Module 1

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Module 1

• Basic principles in population and quantitative
  genetics

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Genes and Genomes
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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
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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

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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
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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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