# Population Genetics Population Genetics Allele frequency Allele

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```					                                                                        Population Genetics
•How do genes behave in populations
Population Genetics                             •What is a population?
–A population is a subdivision of a species
–A population is a community of individuals
Social Patterns and Evolutionary                       where mates are usually found
Forces in Human Populations                         –A population shares a common gene pool
–A population has continuity through time

Allele frequency                                   Allele frequency, Example
•An allele frequency is the proportion of one                 –The frequency of the A allele is equal to the sum
allele relative to all alleles at the locus in the            of all of the A alleles divided by the total number
population                                                    of hemoglobin alleles
= 40 A alleles (in 20 HbA/HbA individuals) + 20 A alleles
–Example: In a population you draw blood samples                (in 20 HbA/HbS individuals) divided by 100 total alleles
and do the lab work to determine the hemoglobin              = 60/100
type of the 50 individuals who comprise the                  = 0.60 or 60%
population. You find:
–S allele frequency
• individuals with only type HbA
20
• 20 S alleles (in 20 HbS/HbS individuals) + 20 S alleles
=
• individuals with both type HbA and type HbS
20                                                         (in 20 HbA/HbS individuals) divided by 100 total alleles
• individuals with only type HbS
10                                                        • 40/100
=
• 0.40 or 40% OR 1 - freq(A)
=

Allele frequency, Example cont.                                      Genotype frequency
–The frequencies of all alleles will always add up to
•A genotype frequency is the proportion of a
1 (or 100% of the alleles)
population that has one genotype relative to
–The total number of alleles (not number of forms
of the gene) for a given population at a given locus
all genotypes at a specific locus
will be equal to two times the population size            –In the previous example, we had 10 homozygous
•Except for traits on the Y chromosome, where            sicklers, genotype HbS / HbS, out of 50
population size and allele count would be the same      individuals for a genotype frequency of 10/50 or
–If there are only two alleles at the locus, there are      one-fifth or 0.20 or 20%
only two allele frequencies and one of the                –A two allele locus will have three genotypes
frequencies will be equal to 1 - the frequency of          (except for Y-linked traits) and the frequencies of
the other allele                                           the three will add up to 1 or 100%

1
Hardy-Weinberg Model
Hardy-Weinberg Equilibrium                     •In the parental generation of a population
•The Hardy-Weinberg model describes a              with a diallelic locus (alleles A and B), if
mathematical relationship that allows the         the frequency of one allele (A) is p and the
prediction of the frequency of offspring          other allele (B) is q, i.e.,
genotypes based on parental allele                 –frequency (A) = p,
frequencies                                        –frequency (B) = q,
•It also predicts that allele frequencies will      then the next generation will have:
not change from one generation to the next,        –frequency of the AA genotype = p2
i.e., it is an equilibrium or non-evolutionary     –The frequency of the AB genotype = 2pq
model                                              –The frequency of the BB genotype = q2

Hardy-Weinberg Example                        Hardy-Weinberg Requirements
•At the MN blood group locus the frequency        •Random mating
of the M allele equals 0.4 and the frequency     •No mutation
of the N allele equals 0.6, the offspring in     •Closed population, no gene flow (or
the next generation will have:                    migration of individuals) in or out
–The frequency of the MM genotype = 0.16
•Infinite size, no stochastic effects or genetic
–The frequency of the MN genotype = 0.48
drift
–The frequency of the NN genotype = 0.36
•Equal fertility for all genotype groups--
meaning no selection is occurring

Mating Types
Random Mating                                Parents                 Offspring
Fathers    Mothers      AA       AB         BB
AA          AA       100%       --         --
•The H-W model requires that mating be
AA          AB       50%      50%          --
random with regard to the locus being               AA          BB         --    100%          --
considered                                          AB          AA       50%      50%          --
AB          AB       25%      50%        25%
–The frequency of mating between males of one      AB          BB         --     50%        50%
genotype and females of another should be         BB          AA         --    100%          --
equal to the product of the two genotype          BB          AB         --     50%        50%
frequencies                                       BB          BB         --       --       100%

