Robustness of the Parsimonious Reconciliation Method in

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Robustness of the Parsimonious Reconciliation
Method in Cophylogeny
Laura Urbini, Blerina Sinaimeri, Catherine Matias, Marie-France Sagot
Trujillo, Spain
June 21-22, 2016
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Introduction
The cophylogeny problem
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Introduction
Reconciliation model
Reconcile the trees through a mapping of S into H (asymmetric role
between the trees).
Events that can be recovered:
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Introduction
Definition
Input: H, S (rooted trees), the map φ : Leaves(S) → Leaves(H) and cost vector
c = hcc , cd , cs , cl i.
Output: A reconciliation function ρ : V (S) → V (H), where ρ extends φ (i.e.
∀v ∈ Leaves(S), ρ(v ) = φ(v )).
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Introduction
Definition
∀v ∈ Leaves(S), ρ(v ) = φ(v )).
ρ partitions the set V (S) into three sets:
Σ vertices associated with cospeciation.
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Introduction
Definition
∀v ∈ Leaves(S), ρ(v ) = φ(v )).
∆ vertices associated to duplication.
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Introduction
Definition
∀v ∈ Leaves(S), ρ(v ) = φ(v )).
Γ vertices associated to host-switches.
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Introduction
Definition
∀v ∈ Leaves(S), ρ(v ) = φ(v )).
The loss events are related to host vertices.
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Introduction
Definition
∀v ∈ Leaves(S), ρ(v ) = φ(v )).
Parsimony Method:
Assign a cost to each
event and minimize the
total cost.
The loss events are related to host vertices.
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Limitations of the reconciliation model
(Multiple associations leaves)
The model makes a strong assumption on the data in input:
One symbiont leaf is mapped to at most one host leaf.
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Datasets obtained for each choice of the multiple associations.
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Datasets obtained for each choice of the multiple associations.
Association changes → Similar reconciliation?
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(Rooting a phylogenetic tree)
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Datasets obtained for each choice of rooting.
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Datasets obtained for each choice of rooting.
Root changes → Similar reconciliation?
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PLATEAU PROPERTY [GET13]: All optimal rooting form a
subtree, called plateau, from which: the rooting along every path
toward a leaf have monotonically increasing cost.
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PLATEAU PROPERTY [GET13]: All optimal rooting form a
subtree, called plateau, from which: the rooting along every path
toward a leaf have monotonically increasing cost.
Coevolution → “many” cospeciations → “low” total reconciliation
cost.
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One symbiont leaf can be associated with more than one host leaf.
Finding the root of a phylogenetic tree is often problematic.
Explore the robustness of parsimonious model, with errors in input
given H, S, φ and c:
Change associations in case of multiple associations leaves.
Change root of symbiont tree.
Try all possible rootings and test the plateau property.
Try the rootings at distance k ≤ max(5%|V (S)|, 3), from the original root.
Input changes → Similar reconciliation?
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EUCALYPT [DBS+ 14]
Problem
Generating all optimal reconciliations.
The number of optimal reconciliations can be exponential in the
size of the trees.
A polynomial delay algorithm: The time between two
successive solutions is polynomial in the size of the input.
eucalypt.gforge.inria.fr
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The Input
The Input
A dataset is a pair of H, S, and map φ. We considering the
following cost vector c = hcc , cd , cs , cl i ∈ C where
C = {h−1, 1, 1, 1i,
h0, 1, 1, 1i,
h0, 1, 2, 1i,
h0, 2, 3, 1i,
h1, 1, 1, 1i,
h1, 1, 3, 1i}.
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The Output
The Output
A reconciliation is summarised as a pattern of integers.
π = hnc , nd , ns , nl i
Definition
For a given input: H, S, the map φ and cost vector c.
