Course on Biostatistics

• Instructors – • Dr. Małgorzata Bogdan• Dr. David Ramsey• Institute of Mathematics and Computer

Science• Wrocław University of Technology• Poland

Course on Biostatistics

• 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

• Locating genes influencing quantitative traits in experimental populations.

• 20.03-30.03. 2006 Małgorzata Bogdan

Course Outline

• 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

• 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

onsubstituti allelic ofeffect average the-

ˆ

GNG

•Var(G) = 2A+ 2

D

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=

• 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 UMM UMT UTT

BMM

BMT

BTT

Cockerham model 1

Z Aa if 1/2

aaor AA if 2/1

aa if 1 aA if 0 AA if 1

XG

Z

X

Cockerham model 2

1/2- 1 11/2 0 11/2- 1- 1

aa

aA

AA

GGG

Cockerham model 3two loci

iiddiidaiiadiiaa

iiiiij

ZZXZZXXX

ZZXXG

21212121

22112211

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 BxP:

AB x BF1:

low fat contenta b q c da b q c d

high fat contentA B Q C DA B Q C D

a b q c dA B Q C D

A B Q C DA B Q C D

A B Q C DA B Q C D

A B q c dA B Q C D

a B Q C dA B Q C D

a b q c dA B Q C D

BC: