring on some inbreeding which serves to increase homozygotes and decrease heterozygotes. Some CC genotypes will be produced by the chance effects of inbreeding and now the "best" genotype is present in the population and selection can "see" it so the frequency of the C allele increases, and the population would go to fixation for C.

The highest fitness state could not be reached by selection alone; Drift can affect the outcome of selection. This has been conceptualized as an Adaptive landscape:

Pick two allele frequencies, one for the A locus and one for the B locus. This defines a "population" (obviously this would be done in many dimensions for all loci in the genome; only two here for illustration). The population will evolve by selection to the top of the nearest peak. If a population starts with f(A) ~ f(B) ~ 0.2, this population would evolve to the top of the peak at the lower right of the diagram. This is not the highest peak, but selection acts to increase average fitness and can only "see" the nearest peak. If drift due to low effective population size rapidly shifted both f(A) and f(B) to higher frequencies, then the population might be in the "domain of attraction" of the highest peak in the upper right corner.

The population would stop evolving when it reached the top of the highest peak because there is no higher peak to shift to unless the environment changes at which point we would have to redraw the adaptive landscape.

Sewell Wright conceived of this view of evolution and believed that this was a more accurate description of how "real" populations evolved sine most species do have some structure to their populations and experience drift. So there will be a shifting balance between allele frequencies and a shifting balance between drift and selection as the causative agents in evolution. This is the so called shifting balance theory.

Wright envisioned different stages of evolution by shifting balance: 1) Drift in local populations would shift allele frequencies to new values and the demes may evolve up a local peak because the allele frequency in such a deme drifted near the 'domain of attraction' of a peak. The assumption is that without drift, a population on a 'flat' section of the adaptive landscape would not evolve by natural selection, because there would be no fitness variation in a flat region of the landscape. 2) intrademic selection where selection within local populations (demes) would drive the various demes to the top of their nearest peak. Even if several populations were at different "locations" on the adaptive landscape, the highest peak may not be reached. One can invoke stage 2.5 by saying that drift in local populations might move such a population's allele frequency off one peak and into the 'domain of attraction' of an adjacent peak with a different maximum fitness. This peak may be lower or higher than the old one, but after several rounds of drift at least one population may evolve to the top of the highest peak. 3) This (these) high-fitness populations will produce many emigrants and tend to change the other demes' allele frequencies closer to their own as a result of gene flow; this third stage is called interdemic selection (selection among demes); emigration rates are proportional to the extent that the fitness of a given population is greater or less than the average fitness of all populations. When all populations are homogenized to the allele frequencies of maximal fitness a new balance will be achieved and the allele frequencies will be maintained by selection until the environment changes the adaptive landscape. (For empirical support of this theory see Wade and Goodnight, 1991 Science vol. 253 pg. 1015-1018 and a commentary on page 973 by Crow).

Alternative way to view the shifting balance theory: consider a surface with troughs and pits in it. Put several marbles on the surface. If marble is near pit it falls in selection ~ gravity. Shake surface and balls will roll up out of pits against gravity and make their way to new pit. Shaking ~ drift. See figures 8.8-8.11, pgs. 215-219.

Before discussing the shifting balance view of evolution we considered selection as if it were acting on a single locus. This is a gross oversimplification because many loci are linked along the chromosome. Who's to say that selection is acting the same way on both loci? Things get much more interesting (but more complicated) when we face the reality of linked loci. Consider the cross between the two two-locus genotypes:

The offspring can be AB/AB, AB/ab or ab/ab. Other two locus genotypes are possible: or . But these can only be produced in the cross if there is recombination between the two loci. We can thus refer to four two-locus gametes AB and ab are the coupling gametes and aB and Ab are the repulsion gametes (another way to think about gametes is to just refer to them as a "chromosome" since this will reflect the linear array of whatever alleles are linked together). The frequency of these four gametes will be determined by two things 1) the frequencies of the respective alleles (p and q for the A locus and a different p and q for the B locus) and 2) the degree of linkage disequilibrium which describes whether recombination has broken up any association between the two linked loci.

