Evolution is the change in the allele frequencies in a population over time.
Make sure you have a clear understanding of this
Then two scientists Godfrey Hardy and Wilhelm Weinberg went on to develop a simple equation that can be used to discover the probable genotype frequencies in a population and to track their changes from one generation to another. This has become known as the Hardy-Weinberg equilibrium equation. In this equation (p² + 2pq + q² = 1), p is defined as the frequency of the dominant allele and q as the frequency of the recessive allele for a trait controlled by a pair of alleles (A and a). In other words, p equals all of the alleles in individuals who are homozygous dominant (AA) and half of the alleles in people who are heterozygous (Aa) for this trait in a population. In mathematical terms, this is
p = AA + ½Aa
Likewise, q equals all of the alleles in individuals who are homozygous recessive (aa) and the other half of the alleles in people who are heterozygous (Aa).
q = aa + ½Aa
Because there are only two alleles in this case, the frequency of one plus the frequency of the other must equal 100%, which is to say
p + q = 1
Since this is logically true, then the following must also be correct:
p = 1 - q
There were only a few short steps from this knowledge for Hardy and Weinberg to realize that the chances of all possible combinations of alleles occurring randomly is
(p + q)² = 1
or more simply
p² + 2pq + q² = 1
In this equation, p² is the predicted frequency of homozygous dominant (AA) people in a population, 2pq is the predicted frequency of heterozygous (Aa) people, and q² is the predicted frequency of homozygous recessive (aa) ones.
From observations of phenotypes, it is usually only possible to know the frequency of homozygous recessive people, or q² in the equation, since they will not have the dominant trait. Those who express the trait in their phenotype could be either homozygous dominant (p²) or heterozygous (2pq). The Hardy-Weinberg equation allows us to predict which ones they are. Since p = 1 - q and q is known, it is possible to calculate p as well. Knowing p and q, it is a simple matter to plug these values into the Hardy-Weinberg equation (p² + 2pq + q² = 1). This then provides the predicted frequencies of all three genotypes for the selected trait within the population.
As an example, let us say that in a particular
population, there are two versions of a gene (i.e. two alleles) in some proportion (e.g. 0.45 &
0.55). In other words, 45% of the alleles in the population are “A” and 55% are “a.” If the
proportion of alleles in a population changes from the parent generation to the offspring
generation (e.g. from 0.45 & 0.55 ? 0.35 & 0.65), the population is said to have evolved. This
is known as the population genetic definition of evolution, and it can be applied to one gene or to
a combination of many genes.
There are several key points here:
- populations evolve, not individuals
o individuals do change throughout their lives, sometimes quite dramatically
(e.g. butterfly life cycle), but this is not evolution
- evolution is a change in the genetic composition of a population
o variation in a population that is due to non-genetic (i.e. environmental)
causes does not evolve
- evolution occurs across generations
The Hardy-Weinberg Principle is a useful tool for understanding the causes of evolution.
If the assumptions of H-W hold in a particular population, then the H-W principle tells us that
after one generation of random mating, the population will be at equilibrium (i.e. the population
will not change). In other words, the H-W principle tells us what to expect if a population is not
evolving. If any of the assumptions are violated, then allele frequencies may change (i.e. the
population may evolve). Investigation of the assumptions of H-W can help us to identify the
causes of evolution.
THE CAUSES OF EVOLUTION
The following are the five assumptions of the Hardy-Weinberg Equilibrium:
1) random mating within the population
2) no mutation
3) no gene flow (population is isolated from other populations)
4) infinite population size
5) no differential reproductive success
In the following discussion, we will investigate each of these assumptions. Specifically,
we will ask, if the assumption is violated, does a change in allele frequency occur? If a violation
of the assumption does change allele frequency, then it is a cause of evolution.
Assumption 1: Random mating
If mating within a population is not random, it is said to be non-random. There are many
examples of non-random mating. For example, individuals are more likely to breed with other
individuals that are close by, than they are with individuals that are very far away.
Let us take an extreme example of non-random mating (complete inbreeding by selffertilization
in plants) to investigate whether it is a cause of evolution. When a plant pollinates
its own ovules with its own pollen, it is said to have self-fertilized (or “selfed”). This is nonrandom
in that the plant does not mate randomly with any individual, but rather only with itself.
