Hardy Weinberg Equilibrium Lectures 4-11: ... 9/17/18 1 Hardy Weinberg Equilibrium Wilhem Weinberg...

Click here to load reader

  • date post

    01-Feb-2020
  • Category

    Documents

  • view

    12
  • download

    1

Embed Size (px)

Transcript of Hardy Weinberg Equilibrium Lectures 4-11: ... 9/17/18 1 Hardy Weinberg Equilibrium Wilhem Weinberg...

  • 9/17/18

    1

    Hardy Weinberg Equilibrium

    Wilhem Weinberg (1862 – 1937)

    Gregor Mendel

    G. H. Hardy (1877 - 1947)

    (1822-1884)

    Lectures 4-11: Mechanisms of Evolution (Microevolution)

    • Hardy Weinberg Principle (Mendelian Inheritance) • Genetic Drift • Mutation • Sex: Recombination and Random Mating • Epigenetic Inheritance • Natural Selection

    These are mechanisms acting WITHIN populations,

    hence called “population genetics”—EXCEPT for epigenetic modifications, which act on individuals

    in a Lamarckian manner

    Evolution acts through changes in allele frequency at each generation

    Leads to average change in characteristic of the population

    Recall from Previous Lectures Darwin’s Observation

    HOWEVER, Darwin did not understand how genetic variation was passed on from generation to generation

    Recall from Lecture on History of Evolutionary Thought

    Darwin s Observation

    Gregor Mendel, Father of Modern Genetics

    • Mendel presented a mechanism for how traits got passed on

    Individuals pass alleles on to their offspring intact

    (the idea of particulate (genes) inheritance)

    Gregor Mendel

    (1822-1884)

    http://www.biography.com/people/gregor-mendel-39282#synopsis

    Gregor Mendel, Father of Modern Genetics

    Mendel s Laws of Inheritance • Law of Segregation – only one allele passes from each

    parent on to an offspring • Law of Independent Assortment – different pairs of alleles are passed to

    offspring independently of each other

    Gregor Mendel

    (1822-1884)

    http://www.biography.com/people/gregor-mendel-39282#synopsis

  • 9/17/18

    2

    Gregor Mendel

    • In cross-pollinating plants with either yellow or green peas, Mendel found that the first generation (f1) always had yellow seeds (dominance). However, the following generation (f2) consistently had a 3:1 ratio of yellow to green.

    Using 29,000 pea plants, Mendel discovered the 1:3 ratio of phenotypes, due to dominant vs. recessive alleles

    • Mendel uncovered the underlying mechanism, that there are dominant and recessive alleles

    • Mathematical description of Mendelian inheritance

    Hardy-Weinberg Principle

    Godfrey Hardy (1877-1947) Wilhem Weinberg

    (1862 – 1937)

    Testing for Hardy-Weinberg equilibrium can be used to assess whether a population is

    evolving

    The Hardy-Weinberg Principle

    • A population that is not evolving shows allele and genotypic frequencies that are in Hardy Weinberg equilibrium

    • If a population is not in Hardy-Weinberg equilibrium, it can be concluded that the population is evolving

  • 9/17/18

    3

    Evolutionary Mechanisms (will put population out of HW Equilibrium):

    • Genetic Drift • Natural Selection • Mutation • Migration

    *Epigenetic modifications change expression of alleles but not the frequency of alleles themselves, so they won’t affect the actual inheritance of alleles

    However, if you count the phenotype frequencies, and not the genotype frequencies , you might see phenotypic frequencies out of HW Equilibrium due to epigenetic silencing of alleles. (epigenetic modifications can change phenotype, not genotype)

    Requirements of HW Evolution

    Large population size Genetic drift

    Random Mating Inbreeding & other

    No Mutations Mutations

    No Natural Selection Natural Selection

    No Migration Migration

    An evolving population is one that violates Hardy-Weinberg Assumptions

    Violation

    Fig. 23-5a

    Porcupine herd range

    Beaufort Sea NORTHWEST

    TERRITORIES

    M AP AREA

    AL AS

    KA

    CA N

    AD A

    Fortymile herd range

    AL AS

    KA YU

    KO N

    •What is a “population?” A group of individuals within a species that is capable of interbreeding and producing fertile offspring

    (definition for sexual species)

    Patterns of inheritance should always be in “Hardy Weinberg Equilibrium”

    Following the transmission rules of Mendel

    In the absence of Evolution…

    Hardy-Weinberg Equilibrium

    • According to the Hardy-Weinberg principle, frequencies of alleles and genotypes in a population remain constant from generation to generation

    • Also, the genotype frequencies you see in a population should be the Hardy-Weinberg expectations, given the allele frequencies

    “Null Model” • No Evolution: Null Model to test if no

    evolution is happening should simply be a population in Hardy-Weinberg Equilibrium

    • No Selection: Null Model to test whether Natural Selection is occurring should have no selection, but should include Genetic Drift – This is because Genetic Drift is operating even

    when there is no Natural Selection

  • 9/17/18

    4

    Example: Is this population in Hardy Weinberg Equilibrium?

