Download Intensity-Dependent Normalization

Course on Biostatistics
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Instructors –
Dr. Małgorzata Bogdan
Dr. David Ramsey
Institute of Mathematics and Computer
Science
• Wrocław University of Technology
• Poland
Course on Biostatistics
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Two parts
1. Locating genes influencing quantitative
traits in experimental populations.
20.03-30.03. 2006, Małgorzata Bogdan
2. Population Genetics
22.05-2.06.2006, David Ramsey
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.
First part
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Locating genes influencing quantitative
traits in experimental populations.
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20.03-30.03. 2006 Małgorzata Bogdan
Course Outline
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Introduction to genetics and
experimental populations.
Basic methods of locating quantitative
trait loci (QTL).
Locating QTL with QTL Cartographer.
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
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.
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.com/topic/dna
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)
• 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.
The Hardy-Weinberg principle
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Random mating
pa- frequency of a allele
pA- frequency of A allele
P(aa)=p2a
P(aA)=2papA
P(AA)=p2A
• Phenotype – observed or measured
characteristic (or trait) for an individual.
• We will be dealing with quantitative traits
like eg. height, yield, blood pressure etc.
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)
The influence of a single locus
Fisher’s 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
G     N    Gˆ  
 - the average effect of allelic substituti on
•Var(G) = 2A+ 2D
Trait Influenced by Two Loci
• Gijkl – mean phenotype for individuals with
genotypes (i j; k l)
• αi = Gi…- G - additive effect of i allele
• δij = Gij..- G - αi - αj - dominance effects at
the first locus
• δkl = Gkl..- G - αk - αl - dominance effects at
the second locus
Possible interactions (epistasis)
• (αα)ik=Gi.k.- G – αi – αk
• (αδ)ikl=
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Gi.kl.- G – αi – αk – αl – δkl- (αα)ik- (αα)il
• (δδ)ijkl= Gijkl.- G – αi – αj – αk – αl – δij - δkl
- (αα)ik- (αα)il-(αα)jk- (αα)jl
- (αδ)ikl- (αδ)jkl - (αδ)ijk- (αδ)ijl
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)
Mean trait values
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
Genotype Frequencies
UMC107
BV302
BMM
BMT
BTT
UMM
UMT
UTT
Cockerham model 1
 1 if

X   0 if
 1 if

AA
aA
aa
 1 / 2 if AA or aa
Z 
 1/2 if Aa
G    X  Z
Cockerham model 2
GAA  1 - 1 - 1/2    
G   1 0 1/2   
 aA  
 
Gaa  1 1 - 1/2   
Cockerham model 3
two loci
Gij    1 X 1i   2 X 2i  1Z1i   2 Z 2i
  aa X 1i X 2i   ad X 1i Z 2i   da Z1i X 2i   dd Z1i Z 2i
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
Genetic map
A
P:
x
low fat content
abqcd
abqcd
F1:
a b q c d
ABQCD
B
high fat content
ABQCD
ABQCD
AB
x
B
ABQCD
ABQCD
BC:
a b q c d
ABQCD
AB q c d
ABQCD
a BQC d
ABQCD
ABQCD
ABQCD