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Population Genetics Population Genetics Allele frequency Allele

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Population Genetics Population Genetics Allele frequency Allele Powered By Docstoc
					                                                                        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.




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