Presented at the 2019 US2TS conference as part of the Reasoning session.

1. Of Trees and Owl:
The challenges of reasoning over
the semantics of shared descent
Hilmar Lapp
Duke University
US2TS 2019 in Durham, NC

2. https://commons.wikimedia.org/wiki/File:Dobzhansky_Evolution_Notre_Dame.jpg

3. Phylogenetic trees express
hypotheses of common descent
Brochu 2003

4. Phylogenetic trees express
hypotheses of common descent
Brochu 2003

5. Most data use Linnaean taxonomy

6. Linnaean names suffer from
fundamental shortfalls
• Names ≠ Identifiers
• Underlying taxon concepts (= semantics) shift
over time, and are computationally inaccessible
• At least 90-95% of estimated biodiversity doesn’t
have a name, and most will never receive one
• The better the Tree of Life is known, the more
groups of organisms without a name

7. The Phyloreferencing Project
• Funded by US National Science Foundation
since 2015
• Goal: Capture and make computable the
semantics of phylogenetic clade definitions for
computational integration of biological data.
• Major expected products:
• Ontology, specification, and tooling for authoring
phyloreferences.
• Ontology of phylogenetic clade definitions
• Online tools for using phyloreferences to retrieve data
phyloref.org

8. Anatomy of a phylogenetic
clade definition
Alligatoroidea =
Alligator mississippiensis and
all crocodylians closer to it than
to Crocodylus niloticus or
Gavialis gangeticus
Crocodylia =
Last common ancestor of
Gavialis gangeticus, Alligator
mississippiensis, and
Crocodylus niloticus and all of
its descendents
Brochu 2003

9. Anatomy of a phylogenetic
clade definition
Alligatoroidea =
Alligator mississippiensis and
all crocodylians closer to it than
to Crocodylus niloticus or
Gavialis gangeticus
Crocodylia =
Last common ancestor of
Gavialis gangeticus, Alligator
mississippiensis, and
Crocodylus niloticus and all of
its descendents
Brochu 2003
“Specifiers”

10. Anatomy of a phylogenetic
clade definition
Alligatoroidea =
Alligator mississippiensis and
all crocodylians closer to it than
to Crocodylus niloticus or
Gavialis gangeticus
Crocodylia =
Last common ancestor of
Gavialis gangeticus, Alligator
mississippiensis, and
Crocodylus niloticus and all of
its descendents
Brochu 2003
Type of definition

11. Anatomy of a phylogenetic
clade definition
Alligatoroidea =
Alligator mississippiensis and
all crocodylians closer to it than
to Crocodylus niloticus or
Gavialis gangeticus
Crocodylia =
Last common ancestor of
Gavialis gangeticus, Alligator
mississippiensis, and
Crocodylus niloticus and all of
its descendents
Brochu 2003

12. Anatomy of a phylogenetic
clade definition
Alligatoroidea =
Alligator mississippiensis and
all crocodylians closer to it than
to Crocodylus niloticus or
Gavialis gangeticus
Crocodylia =
Last common ancestor of
Gavialis gangeticus, Alligator
mississippiensis, and
Crocodylus niloticus and all of
its descendents
Brochu 2003

13. Axiomatization of a tree

14. A phyloreference
Crocodylus niloticus and
all crocodylians
closer to it than to
Alligator mississippiensis
includes_TU some tco:Crocodylus niloticus and
excludes_TU some tco:Alligator mississippiensis

15. Resolving a phyloreference:
axiomatized tree + phyloreference + reasoner
Crocodylus niloticus and
all crocodylians
closer to it than to
Alligator mississippiensis
includes_TU some tco:Crocodylus niloticus and
excludes_TU some tco:Alligator mississippiensis

16. Resolving a phyloreference:
axiomatized tree + phyloreference + reasoner
Crocodylus niloticus and
all crocodylians
closer to it than to
Alligator mississippiensis
includes_TU some tco:Crocodylus niloticus and
excludes_TU some tco:Alligator mississippiensis

17. Resolving a phyloreference:
axiomatized tree + phyloreference + reasoner
Crocodylus niloticus and
all crocodylians
closer to it than to
Alligator mississippiensis
includes_TU some tco:Crocodylus niloticus and
excludes_TU some tco:Alligator mississippiensis

18. Phyloreferences have major
advantages for data integration
• Unambiguous and computable semantics
• Portable between phylogenetic trees, and hence
competing or evolving phylogenetic hypotheses
• Computationally reproducible
• Can be constructed for any clade, and hence
enables unrestricted communication

19. Challenges with OWL-DL:
No set size or path length
Crocodylus niloticus and
all crocodylians
closer to it than to
Alligator mississippiensis
“Maximum clade definition”

