Transcript Population Genetics Evolution by Natural Selection • Unlike Mendel, Charles Darwin made a big splash when his defining work, "On the Origin.

Population Genetics
Evolution by Natural Selection
• Unlike Mendel, Charles Darwin made a big splash when
his defining work, "On the Origin of Species by Means of
Natural Selection, or the Preservation of Favoured
Races in the Struggle for Life" (which we refer to as “The
Origin of Species”) published in 1859.
• Darwin set forth a scientific theory that described how
one species could give rise to another species, given
sufficient time. It was heavily attacked at the time (and
continuing to this day) by people who thought that it
contradicted their religious beliefs. Nevertheless, the
basic theory has survived and flourished, and today it is
one of the main pillars of biological theory.
Fitness
• A fundamental concept in evolutionary theory is “fitness”,
which can defined as the ability to survive and
reproduce. Reproduction is key: to be evolutionarily fit,
an organism must pass its genes on to future
generations.
• Basic idea behind evolution by natural selection: the
more fit individuals contribute more to future generations
than less fit individuals. Thus, the genes found in more
fit individuals ultimately take over the population.
• Natural selection requires 3 basic conditions:
– 1. there must be inherited traits.
– 2. there must be variation in these traits among members of the
species.
– 3. some inherited traits must affect fitness
Genetics of Populations
• Darwin didn’t understand how inheritance worked--Mendel’s work
was still in the future. It wasn’t until the 1930’s when Mendelian
genetics was incorporated into evolutionary theory, in what is called
the “Neo-Darwinian synthesis”.
• Translated into Mendelian terms, the basis for natural selection is
that alleles that increase fitness will increase in frequency in a
population.
• Thus, the main object of study in evolutionary genetics is the
frequency of alleles within a population.
• A “population” is a group of organisms of the same species that
reproduce with each other. There is only one human population: we
all interbreed.
• The “gene pool” is the collection of all the alleles present within a
population.
• We are mostly going to look at frequencies of a single gene, but
population geneticists generally examine many different genes
simultaneously.
Allele and Genotype Frequencies
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Each diploid individual in the population has 2 copies of each gene. The allele
frequency is the proportion of all the genes in the population that are a particular
allele.
The genotype frequency of the proportion of a population that is a particular
genotype.
For example: consider the MN blood group. In a certain population there are 60 MM
individuals, 120 MN individuals, and 20 NN individuals, a total of 200 people.
The genotype frequency of MM is 60/200 = 0.3.
The genotype frequency of MN is 120/200 = 0.6
The genotype frequency of NN is 20/200 = 0.1
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The allele frequencies can be determined by adding the frequency of the homozygote
to 1/2 the frequency of the heterozygote.
The allele frequency of M is 0.3 (freq of MM) + 1/2 * 0.6 (freq of MN) = 0.6
The allele frequency of N is 0.1 + 1/2 * 0.6 = 0.4
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Note that since there are only 2 alleles here, the frequency of N is 1 - freq(M).
Heterozygosity and Polymorphism
• A gene is called “polymorphic” if there is more than 1
allele present in at least 1% of the population. Genes
with only 1 allele in the population are called
“monomorphic”. Some genes have 2 alleles: they are
“dimorphic”.
• In a study of white people from New England, 122
human genes that produced enzymes were examined.
Of these, 51 were monomorphic and 71 where
polymorphic. On the DNA level, a higher percentage of
genes are polymorphic.
• Heterozygosity is the percentage of heterozygotes in a
population. Averaged over the 71 polymorphic genes
mentioned above, the heterozygosity of this population
of humans was 0.067.
Hardy-Weinberg Equilibrium
• Early in the 20th century G.H. Hardy and Wilhelm Weinberg
independently pointed out that under ideal conditions you could
easily predict genotype frequencies from allele frequencies, at least
for a diploid sexually reproducing species such as humans.
• For a dimorphic gene (two alleles, which we will call A and a), the
Hardy-Weinberg equation is based on the binomial distribution:
p2 + 2pq + q2 = 1
where p = frequency of A and q = frequency of a, with p + q = 1.
