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Design and Analysis of Microarray Experiments at CSIRO Livestock Industries. Toni Reverter Bioinformatics Group CSIRO Livestock Industries Queensland Bioscience Precinct 306 Carmody Rd., St. Lucia, QLD 4067, Australia. SSAI – QLD Branch – 6 Apr. 2004.

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Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of

Microarray Experiments at

CSIRO Livestock Industries

Toni Reverter

Bioinformatics Group

CSIRO Livestock Industries

Queensland Bioscience Precinct

306 Carmody Rd., St. Lucia, QLD 4067, Australia

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

CONTENTS

Slides

Minutes

  • Introduction …………………………… 4 6

  • Technical Concerns ……...……………. 2 7

  • Designs ………………..……………….21 15

  • Analysis ……………..…………………14 16

  • Coverage and Sensitivity ...……………. 5 7

  • Summary …………....………………… 2 4

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

This is a Cow

This is a Pig

(female)

This is a Sheep

This is a Chicken

1. Introduction

1.a – The Material

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Tissue Samples

Treat A

Treat B

Analysis

mRNA Extraction & Amplification

+

Image Capture

cDNA “A” Cy5

cDNA “B” Cy3

Laser 1 Laser 2

Hybridization

Optical Scanner

1. Introduction

1.b - The Method

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Logical

cDNA

Distribution

Quantitative

Computer Sci.

Statisticians

Mathematicians

…….

Non-Q

Biochemists

Physiologists

Pathologists

…….

1800s – DATA

30-60s – METHODS

50-70s – SOFTWARE

1980s – COMPUTER

BANANA

EGG

Source

Size

“banana omelette”

Historical Excitement Balance Interdisciplinary

1. Introduction

1.c - The Challenge

Data Dependent

Time Dependent

Human Dependent

Chronology

Skill Integration

Paradigm

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

“The majority of microarray papers

are analysed with substandard methods”

C Tilstone (citing D Allison), Nature 2003, 424:610

CLAIM

REASONS

P Value

1. Introduction

1.c – Human-Dependent Challenge

JOKE

The Biologist and the Statistician are being executed.

They are both granted one last request.

The Statistician asks that he/she be allowed to give one

final lecture on his/her Grand Theory of Statistics.

The Biologist asks that he/she be executed first.

  • Biologists don’t care …………………………………10

  • Statisticians are bad ………………………………….20

  • Unrealistic expectations ………………………………70

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

  • Replication:

    • Animal

    • Sample

    • Array

    • Spot

2. Technical Concerns

  • Biochemist Level:

    • Preparation (Printing) of the Chip

    • RNA Extraction, Amplification and Hybridisation

    • Optical Scanner (Reading)

  • Quantitative Level:

    • Design

    • Image (data) Quality

    • Data Analysis

    • Data Storage

Note:Randomisation intentionally neglected.

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

2. Technical Concerns

2.a – Data Quality: GP3xCLI

2.b – Storage: GEXEX

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Put more arrays

on key questions

Pooling?

$

  • Dye-Swap

  • Dye-Balancing

  • Self-Self

Evaluation of Designs:

O

A

O

A

O

A

B

AB

B

AB

B

AB

Loop

All-Pairs

Reference

Variance of Estimated Effects(Relative to the All-Pairs)

Reference

1

1

3

2

Loop

4/3

1

8/3

1

All-Pairs

1

1

2

1

Main effect of A

Main effect of B

Interaction AB

Contrast A-B

3. Experimental Designs

Key Issues:

  • Identify/Prioritise Questions

  • N of Available Samples

  • N of Available Arrays

  • Consider Dye Bias

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

  • Samples vs Slides vs Configurations

Samples (S)

3

4

12

(S-1)

2

3

11

Arrays

S(S-1)

6

12

132

3. Experimental Designs

Glonek & SolomonFactorial and Time Course Designs for

cDNA Microarray Experiments

  • Definition

  • A design with a total of n slides and design matrix X is said to be admissible

  • if there exists no other design with n slides and design matrix X* such that

  • ci*  ci

  • For all i with strict inequality for at least one i. Where ci* and ci are respectively

  • the diagonal elements of (X*’X*)-1 and (X’X)-1.

N of Configurations?

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

N of Configurations?

SA-1

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

N of Configurations?

Pie-Bald black

Non-Pie-Bald black

Normal

White

Recessive

SA-1 = 53 = 125

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

x5

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

N of Configurations?

0 hr

24 hr

SA-1 = 109 = 1 Billion!

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

Transitivity (Townsend, 2003) & Extendability (Kerr, 2003)

Opt 2: 10 Slides

Opt 1: 10 Slides

Opt 3: 11 Slides

Opt 4: 9 Slides

Opt 5: 9 Slides

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

N of Configurations?

0 hr

24 hr

SA-1 = 1210 = 62 Billion!

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

N of Configurations?

0 hr

24 hr

R

G

R

G

G

R

G

R

G

R

R

G

G

R

R

G

G

R

R

G

G

R

R

G

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

Handling Constraints (Samples & Arrays):

Pooling & Replication

  • Pavlidis et al.(2003) The effect of replication on gene

  • Expression microarray experiments. Bioinformatics 19:1620

>= 5 Replicates

10-15 Replicates

  • Peng et al.(2003) Statistical implications of pooling RNA

  • Samples for microarray experiments. BMC Bioinformatics 4:26

Power: n9c9  95%, n3c3  50%, n9c3  90%

n25c5  n20c20

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

Pooling & Replication

R

G

F HS

G

R

R

M TM

G

R

N of Arrays?

F HS

24: 23 To 552

R

G

pooling

M HS

G

G

G

G

R

F TM

14: 13 To 182

R

R

R

M HS

R

R

G

G

G

F HS

R

G

R

G

M HS

R

G

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

Pooling & Replication

Reference Design

Sum(ABS) 26.8 26.8 39.1 23.1 17.3 7.1 7.1 14.3 14.3

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

Another (NEW?) Constraint:

Amount of RNA

A

M avium slope 18 days 33-3-3

M avium broth 18 days101-2-2-1-2-1-2-1-2-1

B

M para broth 10 weeks 51-2-2-1-1

C

M para broth 12 weeks 61-1-4-5-2-1

D

M para in-vivo 31-1-1

E

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3. Experimental Designs

Another (NEW?) Constraint:

Amount of RNA

A

B

A

C

Importance due to Transitivity of AB with BC and BD

A

D

A

E

B

C

B

D

Procedure:

Five configurations will be proposed and the statistical optimality of each evaluated.

B

E

C

D

C

E

D

E

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

3

3

3

1

2

2

1

2

1

2

1

2

1

1

2

2

1

1

1

1

4

5

2

1

1

1

1

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Configuration 1

3

3

3

1

2

2

1

2

1

2

1

2

1

1

2

2

1

1

1

1

4

5

2

1

1

1

1

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Configuration 2

3

3

3

1

2

2

1

2

1

2

1

2

1

1

2

2

1

1

1

1

4

5

2

1

1

1

1

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Configuration 3

3

3

3

1

2

2

1

2

1

2

1

2

1

1

2

2

1

1

1

1

4

5

2

1

1

1

1

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Configuration 4

3

3

3

1

2

2

1

2

1

2

1

2

1

1

2

2

1

1

1

1

4

5

2

1

1

1

1

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Configuration 5

3

3

3

1

2

2

1

2

1

2

1

2

1

1

2

2

1

1

1

1

4

5

2

1

1

1

1

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

Imp WeightSquared Error

1 2 3 4 5 1 2 3 4 5

46 5 6 6 5 4 1 4 4 1

20 2 1 0 0 4 0 1 4 4

23 2 2 3 4 1 0 0 1 4

10 0 0 0 0 1 1 1 1 1

35 5 4 4 5 4 4 1 1 4

44 5 5 5 5 0 1 1 1 1

10 0 0 0 0 1 1 1 1 1

22 0 2 3 2 0 4 0 1 0

10 0 0 0 0 1 1 1 1 1

43 3 3 3 3 1 1 1 1 1

SSE17 14 11 16 18

01 2 1 0 0 MSE.74 .64 .48 .66 .75

A

B

A

C

A

D

A

E

Conclusion: Configuration 3

B

C

B

D

B

E

C

D

C

E

D

E

Noise

D

D

SSAI – QLD Branch – 6 Apr. 2004


Design and analysis of microarray experiments at csiro livestock industries

Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

4. Data Analysis

My (EDUCATED?) View:

  • Relaxed data acquisition criteria

    • Signal to Noise > 1.00 (relaxer (sp?) exist)

    • Mean to Median > 0.85 (Tran et al. 2002)

  • Moving away from

    • Ratios

    • “heavy-duty” normalisation techniques

  • Mixed-Model Equations

    • Check residuals

    • Check REML estimates of Variance Components

    • Proportion of Total V due to Gene x Variety

  • Process results Gene x Treatment

    • Mixtures of Distributions

  • SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    Mixed-Model Equations

    Log2

    Intensities

    Residual

    (RANDOM)

    Gene x

    Variety

    (RANDOM)

    Comparison Group

    Array|Block|Dye

    (FIXED)

    Main Gene

    Effect

    (RANDOM)

    Gene x

    Array|Block

    (RANDOM)

    DE Genes

    Gene x Dye

    (RANDOM)

    Note:

    missing but (generally) unimportant.

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    Mixed-Model Equations

    Log2(Int.) = CG + Gene + GDye + GArray + GVariety + Error

    Control

    of

    FDR

    The proportion of the Total Variation

    accounted for by the G x Variety Interaction

    anticipates the proportion of DE Genes

    CLAIM

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    Y11

    197,802

    9.33

    1.99

    5.17

    15.99

    768

    257.5

    139

    343

    Y12

    74,030

    10.82

    1.91

    4.95

    15.99

    576

    128.5

    22

    243

    Y21

    110,308

    9.99

    2.07

    4.25

    15.99

    576

    191.5

    27

    319

    Y22

    116,409

    9.89

    2.09

    5.17

    15.99

    576

    202.1

    19

    318

    Y23

    117,687

    10.38

    2.04

    4.91

    15.99

    576

    204.3

    36

    320

    Y31

    106,591

    10.11

    1.77

    6.60

    15.99

    672

    158.6

    37

    278

    Y32

    236,671

    9.44

    2.11

    5.36

    15.99

    1,440

    164.3

    57

    269

    4. Data Analysis

    ObservationsComparison Groups

    Levels Observations

    N Mean SD Min Max Mean Min Max

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    • 54 Array Slides

    • 959,498 Valid Intensity Records (S2N>1, M2M>0.85)

    • 7,638 Elements (genes)

    • 752,476 Equations

    • 56 (Co)Variance Components (REML)

    • BAYESMIX (Bayesian Mixtures of distributions)

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    56 (Co)Variance Components

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    % Total

    Variance

    Due to:

    • Error3.0 – 3.6 5.1 – 6.7 3.0 – 3.7

    • Gene 83.6 – 90.4 78.3 – 81.9 47.5 – 83.9

    • Gene x Array3.5 – 9.8 10.4 – 12.6 10.6 – 43.5

    • Gene x Variety 2.4 – 3.7 2.1 – 2.6 2.5 – 5.4

    • Genetic Correlations Moderate (EXP3) to Strong

    • Gene  Variety Corr Strong (EXP1) to Moderate (EXP2)

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    Measures of (Possible) Differential Expression

    i = 1, …, 7,638 genes

    j = 1, …, 7 variables

    t = 0, …, 5 time points (EXP3 only)

    • Other measure definitions could also be valid

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    Mixtures of Distributions

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    Mixtures of Distributions

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    Differentially Expressed Genes

    Exp1 Exp2 Exp3

    Up Down Up Down Up Down

    High-LowUp 409 0 26 13 36 11

    Down 41 3 0 5 0

    HOL-JBL Up 68 0 0 8

    Down 319 10 6

    TSS-UTSUp 252 0

    Down 109

    10 DE Elements across the 3 Exp

    (2 UP/DOWN/UP; 8 UP/UP/DOWN)