20. Challenges with OWL-DL:
No set size or path length
Last common ancestor of
Alligator mississippiensis
and Crocodylus niloticus
and all of its descendents
“Minimum clade definition”

21. Challenges with OWL-DL:
No set size or path length
Last common ancestor of
Alligator mississippiensis
and Crocodylus niloticus
and all of its descendents
includes_TU some tco:Crocodylus niloticus and
includes_TU some tco:Alligator mississippiensis

22. Challenges with OWL-DL:
No set size or path length
Last common ancestor of
Alligator mississippiensis
and Crocodylus niloticus
and all of its descendents
includes_TU some tco:Crocodylus niloticus and
includes_TU some tco:Alligator mississippiensis

23. Challenges with OWL-DL:
No set size or path length
Last common ancestor of
Alligator mississippiensis
and Crocodylus niloticus
and all of its descendents
has_Child some
(includes_TU some tco:Crocodylus niloticus and
excludes_TU some tco:Alligator mississippiensis)

24. Challenges with OWL-DL:
No set size or path length
Last common ancestor of
Alligator mississippiensis
and Crocodylus niloticus
and all of its descendents
has_Child some
(includes_TU some tco:Crocodylus niloticus and
excludes_TU some tco:Alligator mississippiensis)
• However, this will fail for the general case:
MaxClade(S1, S2) := S1 ~ S2
Parent(S) := has_Child some S
LCA(S1, S2) := Parent(MaxClade(S1, S2))
• If S2 has_Ancestor some (includes_TU some S1) then
MaxClade(S1, S2) == {}, but LCA should be S1
• I.e., in this approach SN cannot itself be a phyloreference
(LCA of a clade).

25. Challenge: Multiple specifiers
• Naïve recursive approach:
LCA(S1,…,SN) = LCA(LCA(S1,…,SN-1),SN)
• However, as shown for LCA(S1, S2), S1 or S2
cannot itself be an LCA
Last common ancestor
of Gavialis gangeticus,
Alligator mississippiensis,
and Crocodylus niloticus
and all of its descendents

26. Challenge: Multiple specifiers
Last common ancestor
of Gavialis gangeticus,
Alligator mississippiensis,
and Crocodylus niloticus
and all of its descendents

27. Challenge: Multiple specifiers
Last common ancestor
of Gavialis gangeticus,
Alligator mississippiensis,
and Crocodylus niloticus
and all of its descendents
Parent(LCA(Cn, Am) ~ Gg)

28. Challenge: Multiple specifiers
Last common ancestor
of Gavialis gangeticus,
Alligator mississippiensis,
and Crocodylus niloticus
and all of its descendents
Parent(LCA(Cn, Am) ~ Gg) Parent(LCA(Cn, Gg) ~ Am) Parent(LCA(Am, Gg) ~ Cn)OR OR

29. Challenge: Multiple specifiers
• The number of binary tree topologies for n
leaves grows very fast, and is > 100 for 5
Last common ancestor
of Gavialis gangeticus,
Alligator mississippiensis,
and Crocodylus niloticus
and all of its descendents

30. Challenge: Scalability
• Eventually we want to apply this to very large
trees, with >1M leave nodes.
• Only OWL-EL reasoners (e.g., ELK) scale well to
this level.
• However, this prevents use of disjunction.

31. Challenge: Scalability
• As a kludge, can use multiple equivalency axioms
instead.
• However, this in essence makes false assertions.
• Can result in unexpected subclass inferences for
other phyloreferences.
Parent(LCA(Cn, Am) ~ Gg) Parent(LCA(Cn, Gg) ~ Am) Parent(LCA(Am, Gg) ~ Cn)
equivalentClass: equivalentClass: equivalentClass:

32. Challenge: “Qualifiers”
• “Qualifiers” are specifiers that are required to be
included or excluded by the clade.
• “Kill switches” – tests that do not alter the
semantics of the clade definition, but render it
invalid if it fails any of the tests
• External qualifiers as property chain:
has_Ancestor o excludes_TU -> excludes_qualifying_TU

33. Summary
• Reproducible large-scale comparative biology
requires taxon concepts with fully computable
semantics
• Phylogenetic clade definitions have well-defined
semantics in the form of necessary and sufficient
conditions for clade membership
• Clade semantics are well expressible in OWL, but
OWL lacks constructs needed for inferring last
common ancestors generically and scalably.

34. Acknowledgements
• Nico Cellinese, Gaurav Vaidya, Anna
Becker (U. Florida)
• Pascal Hitzler and DaSe Lab alumni &
collaborators (see Carral et al. WOP
2017, arXiv:1710.05096)
• Funded by the US National Science
Foundation (DBI-1458484, DBI-1458604)

35. How to find us
• Web: http://phyloref.org (includes link to full
grant proposal)
• Github: http://github.com/phyloref