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Association Mapping
                  Through local genealogies


Thomas Mailund
Bioinformatics Research Center
http://www.birc.au.dk/
Gunshot wounds
Car accidents
Smoking induced
lung cancer       “Genetic” Diseases
Cardiovascular
disease
Obesity
Diabetes 2
Alzheimer
Schizophrenia
BRCA1
breast cancer
Cystic fibrosis
Haemophilia
Disease Mapping...
Locate disease-affecting polymorphism

   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
Disease Mapping...
Markers are locally correlated

   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
Disease Mapping...
Search for indirect signals

   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
Indirect Association
               “Tag” markers                   Unobserved marker


   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
Indirect Association


   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
Indirect Association


   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
Indirect Association


   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
Indirect Association


   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
Indirect
         Multi-Marker
          Association
   Cases (affected)
                        --A--------C--------A----G---X----T---C---A----
                        --T--------G--------A----G---X----C---C---A----
                        --A--------G--------G----G---X----C---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --T--------C--------A----G---X----T---C---A----
                        --T--------C--------A----T---X----T---A---A----

                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------A----G---X----T---C---G----
                        --T--------C--------A----T---X----T---C---A----
                        --A--------C--------A----G---X----T---C---A----
                        --A--------C--------G----T---X----C---A---A----
                        --A--------C--------A----G---X----C---C---G----

Controls (unaffected)
The Ancestral
Recombination Graph




              Hudson 1990, Griffith and Marjoram 1996
Local Phylogenies
For each “point” on the chromosome, the ARG
determines a (local) tree:
Local Phylogenies
For each “point” on the chromosome, the ARG
determines a (local) tree:
Local Phylogenies
For each “point” on the chromosome, the ARG
determines a (local) tree:
Local Phylogenies
For each “point” on the chromosome, the ARG
determines a (local) tree:
Clustering on a Tree
           Disease affecting mutation
Clustering on a Tree
  Complete penetrance


          Incomplete penetrance



  Spurious disease
Clustering on a Tree

  25%
              Case/control clustering
              is not random on the tree...
        75%




                             40%
                    60%
Using “Perfect Phylogenies”
 Use the four-gamete test to find regions that
 can be explained by a tree with no recurrent mutations




                                         Mailund, Besenbacher & Schierup 2006
Using “Perfect Phylogenies”
 Build trees for each such region




                                    Mailund, Besenbacher & Schierup 2006
Using “Perfect Phylogenies”
 Each marker splits a sub-tree in two




                                        Mailund, Besenbacher & Schierup 2006
Using “Perfect Phylogenies”
 Each marker splits a sub-tree in two




                                        Mailund, Besenbacher & Schierup 2006
Using “Perfect Phylogenies”
 Each marker splits a sub-tree in two




                                        Mailund, Besenbacher & Schierup 2006
Scoring the Clustering

                   Red=cases
                   Green=controls



Are the case chromosomes significantly
over-represented in some clusters?
Wild-types



                   Mutation

         Mutants


We can place “mutations” on the tree edges
and partition chromosomes into “mutants”
and “wild-types” and test for different
distributions of cases and controls
Wild-types



                   Mutation

         Mutants


Use average or maximum to score the tree

Average is kosher Bayesian stats; maximum
needs to be corrected for over-fitting.
Whole genome breast cancer
Localisation Accuracy
          A single causal mutation
 Max BF / min p-value used as point estimate
Localisation Accuracy
           Two causal mutations
 Max BF / min p-value used as point estimate
Power to detect
                     association
                                     power
             100
             80
Percentage

             60
             40
             20




                                                             QBlossoc
                                                             Student's t−test
             0




                       0.05                    0.10                0.15

                          Susceptibility allelle frequency
Blossoc
(BLOck aSSOCiation)
Homepage: www.birc.au.dk/~mailund/Blossoc
                           Command line and
                           graphical user interface
                           (with limited functionality)
Blossoc
(BLOck aSSOCiation)
Homepage: www.birc.au.dk/~mailund/Blossoc


                           Fast enough to analyse
                           tens of thousands of
                           individuals in hundred of
                           thousands of markers in a
                           few days on a desktop
                           computer...
Thank you!




