Experiments in Plant Hybridization Mendel 1865

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Experiments in Plant Hybridization (Mendel 1865)

• Mendel is great science, great statistics and a
  good puzzle. There are many intriguing features
  of his work, and it is instructive and enjoyable
  attempting to come to terms with them.
• What was his aim? What was special about peas?
  What was special about Mendel?
• Mendel was not the first to experiment in the way
  he did with peas. He was probably not the first
  to get the results he got, but he seems to have
  been the first to have noticed this regularity,
  to have theorized concerning it, to have tested
  his theory, and to have gone on to do more.
• There are many readily available English
  translations of Mendel's paper Stern and
  Sherwood's book includes a number of related
  documents Fisher's has a few marginal comments,
  which supplement and update his famous 1936
  paper while the most recent by Corcos and
  Monaghan has many useful botanical remarks.

Next few slides courtesy of Terry Speed,
Statistics in Genetics Course, UC Berkeley
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Cliffs Notes to Mendel

• Introductory remarks (1). Literature review. The
  nature of the experiments referred to at the very
  beginning is unclear they are the first
  Mendelian puzzle. He more or less states his aim
  as seeking the laws governing the formation of
  hybrids.
• Selection of experimental plants (2). Here Mendel
  rather clearly answers the question Why peas? It
  is important to be clear - and Mendel was not
  always - on the distinction between a trait and
  variant forms of a trait, e.g. seed shape, and
  the smooth and wrinkled (angular) forms.
• So, why the sweet pea and not something else?

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Genus Pisum
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Cliffs Notes (continued)

• Arrangement and sequence of experiments (3). Much
  has been written concerning the precise set of
  varieties Mendel used. For example did he have
  seven pairs of varieties, each differing in the
  way described, or did he have fewer? (In other
  words, is the sentence opening section 8
  literally true?) If he had fewer than seven
  pairs, did he ignore data on segregating factors
  other than that under discussion? Despite
  referring to the seed, coat color is in fact a
  character of the maternal plant. Mendel certainly
  knew this, and it has significant implications
  for the design and analysis of his experiments.
• Form of the hybrids (4). Here we get the first
  results the appearance of what we now call
  dominance, what Mendel called dominating and
  recessive. Note that he got the same thing when
  he switched seed and pollen parents, i.e. carried
  out what is known as the reciprocal cross. He
  also notes some differences beween the hybrids
  and the corresponding dominant parents.

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Cliffs Notes (continued)

• The first generation from hybrids (5).In this
  section Mendel reports his famous 31 segregation
  ratios, and emphasizes the need for further
  experimentation to ascertain the composition of
  his plants.
• The second generation from hybrids (6).Now
  Mendel has determined that his 31 is in fact
  121. To do so with one seed and all plant
  characters, he had to sample his first generation
  (from hybrid) dominant plants, and take only a
  limited number of seeds from each. Why? He also
  repeated one experiment because the initial
  result deviated too greatly from what he was
  expecting.

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First generation raw data

• Expt. 1. Form of seed. -- From 253 hybrids 7324
  seeds were obtained in the second trial year.
  Among them were 5474 round or roundish ones and
  1850 angular wrinkled ones. Therefrom the ratio
  2.961 is deduced.
• Expt. 2. Color of albumen. -- 258 plants yielded
  8023 seeds, 6022 yellow, and 2001 green their
  ratio, therefore, is as 3.011.

Experiment 1 Experiment 2 Form of Seed
Color of Albumen Plants Round
Angular Yellow Green 1 45 12
25 11 2 27 8 32
7 3 24 7 14 5 4
19 10 70 27 5 32 11 24
13 6 26 6 20 6 7
88 24 32 13 8 22 10
44 9 9 28 6 50
14 10 25 7 44 18
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Cliffs Notes (continued)

• The subsequent generations from hybrids (7).The
  pattern held up. An explanation for the
  phenomenon of reversion was offerred. Mendel's
  argument shows how repeated selfing leads to
  homozygosity.

