Understanding the ways populations evolve: genetic drift and natural selection and population
genetics.
Read chapter 6 of your text.
We saw in chapter 5 that a cross between two individuals heterozygous for a dominant allele produces a
3:1 ratio of individuals expressing the dominant phenotype: to those expressing the recessive
phenotype.
For example brachydachtyly (shortening of the digits) displays this pattern of inheritance. Brachydactyly
is a malformation or shortening of the digits and is inherited as a dominant trait. BB and Bb individuals
show malformed or shortened fingers, whereas bb individuals have normal fingers.
Population genetics
In the early 1900’s when Mendel’s work was rediscovered there was confusion about how these simple
patterns of inheritance affected populations.
Why, for example, were not 3 of every 4 people a person with brachdactyly? Why did dominant alleles
not replace recessive alleles?
The confusion stemmed from confusing what was happening at the level of the individual with what
occurs at the population level.
Individual-level thinking enables us to figure out the result of particular crosses. So, for example, we can
figure out what gametes and what genotypes of offspring are produced from particular crosses. Using
the brachydactyly example we can see that a cross between two Bb heterozygotes would produce on
average 25% BB offspring, 50% Bb offspring and 25% bb offspring. All the BB and Bb offspring (75% of
the total) would have brachydactyly. The reason 75% of all people do not have brachdactyly, however,
is that the B allele is rare. As a result, there are very few people who have a copy of the allele (almost
everyone has the genotype bb).
Clearly, to figure out how the genetic characteristics of populations change over time we need to look
not at the results of individual crosses, we need to look at the frequencies of alleles. To do this,
population level thinking is needed. Population-level thinking enables us to figure out quantitatively
what is happening in a population as a result of evolution. Remember, evolution occurs when genotype
frequencies change over time, i.e. from one generation to the next.
Population genetics is the study of the frequency distribution of alleles in populations and the causes of
allele frequency changes
Key terminology
Diploid individuals carry two alleles at every locus. A locus is the physical location on a chromosome
where a gene is found
Homozygous: the two alleles are the same. Heterozygous: the two alleles are different
Remember Evolution: is the change in allele frequencies from one generation to the next
The Hardy-Weinberg equilibrium model serves as the fundamental null model in population genetics
Null models provide us with a baseline expectation. They tell us what we expect to be the case if certain
forces are not operating.
The Hardy-Weinberg equilibrium tells us what we expect to happen to genotype and allele frequencies
when forces such as natural selection are not operating on a population. In other words, the HardyWeinberg model enables us to determine what allele and genotype frequencies we would expect to find
in a population if all that is happening is alleles are being randomly assigned to gametes when gametes
are made (during meiosis) and those gametes meet up at random.
The Hardy-Weinberg model examines a situation in which there is one gene with two alleles A1 and A2.
Recall that alleles are different versions of a gene.
There are three possible genotypes A1A1,, A2 A2 and A1 A2
Hardy and Weinberg used their model to predict what would happen to allele frequencies and genotype
frequencies in a population in the absence of any evolutionary forces.
Their model produced three important conclusions
The three conclusions of the H-W model. In the absence of evolutionary processes acting on them:
1. The frequencies of the alleles A1 and A2 do not change over time.
2. If we know the allele frequencies in a population we can predict the expected genotype frequencies
(frequencies of A1A1, A2 A2,and A1 A2).
3. A gene not initially at H-W equilibrium will reach H-W equilibrium in one generation. This results from
the fact that sexual reproduction thoroughly mixes alleles and rearranges genotypes in a single
generation.
Assumptions of Hardy-Weinberg
1. No selection.
If individuals with certain genotypes survived better than others, allele frequencies would change from
one generation to the next.
2. No mutation
If new alleles were produced by mutation or alleles mutated at different rates, allele frequencies would
change from one generation to the next.
3. No migration
Movement of individuals in or out of a population would alter allele and genotype frequencies.
4. Large population size.
Population is large enough that chance plays no role. Eggs and sperm collide at same frequencies as the
actual frequencies of p and q. If this assumption was violated and by chance some individuals
contributed more alleles than others to the next generation, then allele frequencies might change. This
mechanism of allele frequency change is called Genetic Drift.
5. Individuals select mates at random.
Individuals do not prefer to mate with individuals of a certain genotype. If this assumption is violated
allele frequencies will not change, but genotype frequencies might.
Deriving the H-W model
We assume that parents combine their gametes (gamete means a sex cell -- egg or sperm) into a single
large gamete pool and that pairs of gametes are drawn at random from that pool.
Obviously, this is not what actually happens in nature. However, in a large population in which
individuals choose their mates at random (i.e. do not take the genotype of their mate into account when
picking a mate) statistically speaking what happens as a result of lots and lots of random independent
mate choice decisions is equivalent to all the gametes being thrown into a single pool and random
drawing of gametes occurring. Using this approach, the frequencies of the offspring genotypes
produced are equal to those expected if the parental generation were to simply combine their gametes
into one large gamete pool, from which pairs of gametes are drawn at random to form new offspring.
