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Module 1

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Module 1 Basic principles in population and quantitative genetics * – PowerPoint PPT presentation

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Title: Module 1


1
Module 1
  • Basic principles in population and quantitative
    genetics

1
2
Genes and Genomes
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3
Quick review Genes and genomes
  • In eukaryotes, DNA is found in the...
  • Nucleus
  • Mitochondria
  • Chloroplasts (plants)
  • Organelle inheritance is often uniparental,
    making it powerful for certain types of
    applications
  • For this workshop, well focus almost exclusively
    on nuclear genes

Plant Cell
3
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Chromosomes
  • Linear strands of DNA and associated proteins in
    the nucleus of eukaryotic cells
  • Chromosomes carry the genes and function in the
    transmission of hereditary information
  • Diploid cells have two copies of each chromosome
  • One copy comes from each parent
  • Paternal and maternal chromosomes may have
    different alleles

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Alleles
  • Alternative forms of a gene
  • Alleles arise through mutation
  • A diploid cell has two copies of each gene (i.e.
    two alleles) at each locus
  • Alleles on homologous chromosomes may be the same
    or different (homozygous vs. heterozygous)

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Genes
  • Units of information on heritable traits
  • In eukaryotes, genes are distributed along
    chromosomes
  • Each gene has a particular physical location a
    locus
  • Genes encompass regulatory switches and include
    both coding and non-coding regions
  • Genes are separated by intergenic regions whose
    function is not understood

6
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The genome
  • An individuals complete genetic complement
  • For eukaryotes, a haploid set of chromosomes
  • For bacteria, often a single chromosome
  • For viruses, one or a few DNA or RNA molecules
  • Genome size is typically reported as the number
    of base pairs in one genome complement (i.e.
    haploid for eukaryotes)
  • Until recently, we studied genes and alleles one
    or a few at a time (genetics)
  • Aided by high throughput technologies we can now
    study 100s to 1000s of genes simultaneously
    (genomics).

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Genome size
  • Lambda phage 4.8 x 103 bp
  • E. coli 4.6 x 106 bp
  • Arabidopsis 1.6 x 108 bp
  • Cottonwood 4.8 x 108 bp
  • Chestnut 9.6 x 108 bp
  • Humans 3.0 x 109 bp
  • Pines 3 x 1010 bp
  • Fritillaria 1.3 x 1011 bp
  • Amoeba dubia 6.7 x 1011 bp

Douglas-fir, Pseudotsuga menziesii, has a
chromosome number of 26. Its diploid, so that
means that n13. Most Conifers have n12.
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Genes and genomes Using what we've learned
  • In this workshop, we will convey many ways that
    our knowledge of genetics and genomics can be
    used by breeders and land managers
  • Our emphasis will be on the study of methods that
    can be used to characterize or dissect complex
    (quantitatively inherited) traits and associate
    phenotype with genotype, leading to marker
    informed applications
  • To do this, we will need to review several
    sub-disciplines of the science of genetics

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Genetics
  • To understand marker-informed breeding, we will
    first set the stage by briefly reviewing
  • Mendelian genetics describes inheritance from
    parents to offspring
  • discrete qualitative traits (including genetic
    markers)
  • predicts frequencies of offspring given specific
    matings
  • Population genetics describes allele and genotype
    frequencies over space and time, including
  • changes in allele frequencies between generations
  • environmental factors contributing to fitness
  • models are limited to a small number of genes
  • analyzes variation within and among populations
  • Quantitative genetics describes variation in
    traits influenced by multiple genes (continuous
    rather than discrete attributes)
  • relies on statistical tools describing
    correlations among relatives
  • each of many genes may have little influence on a
    specific trait

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Mendelian Genetics(and the basis of genetic
markers)
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Mendelian inheritance
  • We begin with family resemblance Like begets
    like.
  • How do we explain it?

www.madeyoulaugh.com
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Traits tend to run in families
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Genotype and phenotype
  • Genotype refers to the particular gene or genes
    an individual carries
  • Phenotype refers to an individuals observable
    traits
  • Only rarely can we determine genotype by
    observing phenotype
  • Genomics offers tools to better understand the
    relationship between genotype and phenotype
  • Individual genetic markers behave as Mendelian
    traits, so understanding Mendelian traits is key
    to understanding markers