In a population of individuals all heterozygous at some gene (A/a), if all the individuals self,
what will be the genetic composition of the next generation? Here are the results of a selffertilization
cross (the progeny from an individual self-fertilizing), and the resulting population
allelic frequency in the next generation. Here and throughout this section, “p” refers to the
proportion, or frequency of the “A” allele in a population, while “q” refers to the frequency of
the “a” allele:
Results of a Cross by Generation 1 Generation 2
Self-fertilization: Aa x Aa ? 1 AA : 2 Aa : 1 aa
Resulting Population Generation p q
Allele Frequencies: 1 0.5 0.5
2 0.5 0.5
Genotypic frequencies do change from one generation to the next (from all Aa to a ratio
of 1 AA : 2 Aa : 1 aa). However, allele frequencies do not change (p = q = 0.5). Nonrandom
mating, by itself1, is not a cause of evolution (defined as change in allele frequencies); however,
it does change the genetic composition (genotypic frequencies) of the population.
Assumption 2: No Mutation
Mutation can change allele frequencies. As an example, let us start with a population of
50 individuals that are homozygous for a gene (all 50 individuals are AA). If a mutation (A ?
a) occurs in a gamete of one of these individuals, and that gamete is passed on to the next
generation, then the genetic composition of the population has changed across generations:
Generation p q
1 1.0 0
2 0.99 0.01
Mutation is a cause of evolution. However, mutation is a rare event, and therefore does
not greatly affect allele frequencies. It is a cause of evolution, but it is not a very important
cause of evolution. The importance of mutation to evolution is not as a cause of evolution, but
as a mechanism of producing genetic variation within populations.
1 Non-random mating, in conjunction with another cause of evolution (e.g. selection) can be very important to the
evolution of a trait. For example, If a female bird chooses to mate only with males that have long tails, this is nonrandom
mating; however, the female preference is a form of selection, called sexual selection.
Assumption 3: No Gene flow
Gene flow is a cause of evolution. Gene flow (also called migration2) is the movement
of alleles from one population to another. Alleles are moved between populations when animals
disperse to new locations, and when pollen and seeds are blown by wind or moved by water or
animals. As an example, let us say that all the individuals on an island are homozygous for “a”
(aa), while all of the individuals on a continent are homozygous for “A” (AA). Gene flow
between these two populations will change the allele frequencies of both populations:
Island Continent
Generation p q p q
1 0 1.0 1.0 0
2 >0 <1.0 <1.0 >0
Assumption 4: Infinite population size
When populations are finite, sampling errors will occur from one generation to the next.
As an example, we will start with a finite population of ten individuals with the genotypes: 3
AA, 4 Aa, 3 aa, thus with allele frequencies of p = q = 0.5. If all other assumptions of H-W hold
(i.e. random mating, no differential reproductive success, etc.) then what will be the allele
frequencies in the next generation? If you simulate this process with a coin toss (using a fair
coin that has an equal probability of getting a “heads” or a “tails”) and designate a heads toss as a
“A” allele and a tails toss as a “a” allele. Flip a coin to determine the genotypes of individuals in
the next generation (i.e. random mating). With the first two tosses, if you get (heads, heads) this
individual is AA; if you get (heads, tails) or (tails, heads), this individual is Aa; if you get (tails,
tails) this individual is aa. Continue until you have a population of ten individuals, then calculate
the allele frequencies. If you do this a hundred times, then some of the time, you will get p = 0.5
in the next generation. However, there is also a probability that you could get p = 0.4, p = 0.6, p
2 Technically, migration is a pattern of seasonal movement of an animal, such as when birds migrate south for the
winter. This is not the same as gene flow, which is when an animal disperses from its natal population to a different
population, and breeds there. This is more appropriately called “dispersal.”
= 0.3, p = 0.7, etc. In fact, there is some probability of getting any allele frequency from p = 0 to
p = 1.0.
Evolution caused by sampling error is called genetic drift (or random genetic drift),
which are random changes in allele frequency in a population due to the unpredictability of
sampling. Genetic drift is a cause of evolution. Since no population is infinite, genetic drift
occurs in every population. But the effects of genetic drift vary depending on the size of the
population. Small populations are more subject to the effects of drift than are large populations.
