Population Genetics

1
Population Genetics
2
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.

3
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

4
Genetics of Populations

• Darwin didnt understand how inheritance
  worked--Mendels work was still in the future.
  It wasnt until the 1930s 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.

5
Allele and Genotype Frequencies

• 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
• 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
• Note that since there are only 2 alleles here,
  the frequency of N is 1 - freq(M).

6
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.

7
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.

8
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 dont match the
  observed frequencies. We will examine the
  reasons for this soon.

9
Rare Alleles and Eugenics

• 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.

10
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."
11
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 cant 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.

12
Necessary Conditions for Hardy-Weinberg
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.
• 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

13
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 H-W 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).

14
Example

• Data 26 MM, 68 MN, 106 NN, with a total
  population of 200 individuals.
• 1. Observed genotype frequencies
• MM 26/200 0.13
• MN 68/200 0.34
• NN106/200 0.53
• 2. Allele frequencies
• M 0.13 1/2 0.34 0.30
• N 0.53 1/2 0.34 0.70
• 3. Expected genotype frequencies and numbers
• 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
• (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 Hardy-Weinberg
  equilibrium.

15
Relaxing the H-W Conditions Random Mating

• 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.

16
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17
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.

18
Example

• Wild oats is a common plant in California, the
  cause of the golden-brown 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
• 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.

19
Inbreeding Depression and Genetic Load

• For most species, including humans, too much
  inbreeding leads to weak and sickly individuals,
  as seen in this example of mice inbred by
  brother-sister 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 dead by 4 weeks
0 7.50 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
20
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.

21
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.

22
Migration Examples

• 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
• 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

23
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.

24
Selection Against Recessive Homozygote

• 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 aas 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.

25
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.

26
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.

27
Fixation of Alleles

• 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.

28
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.

29
Founder Effect Example

• 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 Ellis-van
  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.

30
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.

31
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).