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Single-gene traits in trees are rareHeres one
in alder (f. pinnatisecta)
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Mendels insights were amazing, and yet...
  • Knowledge of biological processes was
    rudimentary, including
  • cell division (mitosis or meiosis)
  • chromosomes were not yet known
  • With the discovery of chromosomes, we realized
  • That genes are packaged on chromosomes
  • That genes on the same chromosome are associated
    (genetic linkage). Very important! We will
    explore this a great deal in future modules

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Markers reflect genetic polymorphisms that are
inherited in a Mendelian fashion
  • DNA markers 'mark' locations where DNA varies
    (sequence or size)
  • Such polymorphisms can vary within and among
    individuals (e.g. heterozygotes vs. homozygotes)
    and populations
  • Markers may be located in genes or elsewhere in
    the genome
  • Historically, we've had too few markers to inform
    breeding
  • Genomics tools provide an almost unlimited supply
    of markers
  • Todays marker applications were only imagined a
    few years ago

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DNA markers reflect sequence variation
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Markers track inheritance
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Trait dissection using markers
Hypothetical genes (QTLs) affecting economic
traits, mapped using genetic markers a-m
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Single Nucleotide Polymorphisms(SNPs) embedded
within a DNA sequence
  • DNA sequences are aligned
  • Polymorphic sites are identified
  • Haplotypes (closely linked markers of a specific
    configuration) are deduced by direct observation
    or statistical inference

atggctacctgaactggt
caactcatcgaaagctaa 1 atggctacctgaactggtcaactcatcg
aaagctaa 1 atgcctacctgaactggtcaactcatcgaaagctaa
2 atgcctacctgaactggtcaactcatcgaaggctaa
3 atgcctacctgaactggtcaacacatcgaaggctaa 4
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Genetic linkage and recombination
  • Genes on different chromosomes are inherited
    independently
  • Genes located on the same chromosome tend to be
    inherited together because they are physically
    linkedexcept that widely separated genes behave
    as if they are unlinked.
  • Recombination during gametogenesis breaks up
    parental configurations into new (recombinant)
    classes
  • The relative frequency of parental and
    recombinant gametes reflects the degree of
    genetic linkage
  • Genetic mapping is the process of determining the
    order and relative distance between genes or
    markers (to be discussed in Module 3)

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Genetic linkage and recombination
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Population Genetics
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Population genetics
  • Population genetics is the study of genetic
    differences within and among populations of
    individuals, and how these differences change
    across generations
  • It extends Mendelian genetics to include
    population dynamics and chance events such as
  • survival
  • frequency of specific matings
  • random sampling from populations, and
  • mutation

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Population genetics
  • Over time, changes among populations can lead to
    genetic isolation and speciation
  • Population genetics describes the mechanics of
    how evolution takes place
  • As we discuss genetic differences, keep in mind
    that
  • polymorphisms reflect differences among
    individuals within a species
  • divergence reflects differences between species
  • Well discuss more specifics on these processes
    later on...
  • (D. L. Hartl 2000. A Primer of Population
    Genetics)

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What do population geneticists measure?
  • Studies limited to simply-inherited traits
  • historically, this involved morphological or
    biochemical markers
  • shifted to allozymes in 1960s to 1980s
  • DNA markers became more common beginning in later
    1980s
  • many types of DNA markers have been developed
  • well re-visit markers in Module 3
  • Key points
  • population geneticists measure discrete
    (Mendelian) traits
  • quantitative geneticists measure continuous
    traits controlled by multiple genes (well talk
    about quantitative genetics later in this Module)

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Why study genes in populations?
  • In natural populations
  • Adaptation, or the ability to survive and exploit
    an environmental niche, involves the response of
    populations, not individuals.
  • In breeding populations
  • Genetic gainimproving the average performance of
    populations for desired breeding
    objectivesdepends on selecting and breeding
    parents with the best genetic potential

