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Author | Topic: Discussion of Phylogenetic Methods | |||||||||||||||||||||||||||||||||||||||||||
Dr Adequate Member (Idle past 309 days) Posts: 16113 Joined: |
The prior probability of a particular tree is the probability that among all possible tree topologies it is the correct one. If we believed that all trees were equally likely, then we could assign a flat prior, where the prior probability of a tree equals one divided by the number of trees. Why don't we believe that?
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RAZD Member (Idle past 1430 days) Posts: 20714 From: the other end of the sidewalk Joined: |
The prior probability of a particular tree is the probability that among all possible tree topologies it is the correct one. If we believed that all trees were equally likely, then we could assign a flat prior, where the prior probability of a tree equals one divided by the number of trees. Why don't we believe that? Well I would think that the probability of the first two of these | | | would be the same but different from the probability of third, (which I would expect to be lower). Enjoy Edited by RAZD, : .by our ability to understand Rebel☮American☆Zen☯Deist ... to learn ... to think ... to live ... to laugh ... to share. Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)
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Dr Adequate Member (Idle past 309 days) Posts: 16113 Joined: |
I think we're meant to assume they're all bifurcating.
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herebedragons Member (Idle past 883 days) Posts: 1517 From: Michigan Joined: |
Well I would think that the probability of the first two of these
| | | / \ / \ /|\ /\ | | /\ / | \ would be the same but different from the probability of third, (which I would expect to be lower). Dr. A is right, only bifurcating trees are evaluated for likelihood. The assumption is that all phylogenies can be resolved given enough information, so the tree space will only contain bifurcating, fully resolved trees. Tree number 3 above would be an unresolved trichotomy, not that 3 lineages diverged from the same ancestor. This would occur when there are not enough differences between two or more taxa to completely resolve the relationship. The question regarding prior probabilities is: is there any reason to favor tree 1 over tree 2 before even analyzing the data? If there is, then a probability could be assigned that gives tree 1 an increased posterior probability. HBDWhoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca "Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem. Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.
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herebedragons Member (Idle past 883 days) Posts: 1517 From: Michigan Joined: |
Why don't we believe that? We do consider that all trees have an equal prior probability unless we have information or prior knowledge of the system that indicates otherwise. For example, if we knew two taxa were sister taxa, we could include constraints that favor topologies that include those taxa as sister groups (or as a monophyletic group). We can also assign priors that reflect our prior knowledge of substitution rates (molecular clock rates), tree age, and branch lengths. So if we had prior knowledge that two lineages diverged a certain amount of time ago based on fossil evidence, we would want to favor topologies that reflect that divergence time. The posterior probability doesn't just take into account topology but other factors that could influence the phylogenetics. MrBayes (probably the most widely used Bayesian inference program) includes 34 prior parameters that can be set. I am not all that familiar with all these subtleties (like exactly how and when to use them), but the point is that Bayesian theory allows us to take into account prior knowledge of a system and that prior knowledge can affect the outcome of the analysis. HBDWhoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca "Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem. Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.
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RAZD Member (Idle past 1430 days) Posts: 20714 From: the other end of the sidewalk Joined: |
Dr. A is right, only bifurcating trees are evaluated for likelihood. ...Tree number 3 above would be an unresolved trichotomy, not that 3 lineages diverged from the same ancestor. This would occur when there are not enough differences between two or more taxa to completely resolve the relationship. Interesting, thanks. So what about:
vs | | a a / \ / \ / \ / \ / \ b \ / b / \ \ c / \ c \ \ / \ / \ / \ \ \ d e f g d e f g I would think the first is more probable than the second as I would not expect all the "activity" to be on one branch. Thoughts? Edited by RAZD, : .by our ability to understand Rebel☮American☆Zen☯Deist ... to learn ... to think ... to live ... to laugh ... to share. Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)
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herebedragons Member (Idle past 883 days) Posts: 1517 From: Michigan Joined: |
I would think the first is more probable than the second as I would not expect all the "activity" to be on one branch.
