Centroid Wheel Tree

Centroid Wheel Tree is an Intuitive, Informative, and Most Balanced representation of phylogenetic trees.


Execute on Web
Key Concept
NHX Format




Dept. Biological Sciences,
Grad. Sch. Science,
University of Tokyo, Japan
iwasaki AT bs.s.u-tokyo.ac.jp


CWT Software:
GNU General Public License
The other content:
Creative Commons License

Wheel Tree Examples

The following is a schematic exapmle of wheel trees.

As seen in this figure, wheel trees intuitively convey rich statistic information on tree distributions in the three ways:

(X) As in ordinary phylogenetic representations, numbers at internal branches are the proportions of the input trees containing the corresponding splits.

(Y) Numbers within circled nodes (wheel nodes) indicate the extent to which each circular ordering of the branches naturally represents the candidate trees. In other words, the numbers indicate the proportion of the input trees that can be restored by just "pulling out" branches without changing the orderings.

(Z) Numbers around wheel nodes indicate the proportions that the flanking splits constitute in a monophyletic group. For example, in the figure above, Z1% of the trees have the 3-furcation { a | d | b,c,e,f } (i.e., the three splits { a | b,c,d,e,f }, { d | a,b,c,e,f }, and { a,d | b,c,e,f }).

For all wheels, The CWT software estimate circular orderings that make the (Y) values largest, reflecting phylogenetic tree distributions.

The figure below is a wheel tree derived from a real data set.
The input trees were 246 phylogenetic trees obtained by applying the maximum likelihood method to reliable single-copy orthologs conserved among 21 fungal species.
The 60% consensus tree, which deletes all edges supported below than this threshold, is used.

For example, the wheel node indicated by the thick arrow connects the four splits Ago, Kla, X, and Y, and visually indicates that:

(1) 73% of the input trees are expected to contain either of the splits { Ago,Kla | X,Y } or { Kla,X | Ago,Y }
(2) 39% and 34% contain the 3-furcations { Ago | Kla | X,Y } and { Kla | X | Ago,Y }, respectively.

Note that the values on the opposite sides of the wheel nodes are the same. This is because in cases of 4-furcating nodes, for example, if the splits Ago and Kla are adjacent (i.e., { Ago | Kla | X,Y }) then X and Y are adjacent (i.e., { X | Y | Ago,Kla }).

The figures below are wheel trees of the same data set as above, based on (a) 80% and (b) 100% consensus trees. To avoid cluttered appearances because of many multifurcations, the color visualization option that uses colors instead of numbers was used to show the support values around the wheel nodes.

Because wheel trees use tree shapes, taxonomic groups at multiple levels can be recognized fairly intuitively.
In particular, wheel trees can suggest the existence of taxonomic groups with support below the consensus-tree threshold, in addition to those making splits on the consensus trees as successive branches around wheel nodes.

(a) The thick gray arc lines α, β, γ, and δ indicate the class Eurotiomycetes, class Sordariomycetes, order Hypocreales, and subphylum Agaricomycotina, respectively.

(b) This is a star-like wheel tree, obtained by specifying high threshold values where no split is supported at a level above the threshold (a special option for this operation is also provided).
It shows "the optimal sequential ordering" of all taxa based on the distribution of the input trees and, as a result, many biological groups appear as successive branches around the wheel node (thick gray arc lines).

By virtue of the sophistication of the present TSP solvers, it takes only a few seconds to obtain wheel trees of these sizes.

Now, please make wheel trees by Executing Online, or learn more by reading Theory.