INTEGRATION OF EVOLUTIONARY FORCES
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:
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
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.
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
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.