Fig. 4

E3 Results. A, B The impact of the size of a subtree (A) or its sister (B) on the probability that an SPR applied to that subtree leads to an improved quartet score. Panels show the impact on the first round, middle rounds (1, 10], and final runs (10, 50]. The starting tree is the result of step-wise additions. In the first round, subtrees with a size around \({n}/{2}\) have a higher probability of improvement while in the final rounds, small and larger subtrees are likely to improve speed. C Improvement probability of an SPR move compared to the distance to the source (ps) or the destination (pd) of the previous move. For each node p, we show the distance from its sister (i.e., the closest node left in the tree after we remove \({T}^\vee _{p}\)) to the node above which the previous SPR move was placed (pd) or the sister of the node that was moved in the previous SPR move (ps). Subtrees close to the previous source or destination have a higher probability of improving the score. The reduction at distance 0 for pd is because this case represents an attempt to move the previously moved node p, or its complement \({T}^\wedge _{p}\), and the former by construction has 0 probability of moving because it is already in its optimal position. D Comparison of the running time for a full Q-SPR search run between different combinations of heuristic methods. The building time for the starting tree is also included.