                More information at
http://www.birc.au.dk/~mailund/association-mapping/

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Association mapping using local genealogies

  • 1. Association Mapping Through local genealogies Thomas Mailund Bioinformatics Research Center http://www.birc.au.dk/
  • 2. Gunshot wounds Car accidents Smoking induced lung cancer “Genetic” Diseases Cardiovascular disease Obesity Diabetes 2 Alzheimer Schizophrenia BRCA1 breast cancer Cystic fibrosis Haemophilia
  • 3. Disease Mapping... Locate disease-affecting polymorphism Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 4. Disease Mapping... Markers are locally correlated Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 5. Disease Mapping... Search for indirect signals Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 6. Indirect Association “Tag” markers Unobserved marker Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 7. Indirect Association Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 8. Indirect Association Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 9. Indirect Association Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 10. Indirect Association Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 11. Indirect Multi-Marker Association Cases (affected) --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Controls (unaffected)
  • 12. The Ancestral Recombination Graph Hudson 1990, Griffith and Marjoram 1996
  • 13. Local Phylogenies For each “point” on the chromosome, the ARG determines a (local) tree:
  • 14. Local Phylogenies For each “point” on the chromosome, the ARG determines a (local) tree:
  • 15. Local Phylogenies For each “point” on the chromosome, the ARG determines a (local) tree:
  • 16. Local Phylogenies For each “point” on the chromosome, the ARG determines a (local) tree:
  • 17. Clustering on a Tree Disease affecting mutation
  • 18. Clustering on a Tree Complete penetrance Incomplete penetrance Spurious disease
  • 19. Clustering on a Tree 25% Case/control clustering is not random on the tree... 75% 40% 60%
  • 20. Using “Perfect Phylogenies” Use the four-gamete test to find regions that can be explained by a tree with no recurrent mutations Mailund, Besenbacher & Schierup 2006
  • 21. Using “Perfect Phylogenies” Build trees for each such region Mailund, Besenbacher & Schierup 2006
  • 22. Using “Perfect Phylogenies” Each marker splits a sub-tree in two Mailund, Besenbacher & Schierup 2006
  • 23. Using “Perfect Phylogenies” Each marker splits a sub-tree in two Mailund, Besenbacher & Schierup 2006
  • 24. Using “Perfect Phylogenies” Each marker splits a sub-tree in two Mailund, Besenbacher & Schierup 2006
  • 25. Scoring the Clustering Red=cases Green=controls Are the case chromosomes significantly over-represented in some clusters?
  • 26.
  • 27. Wild-types Mutation Mutants We can place “mutations” on the tree edges and partition chromosomes into “mutants” and “wild-types” and test for different distributions of cases and controls
  • 28. Wild-types Mutation Mutants Use average or maximum to score the tree Average is kosher Bayesian stats; maximum needs to be corrected for over-fitting.
  • 29.
  • 30.
  • 32. Localisation Accuracy A single causal mutation Max BF / min p-value used as point estimate
  • 33. Localisation Accuracy Two causal mutations Max BF / min p-value used as point estimate
  • 34. Power to detect association power 100 80 Percentage 60 40 20 QBlossoc Student's t−test 0 0.05 0.10 0.15 Susceptibility allelle frequency
  • 35. Blossoc (BLOck aSSOCiation) Homepage: www.birc.au.dk/~mailund/Blossoc Command line and graphical user interface (with limited functionality)
  • 36. Blossoc (BLOck aSSOCiation) Homepage: www.birc.au.dk/~mailund/Blossoc Fast enough to analyse tens of thousands of individuals in hundred of thousands of markers in a few days on a desktop computer...
  • 37. Thank you! More information at http://www.birc.au.dk/~mailund/association-mapping/