When allele frequencies all = 0.5 and all gametes are in equal frequency then f(AB) = f(ab) = f(Ab) = f(aB). But if A alleles tend to be associated (linked) to B alleles then AB gametes will be in higher frequency than expected at random. We can quantify the disequilibrium as follows:

D = [f(AB) f(ab)] - [f(Ab) f(aB)]. (Note frequencies are multiplied) When all gametes are in equal frequency D = 0 i.e., linkage equilibrium. When only the coupling gametes are present D = 0.25; when only the repulsion gametes are present D = -0.25. If the frequencies of the alleles are less than 0.5, then the maximum value for D will be less than 0.25.

Note that when allele frequencies are different from p = 0.5 = q, the maximum value of D (absolute value)will be less than 0.25. For example if p=0.8, q=0.2 and if only the coupling gametes were in the population then D = 0.16

A worked example: gamete frequencies in 1000 observations: 580 AB's, 140 Ab's, 60 aB's and 280 ab's. Thus f(A) allele = (520+140)/1000 = 0.66 so f(a) = .34. f(B) = (520+60)/1000 = 0.58 so f(b) = 0.42. At random we expect the following gamete frequencies: f(AB) should be .66(.58)1000 = 383. f(Ab) should be .66(.42)1000 = 277. f(aB) should be .34(.58)1000 = 197 and f(ab) should be .34(.42)1000 = 143. These numbers of expected gametes are clearly different from the observed gametes. We can thus calculate the linkage disequilibrium as d = [.52(.28)] - [.14(.06)] = 0.1372. This tells us that the A and B alleles are in linkage disequilibrium.

This disequilibrium will be broken up by recombination and the rate of breakup will be determined by the rate of recombination (see figure 8.2, pg. 202).

Now let's say that the A locus was under selection with A alleles favored. If the A and B loci were in linkage disequilibrium in the coupling state what would happen to the B alleles? They too would be selected for, but not because they were under selection. This is a very important phenomenon in population and evolutionary genetics called hitchhiking. It demonstrates a very important distinction we must make about selection and phenotype: we need to distinguish between selection "of" and selection "for" If the A allele is favored, there is selection for the A allele and selection of the B allele due to its linkage to the A allele (i.e., linkage between the A and B loci).

Now consider the situation where the nose length is the result of interactions between the two loci. In the first case the interaction is additive, in the second case there is epistasis

AA Aa aa AA Aa aa
BB 1 2 3 BB 1 2 3
Bb 2 4 6 Bb 4 6 4
bb 3 6 9 bb 9 6 3

In the first case if we selected for long noses, we would tend to drive the a and b alleles to high frequency. If we selected for long noses in the second case we would tend to drive the A and b alleles to high frequency. The important distinction between these two tables is that in the simple two-locus additive case on the left, heterozygotes at one locus are intermediate between the two homozygotes regardless of the genotype at the other locus. In contrast, the table on the right shows that the relationship between genotype and phenotype at one locus depends on the genotype at the other, interacting locus. In a sense, one locus is modifying the expression of the other locus. If selection were to act in favor of nose length in the right-hand epistatic system, the way alleles "marched to fixation" would be very different.

Now consider how linkage and epistasis can affect the response to selection. In the second case above if there was high linkage disequilibrium so that all we had we AB and ab chromosomes in the population (= AB or ab gametes in the gamete pool), there would be less variation to select on (sizes 1, 6 and 3). Now if there was recombination such that Ab and aB chromosomes were produced, then the full range of phenotypic variation would be exposed (up to 9) and selection would rapidly shift the mean phenotype to longer noses and to high frequency of A and b alleles.

The general point is that loci do not act independently and their response to selection depends critically on their linkage relationships and their interaction with other loci. For the ecologically minded, there are some interesting parallels between community ecology and population genetics: there are an uncountable number of ways that the interacting participants can interact. In community ecology one considers species in a community; in population genetics one considers genes in the genome. The fate of each player depends on the degree to which it is "connected" to the other players in the system. Darwin referred to the complexity of nature as a "tangled bank"; this is very true of the genes within genomes within populations.