Working with the Hardy-Weinberg Equilibrium
Assume two alleles A1 and A2 with known frequencies (e.g. A1 = 0.6, A2 = 0.4.). These are the only two
alleles in the population so their allele frequencies must add up to 1.
We can predict frequencies of genotypes we expect to find in the next generation using these allele
frequencies.
There are only three possible genotypes we can make using the two alleles: A1A1 , A1A2 and A2A2
We assume alleles A1 and A2 enter eggs and sperm in proportion to their frequency in population (i.e.
0.6 and 0.4). We also assume sperm and eggs meet at random (one big gene pool).
Then we can calculate genotype frequencies.
A1A1 : To produce an A1A1 individual, egg and sperm must each contain an A1 allele. This probability is
0.6 x 0.6 or 0.36 (probability sperm contains A1 times probability egg contains A1). Conceptually what is
happening here is that you are drawing two gametes at random from the gene pool. As 60% of gametes
contain an A1 allele you have a 0.6 probability of drawing an egg that contains an A1 allele. Similarly, you
have a 0.6 probability of drawing a sperm that contains an A1 allele. The chance of both of these two
independent events occurring is determined by multiplying their individual probabilities together which
is 0.6 x 0.6 = 0.36.
Similarly, we can calculate the frequency of individuals with the A2A2. genotype. This is 0.4 x 04 = 0.16.
The probability of an individual being a heterozygote (A1A2) is given by the probability the sperm
contains an A1 allele (0.6) times the probability that the egg contains an A2 allele (0.4). This is 0.6 x 04 =
0.24.
But, there’s a second way to produce an A1A2 individual (in the second case the egg contains A1 and the
sperm contains A2). Same probability calculation as before gives us 0.6 x 0.4= 0.24.
To calculate the overall probability of producing a heterozygote we have to add together the individual
probabilities for the two ways to make a heterozygote. Therefore the overall probability of an individual
being a heterozygote A1A2 is the sum of the two probabilities which is 0.24 + 0.24 = 0.48.
Therefore, the expected genotype frequencies in next generation are:
A1A1 = 0.36
A1A2 = 0.48
A2 A2= 0.16
Notice that these three genotype frequencies add up to one.
General formula for Hardy-Weinberg.
Let p= frequency of allele A1 and q = frequency of allele A2.
p2 + 2pq + q2 = 1.
Hardy Weinberg Equilibrium with more than 2 alleles
If three alleles with frequencies P1, P2 and P3 such that P1 + P2 + P3 = 1
Then genotype frequencies given by:
P12 + P22 + P32 + 2P1P2 + 2P1 P3 + 2P2P3
Conclusions from Hardy-Weinberg
Allele frequencies in a population will not change from one generation to the next just as a result of
assortment of alleles and zygote formation.
If the allele frequencies in a gene pool with two alleles are given by p and q, the genotype frequencies
will be given by p2, 2pq, and q2.
The frequencies of the different genotypes are a function of the frequencies of the underlying alleles.
The closer the allele frequencies are to 0.5 the greater the frequency of heterozygotes.
Working with the H-W equation
You need to be able to work with the Hardy-Weinberg equation.
For example, if 9 of 100 individuals in a population suffer from a homozygous recessive disorder can
you calculate the frequency of the disease causing allele? Can you calculate how many heterozygotes
are in the population?
p2 + 2pq + q2 = 1. The terms in the equation represent the frequencies of individual genotypes.
P and q are allele frequencies. It is vital that you understand this difference.
9 of 100 (frequency = 0.09) of individuals are homozygotes. What term in the H-W equation is that equal
to? It’s q2.
If q2 = 0.09, what’s q? Get square root of q2, which is 0.3.
If q=0.3 then p=0.7. Now plug p and q into equation to calculate frequencies of other genotypes.
p2 = (0.7)(0.7) = 0.49
2pq = 2 (0.3)(0.7) = 0.42
Number of heterozygotes = 0.42 times population size = (0.42)(100) = 42.
There are three alleles in a population A1, A2 and A3 whose frequencies respectively are 0.2, 0.2 and 0.6
and there are 100 individuals in the population.
How many A1A2 heterozygotes will there be in the population?
Just use the formulae P1 + P2 + P3 = 1 and P12 + P22 + P32 + 2P1P2 + 2P1 P3 + 2P2P3 = 1
Then substitute in the appropriate values for the appropriate term
2P1P2 = 2(0.2)(0.2) = 0.08 or 8 people out of 100.
Remember that the Hardy Weinberg equilibrium principle identifies the forces that can cause evolution.
If a population is not in H-W equilibrium then one or more of the five assumptions is being violated.