Alignment-aware SPR transition kernel decreases burn-in time. We consider the 27-sequence data set of HIV sequences described in the Results section as Example 2. Points represent 200 topologies sampled from a Markov chains with the alignment-aware SPR transition kernel disabled (red; NNI-only) or enabled (blue; NNI+SPR) or from the equilibrium distribution (green). While the convergence time for Markov chains varies widely, this example illustrates the median convergence time. The NNI-only chain takes 2112 iterations to converge versus only 66 iterations for the NNI+SPR chain. Because the convergence times are so different, the figure depicts every 10th tree for the first 2000 iterations, whereas for the NNI+SPR chain the figure depicts every 2nd tree for the first 400 iterations. Points represent trees projected onto the plane using multidimensional scaling based on the Robinson-Foulds distance. This distance depends only on the topology, not the branch lengths.