2
Mating Types and Frequencies
Parents                      Offspring
Shorthand H-W derivation
Mating type Freq          AA          AB           BB
AA x AA       .04       .04         .00         .00
AA x AB       .08       .04         .04         .00                                 Males
AA x BB       .08       .00         .08         .00     Females      Freq(A) = p       Freq(B) = q
AB x AA       .08       .04         .04         .00                           2
AB x AB       .16       .04         .08         .04   Freq(A) = p Freq(AA) = p          Freq(AB) = pq
AB x BB       .16       .00         .08         .08                                                     2
BB x AA       .08       .00         .08         .00
Freq(B) = q Freq(AB) = pq         Freq(BB) = q
BB x AB       .16       .00         .08         .08
BB x BB       .16       .00         .00         .16
Totals      1.00      0.16        0.48        0.36
Parental Genotype Frequencies:
Freq (AA) = 0.20, Freq (AB) = 0.40, Freq (BB) = 0.40

Random Mating
Assortative Mating
•If the frequency of the AA genotype in males is
0.2 and in females is also 0.2, then about 4% of       •If substantially more than the predicted
all matings (0.2 x 0.2 = 0.04) should be                frequency of matings are between males
between AA males and AA females                         and females with the same genotypes, this
would be an example of positive
•If the frequency of mating is significantly
assortative mating
different (test using ) from the prediction,
2
–Positive assortative mating is the occurrence of
then there is significant deviation from random           mating between similar individuals at higher
mating, and the H-W predictions for offspring             than random frequencies, resulting in more
genotype frequencies will be wrong                        homozygotes than the H-W model predicts

Positive Assortative Mating
Parents                      Offspring
Positive Assortative Mating
Mating type Freq          AA          AB           BB
Trait               Spouse
AA x AA       .20       .20         .00         .00   •As with most                           Correlation
AA x AB       .00       .00         .00         .00
AA x BB       .00       .00         .00         .00
mammals, humans      I.Q.                 0.47
AB x AA       .00       .00         .00         .00    tend to mate with
AB x AB       .40       .10         .20         .10    like individuals,    Ear lobe length      0.40
AB x BB       .00       .00         .00         .00    particularly for
BB x AA       .00       .00         .00         .00
BB x AB       .00       .00         .00         .00    visible or           Waist                0.38
BB x BB       .40       .00         .00         .40    noticeable traits.   circumference
Totals      1.00      0.30        0.20        0.50                         Height               0.28
Parental Genotype Frequencies:
Freq (AA) = 0.20, Freq (AB) = 0.40, Freq (BB) = 0.40

3
Negative Assortative Mating                                            Negative Assortative Mating Example
•If substantially fewer than the predicted
•Negative assortative mating appears to be
frequency of matings are between males                                   rare in mammals, but findings on rodents
and females with the same genotypes, this                                suggest that these mammals may have a
would be an example of negative                                          preference for mates with dissimilar major-
assortative mating                                                       histocompatibility-complex (HLA)
haplotypes
–Negative assortative mating is the occurrence
–Ober and colleagues (1997) tested this mate
of mating between individuals with similar
preference in humans by surveying HLA
genotypes at lower than random frequencies,
haplotypes at five HLA loci among 411 Hutterite
resulting in fewer homozygotes and more
couples residing in 31 colonies in South Dakota
heterozygotes than the H-W model predicts

Negative Assortative Mating, 2                                            Negative Assortative Mating, 3
•Hutterites are a North American reproductive isolate                     •The expected number of matches in 411 couples
originating in 1528 in the Tyrolean Alps                                  based on the assumption of random mating and the
–Approximately 400 members settled on three communal                   Hardy Weinberg model of the haplotype (allele)
farms in South Dakota in the 1870s                                    frequencies is 65/411 or 11/2%
–There are now about 350 colonies and 35,000 individuals                 –The observed frequency is significantly lower expected
deriving from those original settlers                                    (Chi-square test significant at p = 0.005)
–Marriage residence follows a patrilocal rule, while marriage         •Variability in HLA haplotypes maximizes potential
may be either endogamous or exogamous with respect to
the colony                                                            immune system response
• couples matched for one haplotype, 2 matched for
41                                                                       •Mice detect HLA haplotype by smell of urine
two haplotypes, and 1 man was homozygous for a                           •Humans may detect this through sweat odor
al y m t i oe f i i ’hp t s
op       cn            s e
hp t e a h g n o h wf s al ye         op                                    –There is evidence that odor preferences may be HLA-linked
–44/411 = 10.7% of couples matched for one or more                        in humans
haplotype

Inbreeding                                                            Inbreeding, 2
AB                ab
•Inbreeding, or mating between biologically
related individuals at higher than random
levels, increases homozygosity
–Incest taboos prohibit mating between closely
related individuals, making inbreeding less
common than simple random mating would
predict, and increasing heterozygosity                                F = (½)(n - 1); where     ego
–The inbreeding coefficient (F) is the probability of                     n = number of links between an ancestor and ego,
picking two alleles that are identical by descent                             summed over all ancestor-ego loops
(ibd) by a random draw in a population                                Above, n = 6, 2 loops, so F = (½)5 + (½)5 = 1/16,
meaning there is a 1 in 16 chance of ego have alleles
that are i.b.d.