| vs | a a / \ / \ / \ / \ / \ b \ / b / \ \ c / \ c \ \ / \ / \ / \ \ \ d e f g d e f gThoughts? Well, let's think about what this means phylogenetically. In the figure on the left, both lineages have diverged at roughly the same rate. In the figure on the right, lineage 'd' has diverged at a much higher rate than has lineage 'g'. What a priori belief about evolution or about this system would cause us to believe that the first tree is more likely? One possibility would be that taxa 'd' and 'e' are Australian taxa and 'f' and 'g' are North American taxa. This prior knowledge may cause us to want to give more weight to the first tree. However, I am not sure how you would decide how to set the prior in this case. Is it 100% certain that given the above prior knowledge that tree 1 is the correct tree? No, it is definitely not 100% certain. It is quite plausible that a North American species, 'f', is more closely related to the Australian species 'd' and 'e' than it is to another N. American species 'g'. Not that I have read a truly representative sample of the literature regarding Bayesian inference, but my impression is that priors are not typically applied to topology but to models of evolution (maybe Genomicus can weigh in on this and say if that is his impression as well). The maths behind these models can be rather complicated and honestly, I am just not familiar enough with some of those finer points. It is something I need to understand better, so maybe I can talk about models more at a later time. For now, I think the important "take-away" is that Bayesian statistics allows us to incorporate our prior knowledge of a system into the calculation of the posterior probability. Because of the way the formula is structured, the posterior probability becomes the probability that our hypothesis is true. Maximum-likelihood does not calculate the probability of the hypothesis, but the probability that the hypothesis could produce the given data - which is kind of backwards from what we really want to know. We want to know if our hypothesis is correct or what the probability is that it is correct. That is the big advantage of Bayesian statistics over ML. Bottom line here, I would consider all topologies to have equal prior probability. At this point, I don't think I could legitimately give weight to one topology over another because I just wouldn't know how to determine how much weight to assign. HBDWhoever calls me ignorant shares my own opinion. Sorrowfully and tacitly I recognize my ignorance, when I consider how much I lack of what my mind in its craving for knowledge is sighing for... I console myself with the consideration that this belongs to our common nature. - Francesco Petrarca "Nothing is easier than to persuade people who want to be persuaded and already believe." - another Petrarca gem. Ignorance is a most formidable opponent rivaled only by arrogance; but when the two join forces, one is all but invincible.
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RAZD Member (Idle past 1430 days) Posts: 20714 From: the other end of the sidewalk Joined: |
Well, let's think about what this means phylogenetically. In the figure on the left, both lineages have diverged at roughly the same rate. In the figure on the right, lineage 'd' has diverged at a much higher rate than has lineage 'g'. What a priori belief about evolution or about this system would cause us to believe that the first tree is more likely? ... Indeed, and if we assume that -- all things being equal -- the rates of evolution should be about the same, then the left model seems more likely, but we'd have to evaluate the probabilities of the rates to determine an approximation of the difference (similar to greatest likelihood?).
... It is quite plausible that a North American species, 'f', is more closely related to the Australian species 'd' and 'e' than it is to another N. American species 'g'. Indeed. Any marsupial (opposums for example) should relate to 'd' or 'e' more than 'g' and any placental mammal in Australia should relate more to N.American taxa. But I would also expect the genetics to provide this information.
For now, I think the important "take-away" is that Bayesian statistics allows us to incorporate our prior knowledge of a system into the calculation of the posterior probability. Because of the way the formula is structured, the posterior probability becomes the probability that our hypothesis is true. Maximum-likelihood does not calculate the probability of the hypothesis, but the probability that the hypothesis could produce the given data - which is kind of backwards from what we really want to know. We want to know if our hypothesis is correct or what the probability is that it is correct. That is the big advantage of Bayesian statistics over ML. Can you combine these? ie - use ML as a gage of prior probability? or is there a conflict? Enjoyby our ability to understand Rebel☮American☆Zen☯Deist ... to learn ... to think ... to live ... to laugh ... to share. Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click)
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vaporwave Member (Idle past 2670 days) Posts: 66 Joined: |
A phylogeny is a hypothesis about the evolutionary history of a group of taxa and since the phylogeny we present is a hypothesis, we want to know how well our hypothesis is supported compared to other hypotheses. Thus, the various phylogenetic methods have been developed to provide researchers with ways to evaluate those hypotheses and determine which hypothesis is the best. In other words, phylogenetic programs don't just build trees but more importantly, they evaluate them so that researchers can present the most well supported hypothesis. Phylogenetics asks: IF common ancestry is true, what is the most likely evolutionary relationship between living things? But it does not investigate that core assumption that common descent has taken place. Evolutionists paint a false picture for the public. They imply that if common ancestry were false, then assembling phylogenetic models would be impossible. The models would break down. But this is not true. Common ancestry could be false, and one could still derive phylogenetic models that gave the appearance of evolution. There are a host of explanatory devices ready to deal with pieces that do not fit in any given phylogenetic model. e.g. If you have arranged branches based on genetic traits, but the morphology and anatomy don't reinforce it, then the evolutionists can propose that some of those traits must have evolved independently of each other... and voila, you have accommodated contradictory data into the model. This is not to disparage the methodology... it is all very practical and extremely interesting. It is just dishonest to present such phylogenetic models as hard evidence that proves common ancestry is true. I guess the idea is that if you present enough numbers, data matrices, complex diagrams, etc. then it will intimidate the opposition into silence. As I mentioned before, this all works off the implied evolutionist bluff that such diagrams would be impossible to generate if common ancestry were false.