This is because, the smaller the sample, the greater the chance of deviation from the expected
frequency (of no change from one generation to the next). Convince yourself of the effect of
genetic drift on population size by doing the following exercise (methods as described in the
previous paragraph): start with a population of 5 individuals (p= 0.5); simulate random mating
by flipping a coin 10 times to get the next generation of individuals; calculate p for the next
generation. Then, do this same experiment with different sized populations (e.g. 5 individuals,
10 individuals, 20 individuals).
Genetic drift can be an important cause of evolution, particularly in small populations
that have recently colonized a new area. The founder effect occurs because the particular
individuals that happen to “found” a new population are unlikely to be a fair genetic
representation of the original population. Some alleles will be over-represented, some alleles
will be under-represented, and some alleles will not be represented at all (lost).
There are many examples of the founder effect in humans. For instance, the
Pennsylvania Amish have descended from a population of only about 200 individuals. One of
these founding individuals happened to have Ellis-van Crevald syndrome, which is a rare type of
dwarfism caused by a single gene. In most populations, the frequency of the allele for this rare
syndrome is: q = 0.001; in the current Pennsylvania Amish population, the frequency is: q =
0.07. This rare syndrome is much more common in the Pennsylvania Amish (70 times as
common), because one of the founding members of the population happened to have the allele
that causes the syndrome.
Assumption 5: No Differential Reproductive Success
The Hardy-Weinberg Principle assumes that there is no differential reproductive success.
In other words, every individual with a certain character state leaves the same number of
offspring as other individuals with a different character state. When there is no differential
reproductive success (along with the other assumptions of H-W) then evolution does not occur.
However, when individuals with different characteristics differ in the number of offspring they
produce, evolution does occur. This is called natural selection.
A famous example of natural selection is industrial melanism. Industrial melanism has
been found in more than 70 moth species, but the best studied is Biston betularia, the peppered
moth. Before the industrial revolution, most of the individuals in B. betularia populations were
the peppered form (speckled white in color), while only a few were melanic (dark black in
color). After the industrial revolution polluted the air and the lichen living on the trunks of trees
died, the melanic form increased to greater than 90%. In unpolluted areas, the peppered form
remained predominant.
Experiments showed that the peppered moths were camouflaged from bird predators on
lichen-covered (unpolluted) trees, while melanics were camouflaged on polluted, dark trees.
Prior to human-caused pollution, individuals with the peppered form survived the best—they
blended with the lichen, and birds could not find them as readily as they could find individuals
that were melanic, which could easily be seen on the lichen. After smog and soot killed the
lichen and the dark tree bark was exposed, the situation changed. Areas with lots of industry had
dark trees, and now the peppered individuals stood out. This suggested that selection by birds
decreased the survivorship of peppered moths on polluted trees. In other words, more peppered
moths were killed and therefore left fewer offspring than melanic moths. Since moth coloration
has a simple genetic basis, when the population changed from mostly peppered to mostly
melanic, the population also changed allele frequencies (from mostly the peppered allele to
mostly the melanic allele). The population had evolved.
The above example is of selection on a discretely varying character: moths are either
peppered or melanic, and this character is determined by variation at one gene. The following is
an example of natural selection acting on a continuously varying character, bill size in Darwin’s
finches, which has a very strong genetic basis (heritability of 0.9, which basically means that
90% of the variation in the population can be attributed to variation in genes, rather than
environment).
Peter and Rosemary Grant have conducted a long-term study on Darwin’s finches
(Geospiza fortis) on the Galapagos Islands. During 1977, there was a severe drought that
changed the relative proportion of seeds on the islands: after the drought, there were far fewer
small seeds, and many more large seeds. Previous work on the finches showed that larger-billed
birds feed more efficiently on large seeds, while smaller-billed birds do better with small seeds.
During the year of the drought, the Grants observed the fate of every bird on the island (several
hundred individually marked individuals) and they noted that birds with smaller beaks starved to
death, while those with bigger beaks survived. In the following year, 1978, the Grants returned
to the island and measured the bill sizes of the surviving population, and found that the
survivors’ bills were significantly larger than those in the previous population (during 1976,
before the drought). Natural selection had favored the birds with larger bills, because they could
feed more efficiently on larger seeds, which were the majority of seeds left after the drought.
This led to a measurable genetic change in the population: more large-billed birds. The
population had evolved. Natural selection was the cause of evolution in both of these
examples.
Quick Reply
