Course on Biostatistics

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Course on Biostatistics

• Instructors
• Dr. Malgorzata Bogdan
• Dr. David Ramsey
• Institute of Mathematics and Computer Science
• Wroclaw University of Technology
• Poland

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Course on Biostatistics

• Two parts
• 1. Locating genes influencing quantitative traits
  in experimental populations.
• 20.03-30.03. 2006, Malgorzata Bogdan
• 2. Population Genetics
• 22.05-2.06.2006, David Ramsey

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Grading

• Students can gain 50 points for each part of the
  course (25 for a project, 25 for an exam).
• The final grade will be based on the total
  percentage.
• To pass the course the student has to gain at
  least 15 points for each part of the course and
  at least 50 points in total.

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First part

• Locating genes influencing quantitative traits in
  experimental populations.
• 20.03-30.03. 2006 Malgorzata Bogdan

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Course Outline

• Introduction to genetics and experimental
  populations.
• Basic methods of locating quantitative trait loci
  (QTL).
• Locating QTL with QTL Cartographer.

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Helpful materials

• Text book
• Genetics and Analysis of Quantitative Traits by
  Michael Lynch and Bruce Walsh
• Software Windows QTL Cartographer
• S.Wang, C.J. Basten, Z-B. Zeng
• Program in Statistical Genetics, North Carolina
  State University
• Can be downloaded from
• http//statgen.ncsu.edu/qtlcart/WQTLCart.htm

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Main Goal

• Learn how to locate regions of the genome hosting
  genes influencing some quantitative traits
  (Quantitative Trait Loci QTL).
• Statistical methods mainly linear models.

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Introduction to Genetics
DNA - A nucleic acid that carries the genetic
information in the cell. DNA consists of two
long chains of nucleotides joined by hydrogen
bonds between the complementary bases adenine
and thymine or cytosine and guanine. The
sequence of nucleotides determines individual
hereditary characteristics. http//www.answers.c
om/topic/dna
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Introduction to Genetics

• Chromosome a long, continuous piece of
  DNA, which contains many genes, regulatory
  elements and other intervening nucleotide
  sequences.
• Diploid organisms chromosomes appear in pairs
  (one from each parent)

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• Allele - any of two or more alternative forms of
  a gene that occupy the same locus on a
  chromosome.
• Example allele of blue eyes, allele of brown
  eyes
• Genotype at a single locus the pair of alleles
  that individual carries at the locus.

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The Hardy-Weinberg principle

• Random mating
• pa- frequency of a allele
• pA- frequency of A allele
• P(aa)p2a
• P(aA)2papA
• P(AA)p2A

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• Phenotype observed or measured characteristic
  (or trait) for an individual.
• We will be dealing with quantitative traits like
  eg. height, yield, blood pressure etc.

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Heritability

• Z - the phenotypic (trait) value of an individual
• G the genotypic value (the sum of the total
  effects of all loci on the trait)
• E an environmental deviation
• Z G E
• Broad sense heritability (population parameter)
• H2 Var (G) / Var (Z)

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The influence of a single locus
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Fishers decomposition of the Genotypic Value

• Consider a biallelic locus with alleles a, A
• N number of alleles a for a given
  individual
• (gene content)
• We regress G on N

• Var(G) ?2A ?2D

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Trait Influenced by Two Loci

• Gijkl mean phenotype for individuals with
• genotypes (i j k l)
• ai Gi- ?G - additive effect of i allele
• dij Gij..- ?G - ai - aj - dominance effects
  at the first locus
• dkl Gkl..- ?G - ak - al - dominance effects
  at the second locus

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Possible interactions (epistasis)

• (aa)ikGi.k.- ?G ai ak
• (ad)ikl
• Gi.kl.- ?G ai ak al dkl- (aa)ik-
  (aa)il
• (dd)ijkl Gijkl.- ?G ai aj ak al dij -
  dkl
• - (aa)ik- (aa)il-(aa)jk- (aa)jl
• - (ad)ikl- (ad)jkl - (ad)ijk-
  (ad)ijl

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Example (Lynch and Walsh)

• Teosinte wild progenitor of cultivated maize
• Two loci (markers) - UMC107 , BV302
• UM, BM maize alleles
• UT, BT teosinte alleles
• Trait the average length of the vegetative
  internodes in the lateral branch (in mm)

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Mean trait values
UMC107 UMC107 UMC107
BV302 UMM UMT UTT
BMM 18.0 40.9 61.1
BMT 54.6 47.6 66.5
BTT 47.8 83.6 101.7
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Genotype Frequencies
UMC107 UMC107 UMC107
BV302 UMM UMT UTT
BMM
BMT
BTT
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Cockerham model 1
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Cockerham model 2
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Cockerham model 3two loci
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Genetic maps

• Markers genetic loci which express
  experimentally detectable variation between
  individuals.
• Genetic map gives an order of markers on a
  chromosome and a distance between them.
• 1 Morgan the expected value of the number of
  crossovers is equal to 1

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Genetic map
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low fat content a b q c d a b q c d
high fat content A B Q C D A B Q C D
A B Q C D A B Q C D
a b q c d A B Q C D
BC
A B Q C D A B Q C D
a B Q C d A B Q C D
a b q c d A B Q C D
A B q c d A B Q C D