Heat map of the decoded tree’s properties.

Obtained by a grid search in , moving one node (green diamond) through embedding space. a, d) joint probability p(T, Y), b, e) symmetric difference from best tree topology and c, f) total length. Top row curvature κ = −1 and bottom row κ = −1000. Black dots are the fixed locations of the remaining nodes.</p

Effect of embedding dimension on the posterior distribution.

Comparison to the true posterior of: a, d) ASDSF, b, e) relative difference in median tree length, c, f) relative difference in the variance of tree length. Top row curvature κ = −1, bottom row κ = −100. Truncated variance ratio in c) for DS3 with d = 2 is 16.41 and 39.05 for DS7.</p

Effect of embedding curvature on the posterior distribution.

Comparison to the true posterior of: a) ASDSF, b) relative difference in median tree length, c) relative difference in the variance of tree length. The truncated variance ratio for DS5 is approximately zero. The right side corresponds to flatter (and Euclidean) curvature (κ = 0 gives log10(−κ) = −∞) and the left side is more curved.</p

Supporting text with appendices.

Appendix A: MCMC details. Appendix B: Wrapping proposal vectors onto the hyperboloid. Appendix C: Impact of Normal prior on posterior. Appendix D: Closed form pf projection Jacobians. Appendix E: Algorithm Run Time. Appendix F: Datasets. Appendix G: Effective sample size. (PDF)</p

Comparison between MrBayes and Dodonaphy’s MCMC starting from the evolutionary distances.

Comparison of (a) posterior probability trace, (b) split frequencies with 95% confidence intervals (CI), (red dots: MrBayes value not covered by CI), (c) mean branch lengths (leaf edges in blue circles, internal edges in red diamonds), (d) total tree length estimation of 10 repeats. Markers in (c) are shaded by the frequency of appearance in the golden run. In (a, d) black lines show the two MrBayes runs and thin blue lines show Dodonaphy’s results.</p

SPR distances of samples about an embedded tree.

SPR distance of trees sampled from a Multivariate Gaussian (covariance Σ × I) about a tree containing 100 leaves embedded in with curvature κ = −1. Distributions are estimated from 2000 samples.</p

Hyperbolic embedding of eight taxa.

Eight points (taxa) lie on a two-dimensional hyperboloid sheet in . Arrows indicate how each two-dimensional point (x1, x2) is deterministically projected up onto the sheet by ϕ. The green dashed line illustrates that the distance between two taxa is the length of the geodesic on the hyperboloid surface.</p

Human <i>P. ovale</i> strains, strain code, geographical location of origin, nucleotide sequence, type and GenBank accession number.

<p>Human <i>P. ovale</i> strains, strain code, geographical location of origin, nucleotide sequence, type and GenBank accession number.</p

Substitutions and their positions in <i>cyt b</i> nucleotide sequences (numbers correspond to base pair positions and were defined according to the complete <i>P. falciparum cyt b</i> gene sequence M76611).

<p>Non synonymous mutation is shown in brackets.</p

Substitutions and their positions in <i>cox1</i> nucleotide sequences (numbers correspond to base pair positions and were defined according to the complete sequence of the <i>P. falciparum cox1</i> gene M76611).

<p>Non synonymous mutations are shown in brackets.</p