    AA Aa aa Generation 1 0.25 0.50 0.25 Generation 2 0.20 0.60 0.20 Generation 3 0.10 0.80 0.10

    Hardy-Weinberg Theorem

    In a non-evolving population, frequency of alleles and genotypes remain constant over generations

    You should be able to predict the genotype frequencies, given the allele frequencies

    important concepts • gene: A region of genome sequence (DNA or RNA), that is

    the unit of inheritance , the product of which contributes to phenotype

    • locus: Location in a genome (used interchangeably with “gene,” if the location is at a gene… but, locus can be anywhere, so meaning is broader than gene)

    • loci: Plural of locus • allele: Variant forms of a gene (e.g. alleles for different eye

    colors, BRCA1 breast cancer allele, etc.)

    • genotype: The combination of alleles at a locus (gene) • phenotype: The expression of a trait, as a result of the

    genotype and regulation of genes (green eyes, brown hair, body size, finger length, cystic fibrosis, etc.)

    important concepts • allele: Variant forms of a gene (e.g. alleles for different eye

    colors, BRCA1 breast cancer allele, etc.)

    • We are diploid (2 chromosomes), so we have 2 alleles at a locus (any location in the genome)

    • However, there can be many alleles at a locus in a population. – For example, you might have inherited a blue eye allele from

    your mom and a brown eye allele from your dad… you can’t have more alleles than that (only 2 chromosomes, one from each parent) –BUT, there could be many alleles at this locus in the

    population, blue, green, grey, brown, etc.

    • Alleles in a population of diploid organisms

    A1

    A2

    A3

    A4 A1

    A1

    A2

    Sperm

    Eggs

    • Genotypes

    Random Mating (Sex)

    Zygotes

    A1A3

    A1A1 A1A1

    A2A4

    A3A1

    A1A1

    A1

    A2 A1

    A1

    A3 A4

    So then can we predict the % of alleles and genotypes in the population at each generation?

    A1

    A2

    A3

    A4 A1

    A1

    A2

    Sperm

    Eggs

    Zygotes

    A1A3

    A1A1 A1A1

    A2A4

    A3A1

    A1A1

    A1

    A2 A1

    A1

    A3 A4

  • 9/17/18

    5

    Hardy-Weinberg Theorem

    In a non-evolving population, frequency of alleles and genotypes remain constant over generations

    Fig. 23-6

    Frequencies of alleles Alleles in the population

    Gametes produced Each egg: Each sperm:

    80% chance

    80% chance

    20% chance

    20% chance

    q = frequency of

    p = frequency of CR allele = 0.8

    CW allele = 0.2

    Hardy-Weinberg proportions indicate the expected allele and genotype frequencies, given the starting frequencies

    • By convention, if there are 2 alleles at a locus, p and q are used to represent their frequencies

    • The frequency of all alleles in a population will add up to 1

    – For example, p + q = 1

    If p and q represent the relative frequencies of the only two possible alleles in a population at a particular locus, then for a diploid organism (2 chromosomes),

    (p + q) 2 = 1

    = p2 + 2pq + q2 = 1

    – where p2 and q2 represent the frequencies of the homozygous genotypes and 2pq represents the frequency of the heterozygous genotype

    What about for a triploid organism? What about for a triploid organism? • (p + q)3 = 1

    = p3 + 3p2q+ 3pq2 + q3 = 1

    Potential offspring: ppp, ppq, pqp, qpp, qqp, pqq, qpq, qqq

    How about tetraploid? You work it out.

  • 9/17/18

    6

    Hardy Weinberg Theorem ALLELES Probability of A = p p + q = 1 Probability of a = q

    GENOTYPES AA: p x p = p2

    Aa: p x q + q x p = 2pq aa: q x q = q2

    p2 + 2pq + q2 = 1

    More General HW Equations • One locus three alleles: (p + q + r)2 = p2 + q2 + r2 + 2pq +2pr +

    2qr

    • One locus n # alleles: (p1 + p2 + p3 + p4 … …+ pn)2 = p12 + p22 + p32 + p42… …+ pn2 + 2p1p2 + 2p1p3 + 2p2p3 + 2p1p4 + 2p1p5 + … … + 2pn-1pn

    • For a polyploid (more than two chromosomes): (p + q)c, where c = number of chromosomes

    • If multiple loci (genes) code for a trait, each locus follows the HW principle independently, and then the alleles at each loci interact to influence the trait

    ALLELE Frequencies Frequenc