Example: Consider a phylogenetic relationship of the four clades is investigated with three candidate trees inferred as shown below.
The most commonly adopted representation is to simply use the "best tree" (in this case, Tree A).
You also may have created such trees.
An apparent drawback of this representation is that it can convey impression too biased to the best tree.
For example, although Tree B is actually supported almost as strongly as is Tree A, this best tree does not reveal anything about it and focuses only on Tree A.
To avoid such potentially misleading bias, the "consensus tree" has been recommended for a long time.
In this tree, branches with less than the desired statistical significance are collapsed.
However, this representation also fails to reveal valuable information about the tree distribution.
Although neither the first nor the second tree is supported with enough confidence individually, they are still more strongly supported than that shown on the third, but this information is not reflected at all in the consensus tree.
Consider that a gene family exists only on the genomes of dogs and mice.
In this case, from Trees A and B, it is supposed that "this gene family was acquired at the mammal ancestor and lost at the human lineage", and
from Tree C, it is supposed that "this gene family was acquired at the common ancestor of dogs and mice."
Because Tree A and B are reliable in sum total, the former hypothesis should be adopted if the whole tree distribution is investigated;
though, the best tree and the consensus tree, wasting phylogenetic information, cannot lead to such hypothesis.
The key idea is to assign special meaning to circular orderings of branches around multifurcating nodes of the consensus trees, to convey rich information while avoiding the biased impression.
Traditionally, in the context of phylogenetic analysis, only connectivity is considered and such circular orderings in layout are usually ignored.
For example, the three consensus trees below have been treated identically.
However, humans can interpret these trees differently.
In the first tree, clade human can be interpreted as more distant from opossum than from mouse and dog.
Most important thing is that, in this miniature data set, human appears next to opossum less frequently and would be represented by this ordering more adequately than by the others.
In Wheel Tree Representation, such multifurcations that consider circular orderings are called "wheel nodes", and are presented with rich statistic information about the candidate tree distribution as below.
We would like to recommend to avoid vizualizing not strongly supported branches in phylogenetic trees.
Instead, Wheel Trees represent information buried in phylogenetic tree distributions in an informative, unbiased, and intuitive manner.
Please proceed to look over some Examples.
(If you are interested in a comparison between the phylogenetic network method, refer to Reference.)