Okay, thanks everyone for all of your help on the “Nested Hierarchy and Bootstrap Values” thread. Using different programs than FastML, I was able to get much more reasonable results. For example, here is the tree (both unrooted and rooted) that I got from 16 random ‘taxa’ (visualized using iTOL: Interactive Tree Of Life):
Apparent polytomies, very low bootstrap values (1-30; avg. 12), and other strange things rarely seen in real-life phylogenies abound.
In contrast, here is the tree (both unrooted and outgroup-rooted) produced by 16 ‘taxa’ that share common ‘ancestry’ (also visualized using iTOL: Interactive Tree Of Life):
All relationships are correctly reconstructed, with bootstrap values of 100 to boot (pun not intended).
The same thing was observed in other tests that I ran; random trees always have low bootstrap values and strange topologies, as opposed to trees produced by taxa that share common ancestry, which always have a clear nested hierarchy.
This falsifies the creationist claim that nested hierarchies are merely an artifact of differing levels of similarity caused by ‘common design.’ In any given set of random ‘taxa,’ there will be differing levels of similarity, such that some ‘taxa’ are more similar to each other than they are to the rest of the ‘taxa.’ But, as this test shows, the differing levels of similarity between random ‘taxa’ do not produce a nested hierarchy like the ‘taxa’ which share common ancestry.
Thus, phylogenetics really is strong evidence for common ancestry. Every time phylogenetic analysis produces a nested hierarchy with high bootstrap values, that is evidence that the taxa at the tips of the tree really do share common ancestry. (Whether or not ‘common design’ happened can’t be determined by phylogenetics because common ancestry is compatible with both design and unguided evolution.)
So do real-life taxa produce the same nested hierarchy structure with high bootstrap values? Yes. Just look at any of the thousands of phylogenetic analyses that have been done in the past by evolutionary biologists – in almost every single case, a nested hierarchy is resolved with very high bootstrap values. For example, see this primate ERV phylogeny, or this whole-genome tetrapod phylogeny, or this comprehensive molecular phylogeny of primates.
Just for fun, though, I generated my own phylogeny of primates, using the cytochrome b, cytochrome c, and cytochrome c oxidase subunit I protein sequences from 14 different primate taxa (including Homo sapiens). Here is the resulting tree, both unrooted and rooted, visualized using iTOL: Primates :
There is an obvious nested hierarchy, with comparatively high bootstrap values (46 - 100; avg. 85), and none of the strange topology that dominated the ‘random’ trees. Furthermore, this tree agrees with previous phylogenies that have been done by real evolutionary biologists, recovering all of the major primate clades, as the color-coded tree below shows.
I also generated a phylogeny of 9 tetrapod taxa, using cytochrome b + cytochrome c + hemoglobin α1 + hemoglobin β1, and the result was similar (visualized using iTOL: Tetrapod):
There is again a clear nested hierarchy, with comparatively high bootstrap values (61 - 100; avg. 86), and none of the strange topologies which dominated the ‘random’ trees. Therefore, we can be pretty certain that all tetrapods are indeed related by common ancestry, whether or not ‘common design’ was also involved in their creation.
Strangely, this phylogenetic analysis recovered turtles (represented by Chelydra serpentina) as the sister group of squamates (represented by Anolis carolinensis), but I didn’t think too much of it since the position of turtles in the tetrapod tree is contested.
Another analysis that I did (which can be found at iTOL: Interactive Tree Of Life) recovered squamates (represented by Anolis carolinensis and Pantherophis guttatus) as a single clade, and turtles (Chelydra serpentina) as the sister group of archosaurs, more in line with recent phylogenomic analysis of tetrapods, but this tree had lower bootstrap values (10 - 100; avg. 63). I would trust a whole-genome analysis more than my own simple tree based on just a few proteins, though.
In summary, phylogenetics does provide a real test of common ancestry, as evidenced by a comparison between ‘random’ trees and trees produced by taxa that share common ancestry. The fact that nearly every single phylogenetic analysis thus far has resolved a nested hierarchy with high bootstrap values is nearly incontrovertible evidence for common ancestry.
My own analysis of primate and tetrapod taxa shows that, at least, all tetrapods (including humans) are related by common ancestry. This can probably be extended even further back, all the way to the base of the phylogenetic ‘tree of life,’ since a recent phylogenetic analysis of taxa from all three domains of life shows that Archaea and Eukarya form a single clade (Eukarya bootstrap value 100%; Archaea + Eukarya bootstrap value 100%) and Bacteria forms a single clade (bootstrap value 100%).