The weight of a true split in Figure 2 is calculated as summing up the split weights of this split in eight underlying trees by switching off one branch in a reticulate event.
In this case, the split weights and therefore the edge lengths in the resulting network are equal to a jackknife support of the corresponding bifurcation, that is, a proportion of input trees that include this bifurcation.
A derivation of the split-weight scheme is given, and numerical observations are given as to what algorithmic change leads to stable algorithm.
If r = 2 then we are done, so we assume r ≥ 3. Let ω be the (circular) split weight function for which d = d ω, so Θ is compatible with ω.
However, simulation studies show that current quartet-based methods are suffered from identifying false-positive and false-negative splits of the taxa set, and the trivial split weights are usually systematically overestimated [ 16].
Using the quartet and triplet weights calculated from the multiple sequence alignment, we compute the full split weights from three methods QuartetS, QuartetA, and QuartetM.
In this section we prove the consistency of Neighbor-Net: Theorem 4.1 If d: X × X → ℝ≥0 is a circular distance function, then the output of the Neighbor-Net algorithm is a circular split weight function ω: Ϭ(X) → ℝ≥0 with the property that d = d ω.
A total of 92 out of 212 splits are compatible with the NJ tree topology and their sum of split weight amounts to 96% of the total network; and thus, the NJ tree explains most of the split variability in the data.
The edge lengths are defined by split weight, which can be of different sense depending on the algorithm used to generate a split set [ 2].
Here, the distance between two taxa in the tree is measured according to "phenetic distance," the length of the path (i.e., the sum of split weights) from one taxon to the other in the tree.
However, just as with rooting trees, this approach to rooting the network can be sensitive to rate variation because split weight can be affected by variation in the rate of sequence change among groups.