4
Inbreeding, 3
Deviations from Random Mating
•Small isolated populations end up with high
levels of inbreeding, even when incest                          •Assortative Mating and Inbreeding will both
taboos are followed                                              influence the relative frequencies of
homozygotes and heterozygotes in the
–Neel estimated that the average relationship                   offspring generation
(based on shared genes) between individuals in
–The frequency of alleles are NOT affected,
a Yanomamo village is nearly the same as                          unless some other forces are at work
between brothers and sisters
–The equilibrium prediction of unchanging allele
–The result is increased homozygosity                              frequencies are not affected by deviations from
–Deleterious recessives show up more often                         panmixia

Mutation                                                         Mutation, 2
•Mutation is the alteration of the genetic                       •Since selection operates to optimize fitness,
material                                                         any give mutation is likely to reduce fitness
–Source of all new variability in the genome                      –That is, any change to the coding sequence
(exon portion, not introns) of a gene is likely to
–Very small quantitative influence on allele and                   be detrimental and selected against
genotype frequencies                                                    Number of new mutations
•Mutation rate (µ) 0.00001 per generation per locus
µ=
number of alleles in the population
–Change allele frequencies by only about 1/100,000 per
generation                                              • Example: Chondrodystrophic Dwarfism (Autosomal
Dominant) D - dwarf; d - normal
–Very significant qualitative impact on
# Dwarfs born to normal parents
µ = 2 times the number of individuals in the population
evolution through the genesis of unique new
alleles, new forms of genes                                     = 79 7,600,000 1/100,000

Gene Flow, 2
Gene Flow, Migration                                          Population A                            Population B
Migration
Freq(A) = p                             Freq(A) = P
m
•Gene Flow is the intermarriage or genetic                             Freq(B) = q                            Freq(B) = Q
mixing between Mendelian populations
–It has the effect of altering allele and genotype             After immigration, in population A:
frequencies so that the two (or more)                                  sedente      migrants
q [(1 - m) q] + (m Q)
=
populations involved come to resemble each
other in terms of genetic frequencies                              =
q q - mq + mQ
Magnitude of change is determined by
q q + [m (Q - q)] the allele frequency
=
difference between the populations

5
Genetic Drift                                                 Random Drift
•An infinite population size eliminates the                    •The genes of each generation are a random
chance or random influences on gene                            sample of preceding generations
frequencies from one generation to the next                      –The laws of probability apply to this sampling
•Mean: The expected value of the allele frequency
which are especially significant in small                            each generation is the same as the previous
populations                                                          generation
–There are two primary manifestations of finite                       – 1 = q0
q
size and random fluctuations                                      •                       )
Standard deviation ( is a measure of
•Random Drift based on population size                         dispersion about the mean, also an estimate
of the probability of fluction from q0
•Founder effect based on a random reduction in
–There is a 67% probability that q1 will be within
population size
,
1of q0; a 95% probability within 2 and a
99% probability within 3

Random Drift, 2                                                Founder Effect
•Example: Assuming a diallelic locus                           •Founder Effect is the random fluctuation in
–freq(A) in generation 0 = p0                                 allele frequencies caused by non-selection
–freq(B) in generation 0 = q0                                 related reduction in population size
–Binomial distribution gives the following                    followed by rapid population growth
formula for the standard deviation of q0:
–The remaining population members become the
 = 02(1 - q0) ;
q 0
q
 N
r dm“ udr o t sbeun
n
a o f ne ” fh usqet
o      s       e
e
population
•Where p0 = 1 - q0
• 2  e = 2 times the effective breeding
and     N                                                 –An example of the founder effect comes from
population size (the number of alleles at the              the island of Tristan da Cunha, settled in 1816
locus)                                                     by a group of 16 Scottish soldiers and their
spouses