• p2 is the frequency of AA homozygotes
• 2pq is the frequency of Aa heterozygotes
• q2 is the frequency of aa homozygotes
• H-W can be viewed as an extension of the Punnett square, using
frequencies other than 0.5 for the gamete (allele) frequencies.
Hardy-Weinberg Example
• Taking our previous example population, where
the frequency of M was 0.6 and the frequency of
N was 0.4.
• p2 = freq of MM = (0.6)2 = 0.36
• 2pq = freq of MN - 2 * 0.6 * 0.4 = 0.48
• q2 = freq of NN = (0.4)2 = 0.16
• These H-W expected frequencies don’t match
the observed frequencies. We will examine the
reasons for this soon.
Rare Alleles and Eugenics
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A popular idea early in the 20th century was
“eugenics”, improving the human population through
selective breeding. The idea has been widely
discredited, largely due to the evils of “forced
eugenics” practiced in certain countries before and
during World War 2. We no longer force “genetically
defective” people to be sterilized.
However, note that positive eugenics: encouraging
people to breed with superior partners, is still
practiced in places.
The problem with sterilizing “defectives” is that most
genes that produce a notable genetic diseases are
recessive: only expressed in heterozygotes. If you
only sterilize the homozygotes, you are missing the
vast majority of people who carry the allele.
For example, assume that the frequency of a gene
for a recessive genetic disease is 0.001, a very
typical figure. Thus p = 0.999 and q = 0.001. Thus
p2 = 0.998, 2pq = 0.002, and q2 = 0.000001. The
ratio of heterozygotes (undetected carriers) to
homozygotes (people with the disease) is 2000 to 1:
you are sterilizing only 1/2000 of the people who
carry the defective allele. This is simply not a
workable strategy for improving the gene pool.
Nazi Eugenics
"The Threat of the Underman. It
looks like this: Male criminals
had an average of 4.9 children,
criminal marriage, 4.4 children,
parents of slow learners, 3.5
children, a German family 2.2
children, and a marriage from
the educated circles, 1.9
children."
Estimating Allele Frequencies from
Recessive Homozygote Frequency
• If Hardy-Weinberg equilibrium is assumed (an assumption we will
examine shortly), it is possible to estimate the allele frequencies for
a gene that shows complete dominance even though heterozygotes
can’t be distinguished from the dominant homozygotes.
• The frequency of recessive homozygotes is q2. Thus, the frequency
of the recessive allele is the square root of this. Very simple.
• For example, the recessive genetic disease PKU has a frequency in
the population of about 1 in 10,000. q2 thus equals 0.0001 (10-4).
The square root of this is 0.01 (10-2), which implies that the
frequency of the PKU allele is 0.01 and the frequency of the normal
allele is 0.99. Thus the frequency of the heterozygous genotype is 2
* 0.99 * 0.01 = 0.198. Abut 2% of the population is a carrier of the
PKU allele.
• Note again: this ASSUMES H-W equilibrium, and this assumption is
not always true.
Necessary Conditions for HardyWeinberg Equilibrium
• The relationship between allele frequencies and genotype
frequencies expressed by the H-W equation only holds if these 5
conditions are met. None of them is completely realistic, but all are
met approximately in many populations.
• If a population is not in equilibrium, it takes only 1 generation of
meeting these conditions to bring it into equilibrium. Once in
equilibrium, a population will stay there as long as these conditions
continue to be met.
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1. no new mutations
2. no migration in or out of the population
3. no selection (all genotypes have equal fitness)
4. random mating
5. very large population
Testing for H-W Equilibrium
• If we have a population where we can distinguish all
three genotypes, we can use the chi-square test once
again to see if the population is in H-W equilibrium. The
basic steps:
– 1. Count the numbers of each genotype to get the observed
genotype numbers, then calculate the observed genotype
frequencies.
– 2. Calculate the allele frequencies from the observed genotype
frequencies.
– 3. Calculate the expected genotype frequencies based on the HW equation, then multiply by the total number of offspring to get
expected genotype numbers.
– 4. Calculate the chi-square value using the observed and
expected genotype numbers.
– 5. Use 1 degree of freedom (because there are only 2 alleles).