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Population genetics Key questions
  • Population genetics provides empirical models to
    predict genetic behavior for these and other
    situations
  • What genotypes are present in a population and at
    what frequency?
  • Are all genotypes equally likely to survive
    and reproduce?
  • Are mating frequencies independent of genotype?
  • Is the population stratified in some way, e.g. by
    proximity, size, or the timing of
    natural events?
  • To what extent does mating occur with individuals
    outside outside the immediate
    area?
  • To what extent are environmental conditions
    stable across generations?
  • Etc

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Population genetics
  • Provides empirical models to predict genetic
    behavior
  • What genotypes are present in a population and at
    what frequencies?
  • Are all genotypes equally likely to survive and
  • reproduce?
  • Are mating frequencies independent of genotype?
  • Is the population stratified in some way, e.g. by
  • proximity, size, or the timing of natural
    events?
  • To what extent does mating occur with individuals
  • outside the immediate area?
  • To what extent are environmental conditions
    stable across generations?

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Population genetics
  • How genetically diverse is a species or
    population?
  • contrast diversity in populations that differ in
    life-history traits, pop size, breeding
    structure, etc
  • Are different populations closely related to one
    another?
  • monitor diversity for conservation purposes
  • What is the potential for inbreeding depression?
  • what is the minimum viable population size from a
    genetic standpoint?
  • How is genetic variation maintained?
  • Identify genes/alleles responsible for phenotypic
    variation
  • Phylogenetic and biogeographic questions

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Populations are groups of individuals whose
relatedness is usually unknown
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The Hardy-Weinberg Principle
  • The frequencies of alleles and genotypes in a
    population will remain constant over time (given
    certain assumptions) describing a static, or
    non-evolving population
  • The frequencies of alleles and genotypes can be
    described mathematically, where p and q are the
    frequencies of the alleles A1 and A2

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HW proportions
  • Predict frequencies of all genotypes based on
    allele frequencies
  • Provide a quantitative measure of variation among
    populations differing in allele frequencies
  • Provide a measure of within-population,
    heterozygosity
  • Expected heterozygosity (He) is the combined
    frequency of all heterozygotes calculated from
    allele frequencies

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Random mating restores HW proportions each
generation
White et al. 2007
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HW and random sampling
  • Strictly speaking, Hardy-Weinberg proportions
    require certain assumptions, such as
  • an infinitely large population (translation
    sampling with replacement)
  • mating is at random (translation all possible
    pairings of mates is equally likely)
  • no selection (which biases genotype frequencies)
  • no migration (since all alleles must be sampled
    from the same pool)
  • no mutation (which introduces new variants)
  • These conditions represent an ideal population
    that is rarely (if ever) never fully realized

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HW and random sampling
  • Minor violations of assumptions usually have
    little impact
  • In practice
  • HW proportions apply for many natural populations
  • breeding populations are different
  • population sizes can be small
  • individuals chosen for breeding may represent a
    subset of relatives
  • matings are often non-random

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HW Non-random mating
  • When individual genotypes do not mate randomly,
    then HW proportions are not observed among the
    offspring
  • Well look at two kinds of non-random mating
  • population substructure/admixture
  • inbreeding (mating among related individuals)

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HW Population admixture
  • Consider mixing individuals from
    non-interbreeding subpopulations (e.g. Offshore
    salmon from different runs)
  • Even if each subpopulation is in HW, the admixed
    group is not (p1 ? p2)
  • The admixed group will appear to have too many
    homozygotes
  • This situation is called Wahlunds effect

Hartl, 2000, Fig. 2.6
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Population structure Wahlunds effect
  • Larger populations may be subdivided into smaller
    groups, which may be difficult to delineate
  • sub-population can have different allele
    frequencies
  • each sub-population may show HW proportions
  • A biologist may unknowingly sample individuals
    from different subpopulations and group them
    together. What would you observe?
  • HW proportions in the entire sample, or
  • more heterozygous individuals than predicted from
    HW expectations, or
  • more homozygous individuals than predicted from
    HW expectations?