Ratios Generation A Aa a A
Aa a ----------------------------------
------------------ 1 1 2 1
1 2 1 2 6 4 6
3 2 3 3 28 8 28
7 2 7 4 120 16
120 15 2 15 5 496
32 496 31 2 31
. .......... ........ n
n n 2 - 1 2 2 - 1
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Cliffs Notes (continued)

• The offspring of hybrids in which several
  differing traits are associated (8). In this
  rather long section, Mendel reported the results
  of his dihybrid and trihybrid experiments. He
  also makes greater use of the algebraic notation
  introduced at the end of section 7. His
  proportions 9331, and the trihybrid analogue
  confirmed the independent segregation of these
  three traits. Note that once he adds seed-coat
  color to the other two seed characters, the
  logistic problems associated with this trihybrid
  experiment become truly formidable.
  Generalization to more than 3 segregating traits
  is discussed briefly.
• The reproductive cells of hybrids (9). This is
  undoubtedly the most interesting (and longest)
  section of the paper, and perhaps the most
  difficult to read. In it Mendel formulates his
  theory, and tells us that it explains his results
  to date. He then describes new experiments which
  test his theory. A cross between a hybrid and one
  of the true-breeding lines that gave rise to the
  hybrid is called a backcross. In every case, the
  resulting plants were permitted to self, to
  confirm their composition. Further confirmation
  of his theory was obtained by carrying out
  similar crosses with plant traits. In the last
  part of this section, he restated his theory in
  algebraic terms, and showed how it also accounted
  for his observations on the independent
  segregation of two or three traits.

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Cliffs Notes (continued)

• Experiments on hybrids of other plant species
  (10). Now Mendel considers the extent to which
  his findings generalize. For some bean traits,
  what he found held true, but for color it did
  not. However, his numbers were small, and is
  results did not rule out the possibility that the
  color trait could be explained by two or more
  independently segregating factors. He displays
  algebra foreshadowing the discovery 40 years
  later of a Mendelian explanation of continuously
  varying traits.
• Concluding remarks (11). This is a rather
  difficult section for us, requiring a knowledge
  of research of Mendel's day. He discusses a
  number of segregating traits, true breeding
  hybrids, and what was termed transformation the
  conversion of one variety into another by
  repeated backcrossing. In each case, his concern
  was with explaining known phenomena from the
  viewpoint of his new theory.

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Mendels Algebraic Form

• A self-cross of the hybrid AaBb
• (A 2Aa a) (B 2Bb b)
• 1 AB
• 1 Ab
• 1 aB
• 1 ab
• 2 ABb
• 2 aBb
• 2 AaB
• 2 Aab
• 4 AaBb

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Genetic phase

• Haplotype alleles received by an individual
  from one parent
• Phase For a doubly heterozygous individual A/a
  B/b, whether the A allele was received in the
  same haplotype as the B or b allele.

PHASE KNOWN
PHASE UNKNOWN
A B
a b
A B
a b
A B
A B
a b
a b
A B
a b
A B
a b
A B
a b
A B
a b
or
Could be
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An exampleMorgans Fly Experiments

• One gene affects eye color(pr, purple, and pr,
  red)The other affects wing length(vg,
  vestigial, and vg, normal).
• Morgan crossed pr/pr vg/vg flies with pr/pr
  vg/vg and then testcrossed the doubly
  heterozygous F1 femalespr/pr vg/vg ?
  pr/pr vg/vg ?.
• Because one parent (tester) contributes gametes
  carrying only recessive alleles, the phenotypes
  of the offspring reveal the gametic contribution
  of the other, doubly heterozygous parent.

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The test cross format
P pr/pr vg/vg pr/pr vg/vg
F1 pr/pr vg/vg
Tester pr/pr vg/vg pr/pr vg/vg
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Reverse phase experiment
P pr/pr vg/vg pr/pr vg/vg
F1 pr/pr vg/vg
Tester pr/pr vg/vg pr/pr vg/vg
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Another example showing the importance of phase
information
1
2
No Disease
HC/Y
HC/hc?
Colorblind
Colorblind Hemophilia
1
2
HC/Y
HC/hc
1
2
3
4
5
6
HC
hc/Y
Hc/Y
HC/Y
hc/Y
hc/Y
HC/Y
What is the genetic distance between these genes?
Could this computation be done without the
grandparents?
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SNPs and Pharmacogenomics

