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Phylogenetic applications of the minimum contradiction approach on continuous characters.

Thuillard M, Fraix-Burnet D - Evol. Bioinform. Online (2009)

Bottom Line: We explain how to discover the main structuring characters in a tree.The second set consists of a sample of 100 galaxies.In that second example one shows how to discretize the continuous variables describing physical properties of the galaxies without disrupting the underlying tree structure.

View Article: PubMed Central - PubMed

Affiliation: La Colline, 2072 St-Blaise (Switzerland). thuillweb@hotmail.com

ABSTRACT
We describe the conditions under which a set of continuous variables or characters can be described as an X-tree or a split network. A distance matrix corresponds exactly to a split network or a valued X-tree if, after ordering of the taxa, the variables values can be embedded into a function with at most a local maximum and a local minimum, and crossing any horizontal line at most twice. In real applications, the order of the taxa best satisfying the above conditions can be obtained using the Minimum Contradiction method. This approach is applied to 2 sets of continuous characters. The first set corresponds to craniofacial landmarks in Hominids. The contradiction matrix is used to identify possible tree structures and some alternatives when they exist. We explain how to discover the main structuring characters in a tree. The second set consists of a sample of 100 galaxies. In that second example one shows how to discretize the continuous variables describing physical properties of the galaxies without disrupting the underlying tree structure.

No MeSH data available.


Top: The taxa are ordered so that the characters f1(i) on the taxa {1, …, i, …, n} can be embedded in a function f(x) fulfilling proposition 1. Bottom: Distance matrix Yi,jn with a colour coding. Larger values are coded red, small values blue. The order is perfect (C = 0 in Eq. 2).
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f3-ebo-2009-033: Top: The taxa are ordered so that the characters f1(i) on the taxa {1, …, i, …, n} can be embedded in a function f(x) fulfilling proposition 1. Bottom: Distance matrix Yi,jn with a colour coding. Larger values are coded red, small values blue. The order is perfect (C = 0 in Eq. 2).

Mentions: Figure 3 illustrates Prop. 1 with a simple example. The matrix Yi,jn is depicted using a colour coding. Large values are coded red, while small values of Yi,jn correspond to small values. The distance matrix is perfectly ordered; the values of Yi,jn decrease away from the diagonal as prescribed by the Kalmanson inequalities. Two clusters are observed, the first cluster corresponds to values smaller than the reference value, the second cluster to values larger than the reference value.


Phylogenetic applications of the minimum contradiction approach on continuous characters.

Thuillard M, Fraix-Burnet D - Evol. Bioinform. Online (2009)

Top: The taxa are ordered so that the characters f1(i) on the taxa {1, …, i, …, n} can be embedded in a function f(x) fulfilling proposition 1. Bottom: Distance matrix Yi,jn with a colour coding. Larger values are coded red, small values blue. The order is perfect (C = 0 in Eq. 2).
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC2747132&req=5

f3-ebo-2009-033: Top: The taxa are ordered so that the characters f1(i) on the taxa {1, …, i, …, n} can be embedded in a function f(x) fulfilling proposition 1. Bottom: Distance matrix Yi,jn with a colour coding. Larger values are coded red, small values blue. The order is perfect (C = 0 in Eq. 2).
Mentions: Figure 3 illustrates Prop. 1 with a simple example. The matrix Yi,jn is depicted using a colour coding. Large values are coded red, while small values of Yi,jn correspond to small values. The distance matrix is perfectly ordered; the values of Yi,jn decrease away from the diagonal as prescribed by the Kalmanson inequalities. Two clusters are observed, the first cluster corresponds to values smaller than the reference value, the second cluster to values larger than the reference value.

Bottom Line: We explain how to discover the main structuring characters in a tree.The second set consists of a sample of 100 galaxies.In that second example one shows how to discretize the continuous variables describing physical properties of the galaxies without disrupting the underlying tree structure.

View Article: PubMed Central - PubMed

Affiliation: La Colline, 2072 St-Blaise (Switzerland). thuillweb@hotmail.com

ABSTRACT
We describe the conditions under which a set of continuous variables or characters can be described as an X-tree or a split network. A distance matrix corresponds exactly to a split network or a valued X-tree if, after ordering of the taxa, the variables values can be embedded into a function with at most a local maximum and a local minimum, and crossing any horizontal line at most twice. In real applications, the order of the taxa best satisfying the above conditions can be obtained using the Minimum Contradiction method. This approach is applied to 2 sets of continuous characters. The first set corresponds to craniofacial landmarks in Hominids. The contradiction matrix is used to identify possible tree structures and some alternatives when they exist. We explain how to discover the main structuring characters in a tree. The second set consists of a sample of 100 galaxies. In that second example one shows how to discretize the continuous variables describing physical properties of the galaxies without disrupting the underlying tree structure.

No MeSH data available.