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Population structure Wahlunds effect
  • Wahlunds effect As long as allele frequencies
    vary among subpopulations, even if each
    subpopulation exhibits HW proportions, then more
    homozygotes will be observed than would be
    expected based on the allele frequency of the
    metapopulation
  • The relative increase in homozygosity is
    proportional to the variance in allele
    frequencies among subpopulations, as measured by
    F (where 0 F 1).
  • There are many versions of F, formulated in
    different ways. Each is a measure of increased
    genetic relatedness

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Inbreeding
  • Inbreeding (mating among relatives) increases
    homozygosity relative to HW
  • rate is proportional to degree of relationship
  • distant cousin lt first cousin lt half-sib lt
    full-sib lt self
  • Recurrent inbreeding leads to a build-up of
    homozygosity, and a corresponding reduction in
    heterozygosity
  • Inbreeding affects genotype frequencies, but not
    allele frequencies
  • How does inbreeding affect deleterious recessive
    alleles?

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Inbreeding and homozygosity
  • F reflects a proportional reduction in
    heterozygosity, and a build-up of genetic
    relatedness. HW implies F 0. With recurrent
    selfing, F goes to 1

White et al. 2007, Fig. 5.6
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Inbreeding depression
  • Inbreeding often leads to reduced vitality
    (growth, fitness)
  • Deleterious recessive alleles are made homozygous
  • Outcrossing species are more likely to suffer
    higher inbreeding depression

White et al. 2007, Fig. 5.7
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Evolutionary forces change allele frequencies
  • Mutation ? a random heritable change in the
    genetic material (DNA) - ultimate source of all
    new alleles
  • Migration (gene flow) ? the introduction of new
    alleles into a population via seeds, pollen, or
    vegetative propagules
  • Random genetic drift ? the random process
    whereby some alleles are not included in the next
    generation by chance alone
  • Natural selection ? the differential, non-random
    reproductive success of individuals that differ
    in hereditary characteristics

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Mutation
  • Heritable changes in DNA sequence alter allele
    frequencies as new alleles are formed
  • Mutations at any one locus are rare, but with
    sufficient time, cumulative effects can be large
  • Mutations are the ultimate source of genetic
    variation on which other evolutionary forces act
    (e.g., natural selection)
  • Effects on populations Mutations promote
    differentiation (but effects are gradual in the
    absence of other evolutionary forces)

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Gene flow Migration of alleles
  • Gene Flow the movement of alleles among
    populations
  • Movement may occur by individuals (via seed) or
    gametes (via pollen)
  • Effects on populations gene flow hinders
    differentiation. It is a cohesive force tends to
    bind populations together

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Genetic drift
  • Drift reflects sampling in small populations
  • Subgroups follow independent paths
  • Allele frequencies vary among subgroups
  • Frequencies in the metapopulation remain
    relatively stable
  • How does F behave?

Hartl Jones, 2004.
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Random genetic drift
  • Genetic bottleneck An extreme form of genetic
    drift that occurs when a population is severely
    reduced in size such that the surviving
    population is no longer genetically
    representative of the original population
  • Effects on populations Drift promotes
    differentiation

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Natural selection
  • Natural selection ? First proposed by Charles
    Darwin in mid-1800s. The differential
    reproductive success of individuals that differ
    in hereditary characteristics
  • not all offspring survive and reproduce
  • some individuals produce more offspring than
    others (mortality, disease, bad luck, etc)
  • offspring differ in hereditary characteristics
    affecting their survival (genotype and
    reproduction are correlated)
  • individuals that reproduce pass along their
    hereditary characteristics to the next generation
  • favorable characteristics become more frequent in
    successive generations
  • Effects on populations
  • Promotes differentiation between populations that
    inhabit dissimilar environments
  • Hinders differentiation between populations that
    inhabit similar environments

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Selection Numerical example
White et al. 2007, Table 5.3
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Selection Equations
White et al. 2007, Table 5.4
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Relative fitness Key considerations
  • Which genotype has the largest relative fitness?
  • determines the direction in which allele
    frequencies will change
  • Are fitness differences large or small?
  • determines rate of change over generationsfast
    or slow
  • What is the fitness of the heterozygote compared
    to either homozygote?
  • reflects dominance
  • complete (heterozygote identical to either
    homozygote)
  • no dominance (additive, heterozygote is
    intermediate)
  • partial (heterozygote more closely resembles one
    homozygote)
  • dominance influences how selection sees
    heterozygotes
  • affects rate of change across generations