Selection
Tristan da Cunha                                 •Selection causes changes in allele and
genotype frequencies from one generation to
Year                       Event                        Size
the next due to differential net reproductive
1816 Settlement of island                                 16    success of individuals with different
1855 Dispute, causing 33 (of 103) to leave                70    genotypes
–If individuals with genotype AA consistently
1885 Population back up to 106, boat wreck              106
have twice as many offspring as individuals with
kills 15 males, families begin to leave
AB and BB genotypes, the frequency of the A
1891 Population starts growing again                      59
allele will increase through time and eventually,
1961 Continued growth from 1891                         270       everyone will have the AA genotype

6
Modeling Selection
Selection, 2
•Selection operates by reducing the completed
•There are two elements contributing to the                    fertility of individuals with a certain phenotype,
differential reproductive success of                          relative to other phenotypes within a population
individuals with differing genotypes                           –Fitness (1.0 > w > 0.0) is the completed fertility for
–Viability or survival: individuals must survive              a given genotype, relative to the genotype with the
to reproductive maturity in order to be able to              highest completed fertility
reproduce                                                   –The selection coefficient (1.0 > s > 0.0) measures
–Fertility: individuals must produce offspring in             the relative reduction in fertility for a genotype
order to pass on their genes on to the next                                      • =1-w
s
generation of the population

Modes of Selection, 2
Modes of Selection
Traits on X Chromosome                                            Females                Males
Autosomal Inheritance                           Genotypes
Selection Against:                                               AA AB BB                A B
Selection Against:                             AA AB BB
Complete Dominance
Complete Dominance
Dominant                                                      sAA sAA             sAA
o n tH ni tn i s )
a        n    s e
D mi n ( u t go ’Ds a e                     sAA   sAA
Recessive (Hemophilia A)                                                   sBB              sBB
Recessive (PKU, Tay Sachs)                              sBB
Incomplete Dominance
Incomplete Dominance/Codominance
Heterozygote                                                      sAB
Heterozygote                                      sAB
1 homozygote, heterozygote                                    sAA sAB     sAA
One homozygote, heterozygote                sAA   sAB
Both homozygotes (G6PD)                                       sAA     sBB sAA sBB
Both homozygotes (sickle cell)              sAA         sBB   Traits on Y Chromosome
Any allele (A)                                                                       sAA

Selection against a recessive                                                    Selection against a recessive
AA       AB          BB                               0.5
2                    2
Hardy-Weinberg Freq:             p        2pq         q
Fitness (w)                      1.0      1.0     1–s                                  0.4
Allele Frequency

(BB)
2                   2
Frequency after selection    p (1) 2pq (1) q (1-s)                                  0.3
2           2   2        2                                                                               s = 0.2
New Total Frequency (w) = p + 2pq + q - q s = 1 - q s
Relative frequency after
2
(p )     (2pq)
2
(q –qs)
2                           0.2                              s = 0.5
2       2            2
selection                    (1 - q s) (1 - q s) (1 - q s)                             0.1           s=1

Frequency of B in next generation = freq (BB) + ½ freq (AB)                             0
0   2    4    6   8   10     12   14   16    18   20    22    24
q1 = (q –q2s) (1 - q2s)
Generations of Selection

7
Overdominance
AA
2
AB      BB
2
Natural Selection
Hardy-Weinberg Freq:            p         2pq      q
Fitness (w)                    1.0        1.0   1–s  (BB)
2
2
2
Frequency after selection p (1-sAA) 2pq (1) q (1-sBB)
2
•Darwinian natural selection is a two-step
New Total Frequency (w) = 1 - p sAA - q sBB                   process:
2    2             2    2
Relative frequency after  (p - p sAA) (2pq) (q –qsBB)
selection                      (w )       (w )    ( w)         –The production of new genetic variation
Frequency of B in next generation = freq (BB) + ½ freq (AB)      through the process of mutation
q1 = (q –q2sBB) (1 - p2sAA - q2sBB)            –The differential reproduction of favorable
Equilibrium is attained if  = 0;
q                                    variants through the process of selection
 = q1 - q0 = [(q –q2sBB) (1 - p2sAA - q2sBB)] - q
q
= [pq (psAA –qsBB)] (1 - p2sAA - q2sBB)
 = 0 if psAA –qsBB = 0; that is, if q = sAA (sAA + sBB)
q

Sources
•Ober, C.; Weitkamp, L.R.; Cox, N.; Dytch,
H.; Kostyu, D.; Elias, S. 1997. HLA and
mate choice in humans. American Journal
of Human Genetics, 61:497-504.

8

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