• Refers to the complete list of genes that
  determine the overall efficacy and toxicity of a
  drug
• Tries to account for all genes that influence
• Drug metabolism
• Drug transport/export
• Receptors
• Signaling pathways, etc.
• Your genotype would allow a physician to
  determine the optimal dose and medication for
  optimal therapy
• Pharmas are spending a lot of money to discover
  clinically relevant SNPs

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Population Genetics 101Measuring Genetic
Variation

• Hardy-Weinberg equilibrium (HWE)
• Genotype frequencies depend only on gene
  frequencies
• pA frequency of allele A
• pB frequency of allele B
• P(A/A) pA2 P(A/B) pB2 P(A/B) 2pApB
• pA pB 1
• pA2 2pApB pB2 1

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Population Genetics 101Measuring Genetic
Variation

• Observed vs. expected heterozygosity
• Ho Observed fraction of heterozygous
  individuals
• He Expected fraction based on allele
  frequencies
• The frequency f(X) of allele X is the fraction of
  times it occurs over all loci (2 per individual)
• He 1 the probability of homozygosity
• 1 f2(X) f2(Y) for all alleles
  (X,Y,)

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Example 10 Unique Genotypes(in bp lengths of
microsatellite)
Ho 0.30 He 0.69
H 1 high diversity H 0 asexual
mitotic reproduction Ho ltlt He indicates
selective pressure or non-random mating
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Components of the genetic model

• Components of the genetic model include
  inheritance pattern (dominant vs. recessive,
  sex-linked vs. autosomal), trait allele frequency
  (a common or rare disease?), and the frequency of
  new mutation at the trait locus.
• Another important component of the genetic model
  is the penetrance of the trait allele. Knowing
  the penetrance of the disease allele is crucial
  because it specifies the probability that an
  unaffected individual is unaffected because he's
  a non-gene carrier or because he's a
  non-penetrant gene carrier. The frequency of
  phenocopies is an important component, too.
• Rough estimates of the disease allele frequency
  and penetrance can often be obtained from the
  literature or from computer databases, such as
  Online Mendelian Inheritance in Man
  (http//www3.ncbi.nlm.nih.gov/Omim/). Estimates
  of the rate of phenocopies and new mutation are
  frequently guesses, included as a nuisance
  parameter in some cases to allow for the fact
  that these can exist.
• Linkage analysis is relatively robust to modest
  misspecification of the disease allele frequency
  and penetrance, but misspecification of whether
  the disease is dominant or recessive can lead to
  incorrect conclusions of linkage or non-linkage.

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Steps to linkage analysis

• In pedigrees in which the genetic model is known,
  linkage analysis can be broken down into five
  steps
• State the components of the genetic model.
• Assign underlying disease genotypes given
  information in the genetic model.
• Determine putative linkage phase.
• Score the meiotic events as recombinant or
  non-recombinant.
• Calculate and interpret LOD scores.
• Let's take a look at each of these steps in
  detail.

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State the components of the model

• In this example, the disease allele will be
  assumed to be rare and to function in an
  autosomal dominant fashion with complete
  penetrance, and the disease locus will be assumed
  to have two alleles
• N (for normal or wild-type)
• A (for affected or disease)

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Assign underlying disease genotypes

• The assumption of complete penetrance of the
  disease allele allows all unaffected individuals
  in the pedigree to be assigned a disease genotype
  of NN. Since the disease allele is assumed rare,
  the disease genotype for affected individuals can
  be assigned as AN.

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Determine putative phase

• Individual II-1 has inherited the disease trait
  together with marker allele 2 from his affected
  father. Thus, the A allele at the disease locus
  and the 2 allele at the marker locus were
  inherited in the gamete transmitted to II-1.
  Once the putative linkage phase (the disease
  allele "segregates" with marker allele 2) has
  been established, this phase can be tested in
  subsequent generations.

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Score the meiotic events asrecombinant (R) or
non-recombinant (NR)

• There are four possible gametes from the
  affected parent II-1 N1, N2, A1, and A2. Based
  on the putative linkage phase assigned in step 3,
  gametes A2 and N1 are non-recombinant.

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Calculate LOD scores

• In this example, the highest LOD score is -0.09
  at q 0.40. At no value of q is the lod score
  positive, let alone gt3.0, so this pedigree has no
  evidence in favor of linkage between the disease
  and marker loci.