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Natural selection
  • Fitness the relative contribution an individual
    makes to the gene pool of the next generation

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Gene action Additive vs. dominance
Jennifer Kling, OSU
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Dominance and rate of change
Hartl, 2000
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What if selection is weak or absent?
  • Weve already seen that mutation can supply new
    variation that selection may act upon
  • Most mutations are deleterious and are lost, but
    rarely, advantageous mutations can occur
  • What about mutations that cause no effect either
    way?
  • Neutrality theory pertains to alleles that confer
    no difference in relative fitnessas if selection
    is oblivious to them
  • Well revisit the behavior of neutral alleles
    later on

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Measuring population structure
  • Generically speaking, population structure
    measures the degree to which allele frequencies
    vary among subpopulations
  • This can be thought of in several ways
  • variance among subpopulations
  • heterozygosity among pairs of alleles drawn at
    random
  • Recall, expected heterozygosity measures
  • the frequency of heterozygous genotypes in a HW
    population
  • which equals the frequency of random pairs of
    haploid gametes with different alleles
  • Whenever allele frequencies vary among
    subpopulations (regardless of the cause), the
    variance in allele frequencies can be measured by
    F
  • Well revisit this in Module 4

F (He Ho)/He
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Population genetics A final concept
  • Linkage disequilibrium (LD, also called gametic
    phase disequilibrium)
  • ConceptuallyLD is a correlation in allelic state
    among loci
  • Numerically
  • expected haplotype (gamete) frequency is the
    product of the two allele frequencies, i.e. f(AB)
    f(A) x f (B)
  • if f(AB) f(A) x f (B), then LD 0
  • if f(AB) ? f(A) x f (B), then LD ? 0
  • LD may arise from factors such as
  • recent mutations
  • historical selection (hitchhiking effect)
  • population admixture
  • Recombination causes LD to decay over generations
  • LD plays a major role in association genetics.
    We will revisit!

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A numeric example of LD
  • determine allele frequencies
  • ask whether f(A) x f(B) f(AB)
  • repeat for f(Ab), f(aB), and f(ab)
  • linkage disequilibrium (LD) reflects this
    difference

Gamete Frequency
Gamete Type (linked)
No LD Higher LD Lower LD
0.42 0.60 0.55
0.28 0.10 0.15
0.18 -- 0.05
0.12 0.30 0.25
f(A) 0.7 f(a) 0.3
f(B) 0.6 f(b) 0.4
Allele Frequencies
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Summary Population Genetics
  • Population genetics extends Mendelian genetics to
    describe how allele and genotype frequencies can
    be predicted given certain dynamic population
    processes
  • For populations in Hardy-Weinberg (HW)
    proportions, genotype frequencies are easily
    calculated given allele frequencies
  • HW proportions are used as a comparative baseline
  • Population genetics questions include
  • How much genetic diversity (heterozygosity) are
    in populations?
  • How is genetic diversity distributed?
  • What mechanisms have shaped the diversity we
    observe?
  • Our challenge How can we measure, interpret,
    and utilize genetic diversity?

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Population Diversity
  • Baseline Metrics

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Locus, allele, and allele frequencies
  • Locus A fixed position on a chromosome (e.g.,
    position of gene or marker)
  • Allele Variant of a specific locus
  • Allele frequency Proportion of a certain allele
    within a population

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How to define the distribution of genotypes?
  • For two alleles we have three
    diploid genotypes
  • Let
  • p the frequency of A1 , and
  • q the frequency of A2
  • (so that p q 1)
  • What is the frequency of

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Hardy-Weinberg Equilibrium (HWE)
p2 2pq q2 1 (p q)2 1
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Assumptions of HWE (or it works when)
  • Random mating
  • No mutation
  • No migration
  • No selection
  • Infinite population size
  • But does it really work?!