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Modulous Member Posts: 7801 From: Manchester, UK Joined: |
I guess the idea is that if you present enough numbers, data matrices, complex diagrams, etc. then it will intimidate the opposition into silence. As I mentioned before, this all works off the implied evolutionist bluff that such diagrams would be impossible to generate if common ancestry were false. Of course, this doesn't explain how we can create those trees from morphology and from DNA evidence and come to very similar answers. This strongly suggests common descent is indeed correct.
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vaporwave Member (Idle past 2670 days) Posts: 66 Joined: |
Of course, this doesn't explain how we can create those trees from morphology and from DNA evidence and come to very similar answers. This strongly suggests common descent is indeed correct. Evolutionists fall back on a strange sort of metaphysics... they work off the assumption that if common descent were false, the pattern of morphology and DNA would necessarily be in discord. This assumption cannot be demonstrated or tested in any way of course. The typical rebuttal here has the evolutionist quickly retreating to teleological territory and he begins rambling about how a Creator could do X or Y, etc.... Furthermore, back to phylogenetics... when DNA and morphological traits actually are in conflict, evolutionists simply say the morphology evolved twice or more, significantly insulating the theory from potential falsification. Ask an evolutionist what the evolutionary limits are to "Convergent Evolution", with regards to morphology. They won't be able to give you any kind of specific answer, because tomorrow, in order to reconcile the phylogenetic data, they may have to assume an even more complex morphological trait evolved multiple times. Again, the whole phylogenetic practice boils down to: IF evolution is true, this is likely how it happened. But it doesn't reveal more than that. Edited by vaporwave, : No reason given.
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jar Member (Idle past 419 days) Posts: 34026 From: Texas!! Joined: |
vaporwave Really apt user name writes: Again, the whole phylogenetic practice boils down to: IF evolution is true, this is likely how it happened. But it doesn't reveal more than that. Not at all. That is simply nonsense and not at all what any honest scientist would say. Rather what is said is that all of the evidence shows that evolution is a fact, that living things have changed over time and the the Theory of Evolution is the only explanation that has ever be presented that actually does explain what is seen.
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Modulous Member Posts: 7801 From: Manchester, UK Joined: |
Evolutionists fall back on a strange sort of metaphysics... they work off the assumption that if common descent were false, the pattern of morphology and DNA would necessarily be in discord. This assumption cannot be demonstrated or tested in any way of course. Nope. I'll just say the theory of evolution explains this phenomena. No proposed alternative has.
The typical rebuttal here has the evolutionist quickly retreating to teleological territory and he begins rambling about how a Creator could do X or Y, etc.... Unless you provide a coherent theory of the Creator I cannot do this.
Furthermore, back to phylogenetics... when DNA and morphological traits actually are in conflict, evolutionists simply say the morphology evolved twice or more, significantly insulating the theory from potential falsification. I dispute this. Now you get to provide your evidence!
Ask an evolutionist what the evolutionary limits are to "Convergent Evolution", with regards to morphology. There must not be a large path of reduced fitness through morphspace that can be achieved through incremental changes to the genome.
They won't be able to give you any kind of specific answer Boy, is the egg on your face!
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Tangle Member Posts: 9509 From: UK Joined: Member Rating: 4.8
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vaporwave writes: Phylogenetics asks: IF common ancestry is true, what is the most likely evolutionary relationship between living things? Not true. You have it entirely the wrong way around. The ToE makes the prediction that if it is true, all organisms will have common ancestry. This prediction is entirely falsifiable. For example, taxomic trees were built based on the phyiscal features and functionalities of organisms and their assumed relationships. DNA came along and could have completely debunked the entire concept, yet it confirmed it. If you can find a organism without an ancestor, you win. If you find a bunch of creatures using different polypeptides to the rest of 'creation' you win. If you can find a modern mammal in the fossil record alongside dinosaurs, you win. We've been waiting for 150 years. Edited by Tangle, : No reason given. Edited by Tangle, : No reason given.Je suis Charlie. Je suis Ahmed. Je suis Juif. Je suis Parisien. "Life, don't talk to me about life" - Marvin the Paranoid Android "Science adjusts it's views based on what's observed.Faith is the denial of observation so that Belief can be preserved." - Tim Minchin, in his beat poem, Storm.
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jar Member (Idle past 419 days) Posts: 34026 From: Texas!! Joined: |
Tangle writes: If you can find a mammal in the fossil record alongside dinosaurs, you win. Not too sure about that. I can think of no reason a mammal fossil should not be found alongside dinosaurs and a bunch of reasons to expect that we should see mammal fossils concurrent with dinosaurs. After all we find mammals filling many of the niches once filled by dinosaurs not all that long after the dinos exited stage left.
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