I have never understood the phrase "common ancestor" to refer to a single individual organism, but to a population or species from which two or more distinct evolutionary lineages arose.
In this view (which I think is the typical view in biology), a common ancestor is unavoidable.
Surely, even if 'common ancestor' is taken to refer to a single individual, it's still a logical necessity for everything to have a common ancestor with everything else (assuming common descent). There wouldn't be a unique individual, and we could never hope to find or know if we've found such an individual, but how could they not exist?
Evolution is not a linear process. The better question, then, is how would we know when we found it?
As I noted above, we couldn't. From what you've said here, I don't think you disagree with anyone except the OP, which seemed to imply we should be looking for one specific species (or individual) that confirms the common ancestor.
However, it's still clear that evolutionary theory requires common ancestors rather than precluding them, as you said in Message 14. I understand that you're making the point that it would never be practically possible to identify a 'last common ancestor', and that species divisions are going to be messy and rarely conform to the idealised case of siblings swept to different islands to establish founder populations, with no further genetic flow. It's confusing and misleading to say this means there are no common ancestors, however.
If we take a strict gradualistic approach, any new evolutionary development must have occurred within a pool of organisms (or proto-organisms) that was just one step short of the new development. Interactions and exchanges between the organism with the new development and the other organisms in the pool are probably unavoidable.
I think this is probably true of every step in evolutionary history, although the very first true cell might be an exception (I don't think so though: HGT, prions and viruses were probably major contributors around that time).
There seems to be a bit of confusion here. Of course the organism will be interacting with other organisms in the pool, but so what? If you have some Miocene ape sat somewhere in Africa, who is an ancestor of chimpanzees and an ancestor of humans, then he is a common ancestor of apes and humans, and he is also a direct common ancestor of apes and humans. Yes, he'll be interacting with other apes, and some of those will also be common ancestors of humans and chimps.
I'm not sure exactly where the confusion is arising. It seems to me that objections from both you and Jon seem to be based around the idea that saying there are individuals that are common ancestors means this individual must have been seperated from all individuals at the time, and produce two group of offspring which themselves separate off and don't interact. But all a common ancestor is, with a literal reading of the term, is an ancestor who's common to both or all the populations under consideration. His or her parents would also be common ancestors, many of his or her contemporaries would be common ancestors, some of his descendants may be common ancestors. A common ancestral population is made up of a bunch of individual common ancestors, plus others who had no descendants or whose descendants didn't make it to today.
If we could go back in time and take any population of organisms, and then we took a selection of modern day organisms, each individual in the ancient population would either be the direct common ancestor of all the modern day organisms, the direct ancestor of just some of the modern day organisms, or the ancestor of no modern day organisms. The fact that it's not possible to look at a fossil and place it in any group doesn't change this basic fact.
As for the question of the idealised scenario of one couple or one pregnant individual going off to found a new population, with no further gene flow with the original population, of course this happens! The sheep population of the Kerguelen archipelago was founded by one pair brought by humans in 1957. As long as we don't bring any new sheep to the island or take any away, this population will remain isolated and have no gene flow with the outisde world. Similar things have probably happened on oceanic islands many times in the past, as local populations were founded by individuals or pairs drifted there by chance. This is not the typical method of speciation, but it's wrong to say it doesn't happen.
PC@t3 is the most recent common ancestor of C and H@t5 in your diagram.
PC and C at t3 are equally recent common ancestors, both being the grandparents of C and H at t5.
The important point here, though, is that Jon's hypothetical drawings seem to be clearly demonstrating Dr. A's argument to be correct, as both examples clearly fit what Dr. A was saying. In the second, more complicated example, PC@t3 and C@t3 are in Dr. A's Set B - they have human and chimp living descendants. PC@t3 has three children listed - two of which (PC@t4 and C@t4) are in Set C (they have only chimp descendants) while one (?@t4) is in Set H - it has only human descendant. The same applies to C@t3, who has one child in Set C (C@t4) and one child in set H (?@t4).
What I think Job is discussing (correct me if I'm wrong!), is the idea that two populations may diverge, and then start to change such that they're recognisable as distinct populations, without genetic flow between them ceasing. So we'd have our protochimps and protohumans, still occasionally interbreeding for many, many generations even after recognisably seperating. This doesn't change the fact that the populations eventually do seperate completely with no further interbreeding, and there must at some point be the final ancestor who has both human and chimp descendants, but whose children do not.
Minor point: the line down from C crosses the line across from PC, it doesn't lead to H at all
So it does - it might have helped if I actually read the note next to the diagram! It would have made my explanation a lot simpler - PC@t3 is in Set B, and has two children - PC@t4 (in Set C) and ?@t4 (in Set H).
The dog ancestry is a dead end. Apparently the specific breed ancestry was never documented.
I'm not sure how this is supposed to be important, but the specific ancestry of many dog breeds is documented. I was reading about Alsatians the other day, for example, as a friend recently bought one. Alsatians are all descended from a few, closely related German working dogs intentionally inbred at the turn of the 20th century. Even details like the name of each dog are recorded by breeding societies. With the obsessiveness of some hobbyists and recording in breed registries, it's probably possible to trace the exact ancestry of certain modern dogs back to the founders of the breed a century ago.
Artificial selection works basically the same way as natural selection, except that artificial selection doesn't just favor survival and reproductive ability: it could favor any number of things (aesthetics, or human utility, for example).
This seems to me a pretty artifical distinction. What's being selected for in artificial selection is still reproductive ability, it's just taking place in an environment where reproduction is controlled by humans. It seems silly to say it's aesthetics that's being selected when some human only allows dogs who look in a certain way to breed, whlist it's reproductive ability being selected when some female wolf only allows wolves that look a certain way to mate with her. In both cases the animal being selected is the one best able to reproduce in its own environment.
PaulK mentioned Orrorin tugenensis (Message 4). Perhaps this will be a good beast with which to begin? So, what do we know about him?
Not a great deal. It was found in Kenya, and there are thirteen bones believed to come from about 5 individuals. They're dated to around 6 or 7 million years ago, which is about the same or slgihtly older than the usual molecular clock estimates for the human/chimpanzee split. The fossils include two femurs, which are claimed to show that they were supporting an upright body, but this is a bit controversial, I think. The teeth indicate they ate mostly fruit and veg, with some meat. You can see a quick summary of the claims of the discoverers here
It's a pity that website does not show the margins of error on its estimates. The separation of nuclear and mitochondrial DNA need not be exactly the same in time, but is unlikely to be as different as suggested by the figures you gave.
Everyone keeps complaining that the website doesn't give margins of error, but it does. When you search for a split, you get a big list of molecular studies which looked at that split. Each has the estimate and the margin of error. The numbers at the top are just mean averages of all the different studies put together.