Example
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Data: 26 MM, 68 MN, 106 NN, with a total population of 200 individuals.
1. Observed genotype frequencies:
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2. Allele frequencies:
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MM: p2 = (0.30)2 = 0.09 (freq) x 200 = 18
MN: 2pq = 2 * 0.3 * 0.7 = 0.42 (freq) * 200 = 84
NN: q2 = (0.70)2 = 0.49 (freq) * 200 = 98
4. Chi-square value:
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M: 0.13 + 1/2 * 0.34 = 0.30
N: 0.53 + 1/2 * 0.34 = 0.70
3. Expected genotype frequencies and numbers:
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MM: 26/200 = 0.13
MN: 68/200 = 0.34
NN:106/200 = 0.53
(26 - 18)2 / 18 + (68 - 84)2 / 84 + (106 - 98)2 / 98
= 3.56 + 3.05 + 0.65
= 7.26
5. Conclusion: The critical chi-square value for 1 degree of freedom is 3.841. Since
7.26 is greater than this, we reject the null hypothesis that the population is in HardyWeinberg equilibrium.
Relaxing the H-W Conditions:
Random Mating
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The fullest meaning of “random mating” implies that any gamete has an
equal probability of fertilizing any other gamete, including itself. In a sexual
population, this is impossible because male gametes can only fertilize
female gametes.
More or less random mating in a sexual population is achieved in some
species of sea urchin, which gather in one place and squirt all of their
gametes, male and female, out into the open sea. The gametes then find
each other and fuse together to become zygotes.
In animal species, mate selection is far more common than random
fertilization. A very general rule is “assortative mating”, that like tends to
mate with like: tall people with tall people, short people with short people,
etc. This rule is true for externally detectable phenotypes such as
appearance, but invisible traits like blood groups are usually close to H-W
equilibrium in the population.
Assortative mating is most easily analyzed as a tendency for inbreeding.
You are more like your relatives than you are to random strangers. Thus
you are somewhat more likely to mate with a distant relative than would be
expected by chance alone.
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Best
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Worst
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Introverted, obsessive, stubborn, self
conscious, and uptight
Type B
Best
Traits
Creative and passionate. Animal loving.
Optimistic and flexible
Worst
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Measuring Inbreeding
• Recall that inbreeding decreases the number of
heterozygotes in the population: each generation of
selfing decreases the number of heterozygotes by 1/2.
• By comparing the number of heterozygotes observed to
the number expected for a population in H-W
equilibrium, we can estimate the degree of inbreeding.
• A measure of inbreeding in the “inbreeding coefficient”,
F.
F = 1 - (obs hets) / (exp hets).
• If F = 0, the observed heterozygotes is equal to the
expected number, meaning that the population is in H-W
equilibrium.
• If F = 1, there are no heterozygotes, implying a
completely inbred population.
• Thus, the higher F is, the more inbred the population is.
Example
• Wild oats is a common plant in California, the cause of the goldenbrown hillsides all summer out there.
• Wild oats can pollinate itself, but the pollen also blows in the wind so
it can cross fertilize. The task is to estimate the relative proportions
of these two types of mating.
• Data for the phosphoglucomutase (Pgm) gene:
– 104 AA, 9 AB, 42 BB = 155 total individuals
• H-W calculations:
– freq of A = 104 + 1/2 * 9 = 108.5 / 155 = 0.7
– freq of B = 1 - freq(A) = 0.3
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exp heterozygotes = 2pq = 2 * 0.7 * 0.3 = 0.42 (freq) * 155 = 65.1
F = 1 -(obs hets) / (exp hets) = 1 - 9 / 65.1 = 1 - 0.14
F = 0.84
This is a very inbred population: most matings are self-pollination.
Inbreeding Depression and Genetic
Load
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For most species, including humans,
too much inbreeding leads to weak
and sickly individuals, as seen in this
example of mice inbred by brothersister matings.
Inbreeding depression is caused by
homozygosity of genes that have slight
deleterious effects. It has been
estimated that on the average, each
human carries 3 recessive lethal
alleles. These are not expressed
because they are covered up by
dominant wild type alleles. This
concept is called the “genetic load”.
