Strong evidence that a search algorithm can find high functionality in an astronomically large search space

True, but it always indicates a temporal series of event, one of which is the cause (or source in this context) of the other. In this case there is something ancestral to trace back to, our microbial mother, LUCA.

Vertical descent produces a generally consistent nested hierarchy, that is, regardless of how you look at it you will generally get the same flow of relationships through time. Its similar to your family tree: DNA analysis, for example, will consistently place you as a descendant to your biological parents because you indeed descended from them.

Again, realize that a consistent nested hierarchy is a prediction of common descent and that’s what we see in datasets.

Sure and that’s due to common descent. At different levels and time points of the hierarchy we share pseudogenes, ERVs, transposons, LINES, SINES, all of which are genetic markers: these markers are great for testing common descent. All great apes, for example, have the same GULO pseudogene mutations, in the same place and with almost exactly the same mutations (exon deletions and more) . At the universal level, we see highly conserved systems spread out across all the domains of life like nearly universal metabolic pathways or the core of the ribosomes. All of these things are predictions of common descent and they pan out.

Sure, but that’s not what the data tells us. One of my favorite studies looked at this in some detail.

Another cool paper is the one below. They didn’t investigate universal common descent, but they showed how evolutionary biologists quantitatively test common descent using biological data. They directly competed special, independent creation with common descent and just like in the previous study I linked a above, common descent sealed the deal.

https://onlinelibrary.wiley.com/doi/full/10.1111/evo.12934

If there are things you don’t understand in the paper, @Chris_Falter (a statistician) and @John_Harshman (a phylogeneticist) can help out.

One more thing though. These papers demonstrate that we don’t assume common descent like you always say. Rather, they are conclusions reached after rigorous evaluation.

Its one, LUCA.

However, it is possible that there were multiple starting points prior to LUCA. We don’t just know yet.

HGT moves genes or other genomic elements across species and that can complicate phylogenetic analysis. Instead of getting this neat diagram of genes flowing down from ancestors to descendants in a tree-like manner (as Darwin naively thought), we see this web of gene transfers all across mainly prokaryotes and unicellular eukaryotes. This web, “forest”, “network” makes it a lot harder to detect the signal of common descent. When we get to multicellular organisms the signal gets a lot clearer and when we look at lifeforms together, the signal of common descent is strongest close to the tips, but diminishes as we go to deeper branching times (which is not surprising).

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