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    Residuals Plots

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    178 @ Day 82

    • Homologs

    • Orthologs

    • Paralogs

    Allocation of

    238 DE Genes

    55

    123

    30

    93

    12

    43

    40

    11

    42

    36

    53

    36

    36

    46

    36

    10

    75

    41

    5

    5

    22

    5

    14

    5

    114 @ Day 105

    171 @ Inguinal

    24

    26

    21

    81

    27

    26

    99

    39

    44

    130

    25

    12

    43

    12

    12

    31

    12

    22

    23

    45

    16

    55

    71

    68

    Bovine

    Up-Regulated

    Down-Regulated

    Ovine

    139 @ Day 120

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    4. Data Analysis

    The “Real” Target: Molecular Interaction Maps

    Adapted from Aladjem et al. 2004, Sciences’s STKE

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    MPSS Test Data

    No Tags = 25,503

    S 1 S 2

    100.00 100.00

    57.14 49.87

    36.11 33.66

    10.89 10.74

    5.73 5.67

    1.21 1.13

    0.57 0.55

    0.15 0.11

    0.05 0.05

    cDNA Noise Paper

    PNAS 02, 99:14031

    100.00

    56.19

    36.79

    11.76

    6.95

    1.94

    1.11

    0.29

    0.16

    5. Coverage and Sensitivity

    MPSS Paper

    PNAS 03, 100:4702

    tpmN Tags %

    > 1(0.0)27,965 100.00

    5(0.7)15,145 54.16

    10(1.0)10,519 37.61

    50(1.7) 3,261 11.66

    100(2.0) 1,719 6.15

    500(2.7) 298 1.07

    1,000(3.0) 154 0.55

    5,000(3.7) 26 0.09

    10,000(4.0) 7 0.02

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    5. Coverage and Sensitivity

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    %

    Flat line (except Upper Bound)

    x

    5. Coverage and Sensitivity

    LetNT = N of “Total” Genes

    ND = N of “Differentially Expressed” Genes (ND  NT)

    • The relevance of f(xi) is limited to the Concentration  Signal mapping.

    • At equilibrium the probability of an error either way equals.

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    5. Coverage and Sensitivity

    ~ 5 tpm

    ~ 100 tpm

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    5. Coverage and Sensitivity

     < 

     = 

     > 

    Not many DE genes

    High Confidence

    Few False +ve

    Lots of DE genes

    High Power

    Few False -ve

    SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    6. Summary

    • General (ie. not only CSIRO LI):

    • Still in its infancy (…possibly even embryonic stage)

    • Many decisions have a heuristic rather than a theoretical foundation

    • Prone to miss-conceptions:

      • Amount of Expression = Amount of Response

      • Same cut-off point to judge all genes

      • Over-emphasis in normalization (hence, despise “Boutique Arrays”)

      • Over-emphasis in variance stabilization

      • Over-emphasis in controlling false-positives

      • Over-emphasis in biological replicates (DANGER )

  • No hope for a “One size fits all” software (even method)

  • Safer to aim towards “Tailor to individual’s needs”

  • Integration of interdisciplinary skills is a must

  • SSAI – QLD Branch – 6 Apr. 2004


    Design and analysis of microarray experiments at csiro livestock industries

    Design and Analysis of Microarray Experiments at CSIRO Livestock Industries

    6. Summary

    • Livestock Species:

    • Tailing humans (…at the moment)

      • Andersson & Georges (2004) Domestic-animal genomics: Deciphering the genetics of complex traits. Nature Genetics, March 2004, Vol 5:202-212

  • Several key advantages

    • More relaxed ethical issues (…relative to R&D in humans)

    • Very strong similarities at the genome level with humans

    • The genome is (being) sequenced for several species

  • Strong background knowledge of genetics accumulated

    • Quantitative genetics

    • Mixed-Model equations

    • Computing expertise

  • Journals will soon be inundated

  • We have the opportunity to participate

  • SSAI – QLD Branch – 6 Apr. 2004


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