Optimal solution: Multisets of patterns ΛH,S,φ,c = {π; π has optimal
cost}
Dissimilarity between two multisets of patterns:
P
P
|| π∈Λ1 π − π∈Λ2 π||
d(Λ1 , Λ2 ) =
(|Λ1 | + |Λ2 |) ∗ maxπ∈Λ1 ∪Λ2 ||π||
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The Output
The Output
P
P
|| π∈Λ1 π − π∈Λ2 π||
d(Λ1 , Λ2 ) =
(|Λ1 | + |Λ2 |) ∗ maxπ∈Λ1 ∪Λ2 ||π||
Example 1:
Λ1 = {[4, 2, 0, 1], [4, 2, 0, 1], [5, 1, 1, 0]}
Λ2 = {[4, 1, 0, 1]}
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The Output
The Output
P
P
|| π∈Λ1 π − π∈Λ2 π||
d(Λ1 , Λ2 ) =
(|Λ1 | + |Λ2 |) ∗ maxπ∈Λ1 ∪Λ2 ||π||
Example 1:
Λ1 = {[4, 2, 0, 1], [4, 2, 0, 1], [5, 1, 1, 0]}
Λ2 = {[4, 1, 0, 1]}
d(Λ1 , Λ2 ) =
|| {[4, 2, 0, 1] + [4, 2, 0, 1] + [5, 1, 1, 0]} − {[4, 1, 0, 1]} ||
(3 + 1) ∗ max(7, 7, 7, 6)
d(Λ1 , Λ2 ) =
L. Urbini
||[9, 4, 1, 1]||
= 0.536
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Tested Dataset
Datasets
Biological Datasets:
15 Datasets:
EC - Encyrtidae (7 leaves) & Coccidae (10 leaves)
PP - Primates (36 leaves) & Pinworms (40 leaves), RH Rodents (34 leaves) & Hantaviruses (42 leaves),
Multiple Associations:
3 of these datasets present multiple associations (namely MP,
SBL, SFC)
Simulated Datasets:
For each Biological Dataset we created 50 Simulated Datasets.
The simulated datasets will be used only for testing the rooting of
the trees.
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Results
Perturbation of associations
SBL dataset, 5 out the 8 leaves of the symbiont tree have multiple
associations → 560 datasets.
Cost vector h0, 1, 1, 1i.
70% have cost 7
30% change the optimum cost value (from 7 to a value 6,8,9)
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Results
70% have cost 7
30% change the optimum cost value (from 7 to a value 6,8,9)
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Results
65.5% dissimilarity different to 0
8.5% biggest dissimilarity (0.6)
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Results
Rerooting
(Testing the plateau property)
2 biological datasets and several simulated datasets have more
than one plateau.
plateau property is not valid in our model (because of the host
switch).
in 37% of biological datasets and in 17% of simulated datasets,
the original root is not in the plateau.
Hypothesis for real datasets, the original root is not in the
correct position.
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Results
Rerooting
(At distance k )
Distance k ≤ max(5%|V (S)|, 3), from the original root.
Real Datasets:
Dissimilarity of reconciliation globally increases as k also increases.
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Results
Rerooting
(At distance k )
Distance k ≤ max(5%|V (S)|, 3), from the original root.
Simulated Datasets:
Dissimilarity of reconciliation globally increases as k also increases.
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Conclusions
Conclusions
Associate a symbiont to a unique host in case of multiple associations:
Not big impact for the reconciliation cost.
The choice of leaf associations may have a strong impact on the variability
of the reconciliation output.
Open problems:
Simulating the coevolution of symbiont and host allowing multiple
associations.
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Conclusions
Conclusions
Rerooting:
The number of plateaux depends on the presence of host switches.
The original root may not be inside the plateau.
In general the variance of dissimilarity of reconciliations increases with the
increase of the distance k.
Open problems:
Is there a relation between the number of plateaux and the level of
dissimilarity of pattern?
Is there a relation between the number of plateaux and the number of host
switches in the optimal solutions?
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Thank you
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References I
[DBS+ 14] Beatrice Donati, Christian Baudet, Blerina Sinaimeri,
Pierluigi Crescenzi, and Marie-France Sagot.
EUCALYPT: efficient tree reconciliation enumerator.
Algo. Mol. Biol., 10(1):3, 2014.
[GET13]
Pawel Górecki, Oliver Eulenstein, and Jerzy Tiuryn.
Unrooted tree reconciliation: A unified approach.
IEEE/ACM Trans. Comput. Biology Bioinf., 10(2):522–536,
2013.
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Time feasibility of the solutions
If no time information then finding a optimal time feasible solution is
NP-hard.
Allow for time infeasible host switches → polynomial time.
Check tome consistence of a solution → polynomial time.
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Robustness of the Parsimonious Reconciliation Method in

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