A Higher-Dimensional Phylogenetic "Tree"

Here is an example of a higher-dimensional phylogenetic "tree", as described by Bernd Sturmfels in the Mathematics of Phylogenetic Trees seminar.

Loading higher-dimensional phylogenetic tree.

This figure, created by Josephine Yu using polymake and displayed here using JavaView, came from the following distance matrix:

Distance Matrix for Eight Animals
Zebrafish Tetraodon Fugu Rat Mouse Rabbit Horse Pig
0 0.38166 0.38224 0.47441 0.47132 0.44783 0.43305 0.44488
0.38166 0 0.20756 0.43245 0.43225 0.42395 0.40943 0.41648
0.38224 0.20756 0 0.43995 0.44269 0.42933 0.41666 0.42485
0.47441 0.43245 0.43995 0 0.14313 0.35614 0.33370 0.34954
0.47132 0.43225 0.44269 0.14313 0 0.35490 0.33096 0.34624
0.44783 0.42395 0.42933 0.35614 0.35490 0 0.26176 0.28836
0.43305 0.40943 0.41666 0.33370 0.33096 0.26176 0 0.19227
0.44488 0.41648 0.42485 0.34954 0.34624 0.28836 0.19227 0

*Distance Matrix for Eight Animals*
Zebrafish	Tetraodon	Fugu	Rat	Mouse	Rabbit	Horse	Pig
0	0.38166	0.38224	0.47441	0.47132	0.44783	0.43305	0.44488
0.38166	0	0.20756	0.43245	0.43225	0.42395	0.40943	0.41648
0.38224	0.20756	0	0.43995	0.44269	0.42933	0.41666	0.42485
0.47441	0.43245	0.43995	0	0.14313	0.35614	0.33370	0.34954
0.47132	0.43225	0.44269	0.14313	0	0.35490	0.33096	0.34624
0.44783	0.42395	0.42933	0.35614	0.35490	0	0.26176	0.28836
0.43305	0.40943	0.41666	0.33370	0.33096	0.26176	0	0.19227
0.44488	0.41648	0.42485	0.34954	0.34624	0.28836	0.19227	0

The figure shows the bounded complex projected to 3 dimensions. A spring embedder was applied to make it easier to see (so the figure doesn't reflect the actual metric). If you'd like to learn more, please visit this webpage.

Return to the Mathematics of Phylogenetic Trees webpage.