However, it has been argued that
some amount of inbreeding is good,
because it allows the expression of
recessive genes with positive effects.
The level of inbreeding in the US has
been estimated (from Roman Catholic
parish records) at about F = 0.0001,
which is approximately equivalent to
each person mating with a fifth cousin.
gen litter
size
0
7.50
% dead
by 4
weeks
3.9
6
7.14
4.4
12
7.71
5.0
18
6.58
8.7
24
4.58
36.4
30
3.20
45.5
Mutation
• Mutation is unavoidable. It happens as a result of
radiation in the environment: cosmic rays, radioactive
elements in rocks and soil, etc., as well as mutagenic
chemical compounds, both natural and artificially made,
and just as a chance event inherent in the process of
DNA replication.
• However, the rate of mutation is quite low: for any given
gene, about 1 copy in 104 - 106 is a new mutation.
• Mutations provide the necessary raw material for
evolutionary change, but by themselves new mutations
do not have a measurable effect on allele or genotype
frequencies.
Migration
• Migration is the movement of individuals in or
out of a population. Migration is necessary to
keep a species from fragmenting into several
different species. Even as low a level as one
individual per generation moving between
populations is enough to keep a species unified.
• Migration can be thought of as combining two
populations with different allele frequencies and
different numbers together into a single
population. After one generation of random
mating, the combined population will once again
be in H-W equilibrium.
Migration Examples
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Population X has 20 individuals with frequency of the A allele = 0.8.
Population Y has 10 individuals with frequency of the A allele = 0.2. The
two populations mix. What is the frequency of A in the final population?
There are 20 + 10 = 30 individuals in the final population, for a total of 60
copies of the gene.
– For population X, 40 * 0.8 = 32 copies are A, and 8 are a.
– For population Y, 20 * 0.2 = 4 copies are A, and 16 are a.
– Adding these together, the final population has 32 + 4 = 36 A alleles and 8 + 16 =
24 a alleles. Out of 60 alleles, the frequency of A is 36/60 = 0.6
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A real example: African Americans have a large proportion of African
ancestry, but also some European ancestry. The Duffy blood group has an
allele with a frequency of 0 among West African populations, and an
average frequency of 0.43 among European populations. Other blood
groups can also be used in this technique: very little assortative mating
occurs on the basis of blood group.
– In Oakland CA, African-Americans are reported to have about 22% European
ancestry
– In Charleston South Carolina, the proportion is about 3.7%
Selection
• Selection is the primary factor driving evolution. Genes that confer
increased fitness tend to take over a population. Note that random
events also play a big factor: sometimes a “good” gene is lost due to
chance events. Also, a gene that confers increased fitness in one
environment may confer decreased fitness in another environment.
• Selection can occur at many places in the life cycle: the embryo
might be defective, the fetus might not survive to birth, the immature
offspring might be killed, the individual might not be able to find a
mate or might be sterile.
• We will simplify all of this by assuming that the gametes are
produced at random and combine at random, to produce a
population of zygotes in H-W equilibrium. Then, we will apply
selection to the zygotes, killing off different proportions of the
different genotypes.
• Fitness is a function of the genotype. We will define the “relative
fitness” of the best genotype as equal to 1.0, and the fitnesses of the
two other genotypes as equal to or less than 1.
Selection Against Recessive
Homozygote
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This situation is what happens with a recessive genetic disease.
Heterozygotes and dominant homozygotes are indistinguishable and have
the same relative fitness: 1.0. The recessive homozygote has the genetic
disease and a fitness less than 1. The exact fitness depends on the nature
of the disease.
Start with a population where p = 0.6 and q = 0.4, and assume that the aa
homozygote has a relative fitness of 0.1 (i.e. 90% of the aa offspring die
without reproducing).
The zygotes produces (in H-W equilibrium) are 0.36 AA, 0.48 Aa, and 0.16
aa.
Selection on the zygotes reduces the aa’s by 90%, to 0.016.
However, proportions must add to 1.0, so we divide each proportion by a
correction factor. The correction factor is the sum of the remaining
proportions: 0.36 + 0.48 + 0.016 = 0.856.
