Fig 3. Traversing likelihood space.

The z-axes above are the log-likelihoods of the genetic distance r × τ between two simulated nucleic acid sequences of length L, under the Jukes-Cantor substitution model [40]. Two possible proposals from the current state (white circle) are depicted. These proposals are generated by the RandomWalk (RW) and ConstantDistance (CD) operators. In the low signal dataset (L = 0.1kb), both operators can traverse the likelihood space effectively. However, the exact same proposal by RandomWalk incurs a much larger likelihood penalty in the L = 0.5kb dataset by “falling off the ridge”, in contrast to ConstantDistance which “walks along the ridge”. This discrepancy is even stronger for larger datasets and thus necessitates the use of operators such as ConstantDistance which account for correlations between branch lengths and rates.