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Insights provided by HWE
  • Genotypes are transient, broken up every
    generation, and reconstituted each generation as
    zygotes
  • HW equilibrium Implies that allele and genotype
    frequencies are constantthey remain unchanged
    across generations
  • Even if populations with different allele
    frequencies are brought together, these
    non-equilibrium populations reach equilibrium
    in single generation (at least for individual
    loci!)
  • Rare alleles mostly occur as heterozygotes
  • HWE also means that genotypic frequencies can be
    calculated from allele frequencies, so allele
    frequencies alone are sufficient parameters for
    population genetic models

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Null hypothesis My sample is in HWE
  • How do we test this null hypothesis?
  • Estimate allele frequencies (p, q)
  • Generate expected HW genotypic frequencies
  • p2, 2pq, q2
  • Compare observed vs. HWE genotypic frequencies
  • ?2 goodness-of-fit, G-test (likelihood method),
    exact tests (small samples)
  • Power to reject hypothesis depends on
  • Actual difference
  • Sample size
  • Complexity of model (degrees freedom)
  • Programs GENALEX, FSTAT, GenePop, Arlequin,
    others

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Testing for HWE An example using c2
  • Australian aborigine sample
  • Assume N 2000

MM MN NN f(M) f(N)
OBS 48 608 1344 0.176 0.824
EXP 62 580 1358
c2 (48-62)2/62 (608-580)2/580
(1344-1358)2/1358 3.161 1.352 0.144 4.66
(significant at Plt 0.05)
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How Diversity is Organized
  • Population Structure

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Population structure A deviation from HWE
  • F the fixation index
  • Another measure of departure from HW
  • F is a measure of within population inbreeding

F (He - Ho )/ He
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F statistics can be extended to hierarchical
populations
  • The hierarchical F statistics (also called
    Wrights F statistics)
  • Provide a way to distinguish within-population
    inbreeding from among-population divergence
  • Provide a measure of the proportionate
    distribution of variation (or population
    structure)

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Partitioning variation in populations Wrights F
  • F-statistics can be interpreted in many ways,
    e.g.
  • as a measure of inbreeding
  • identity by descent from common ancestor
  • identity in allelic state (homozygosity) or not
    (heterozygosity)
  • From a sampling perspective, ask What are the
    chances of drawing two alleles having the same
    allelic state?
  • Where the alleles are randomly drawn from either
  • Individuals
  • Subpopulations
  • Total population (metapopulation)
  • Individuals
  • Subpopulations
  • Total

X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
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X
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Defining Wrights F statistics
  • We begin by discussing heterozygosity at
    different levels
  • HI Observed heterozygosity within subpopulations
    (similar to Ho above)
  • HS Expected heterozygosity within subpopulations
    (similar to He above)
  • HT Expected heterozygosity if the combined
    population (metapopulation) were random mating.
    This would be HT 2pavgqavg (average allele
    frequencies over metapopulation)

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F statistics are defined in terms of H
  • FIS (HS HI)/HS (measuring departures from HW
    within subpopulations or local inbreeding)
  • FST (HT - HS)/HT (measuring departures from HW
    due to population differences, which is same as
    admixture, or Wahlunds effect)
  • FIT (HT HI)/HT (includes both local
    inbreeding and population structure)
  • Together, they are related as
  • (1 FIS) (1 FST) (1 FIT)
  • Of these measures, FIS and FST are the most
    meaningful since they partition local inbreeding
    vs. population subdivision and describe how
    variation is proportioned

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Individual to subpopulation Wrights FIS
  • A measure of the proportion of variation among
    subpopulations
  • Selfing, mating to relatives, and assortative
    mating create "local" deficiency of
    heterozygosity (localized inbreeding)
  • Individual to subpopulation" F
  • Scale
  • 0 (no inbreeding) to 1 (complete
  • inbreeding)

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Subpopulation to total Wrights FST
  • A measure of the proportion of variation among
    populations
  • Reduction of heterozygosity compared to random
    mating
  • Measure of the probability that two gene copies
    chosen at random from different subpopulations
    are identical-by-descent.
  • Scale 0 (heterozygosity identical across
    populations) to 1 (populations maximally
    different)

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