So, after selection, the frequency of AA is 0.36 / 0.856 = 0.42. The
frequency of Aa is 0.48 / 0.856 = 0.56. The frequency of aa is 0.016 / 0.856
= 0.019.
Final allele frequencies: A = 0.42 + 1/2 * 0.56 = 0.70. a = 1 - freq(A) = 0.3.
Selection Favoring the
Heterozygote
• Some genes maintain 2 alleles in the population by
having the heterozygote more fit than either
homozygote.
• An example is HbS, the sickle cell hemoglobin allele. In
rural West Africa, where malaria is endemic and medical
support is rudimentary, the relative fitness of the HbA
homozygote is estimated at 0.85, due to susceptibility to
malaria. The relative fitness of the HbS homozygote is
estimated at approximately 0, with almost none reaching
reproductive age due to sickle cell disease. The
heterozygote is the most fit, so it given a relative fitness
of 1.0. Under these conditions, it is possible to predict
an equilibrium frequency of the HbS allele of about 0.13.
This is approximately what is seen in various West
African countries.
Genetic Drift
• Genetic drift is the random changes in allele frequencies. Genetic
drift occurs in all populations, but it has a major effect on small
populations.
• For Darwin and the neo-Darwinians, selection was the only force
that had a significant effect on evolution. More recently it has been
recognized that random changes, genetic drift, can also significantly
influence evolutionary change. It is thought that most major events
occur in small isolated populations.
• Simple example: A population of 1 female and 2 males, where the
female chooses only 1 male to mate with. Assume that the female
has the Aa genotype, male #1 is AA, and male #2 is aa.
– initially the allele frequencies are 0.5 A and 0.5 a
– if male #1 gets to mate, the offspring will have a 0.75 A, 0.25 a
frequency
– if male #2 mates, the offspring will be 0.25 A and 0.75 a.
Fixation of Alleles
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Genetic drift causes allele
frequencies to fluctuate randomly
each generation. However, if the
frequency of an allele ever
reaches zero, it is permanently
eliminated from the population.
The other allele, whose frequency
is now 1.0, is “fixed”, which means
that all individuals in the
population will be homozygous for
that allele. This continues for all
future generations (in the absence
of mutation).
The average rate at which alleles
become fixed is a function of the
population size. The larger the
population, the longer it takes for
fixation to occur.
Population Bottlenecks and
Founder Effect
• Bottlenecks and the founder effect are closely
related phenomena.
• Founder effect: If a small group of individuals
leaves a larger population and develops into a
separate, isolated population, the allele
frequencies in the new population are
determined by the allele frequencies in the
founders. Since these frequencies are probably
different from those found in the general
population, the new population will have a
different set of frequencies.
• This is especially true for rare alleles, which can
suddenly become prominent if one of the
founders has the rare allele.
Founder Effect Example
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Founder effect example: the Amish are
a group descended from 30 Swiss
founders who renounced technological
progress. Most Amish mate within the
group. One of the founders had Ellisvan Crevald syndrome, which causes
short stature, extra fingers and toes,
and heart defects. Today about 1 in
200 Amish are homozygous for this
syndrome, which is very rare in the
larger US population.
Note the effect inbreeding has here:
the problem comes from this recessive
condition becoming homozygous due
to the mating of closely related people.
Bottlenecks
• A population bottleneck is essentially the same phenomenon as the
founder effect, except that in a bottleneck, the entire species is
wiped out except for a small group of survivors. The allele
frequencies in the survivors determines the allele frequencies in the
population after it grows large once again.
• Example: Pingalop atoll is an island in the South Pacific. A typhoon
in 1780 killed all but 30 people. One of survivors was a man who
was heterozygous for the recessive genetic disease achromatopsia.
This condition caused complete color blindness. Today the island
has about 2000 people on it, nearly all descended from these 30
survivors. About 10% of the population is homozygous for
achromatopsia This implies an allele frequency of about 0.26.
Human Bottleneck
• The human population is
thought to have gone through
a population bottleneck about
100,000 years ago. There is
more genetic variation among
chimpanzees living within 30
miles of each other in central
Africa than there is in the entire
human species.
• The tree represents mutational
differences in mitochondrial
DNA for various members of
the Great Apes (including
humans).