Fig. 4.

Adequate representation of the solution space $\mathcal{T}$ requires k = 2 consensus trees. This simulated instance contains $n=\left|\mathcal{T}\right|=9$ input trees. (a) Top plot shows the mean normalized distance inferred by the coordinate ascent algorithm as a function of the number k of clusters. Bottom plot shows the number of trees per cluster. Using the BIC criterion, we summarize $\mathcal{T}$ with k = 2 clusters. (b) Parent-child graphs $G_{{\mathcal{T}}_1},G_{{\mathcal{T}}_2}$ and consensus trees R₁, R₂ (colored edges) of computed clustering. (c) Parent-child graph $G_{\mathcal{T}}$ (bottom) and corresponding consensus tree R (top) do not adequately represent the topological features in input trees $\mathcal{T}$. That is, edge (b, e) does not co-occur with edges (b, d) or (b, g) in $\mathcal{T}$, which cannot be concluded from $G_{\mathcal{T}}$. Moreover, consensus tree R does not contain the edge (b, e), which occurs in 4 out of 9 input trees. Hence, R is an incomplete summary of $\mathcal{T}$