A cladogram issue illustrated

This post is dedicated to
reader Neil B. who suggested I review the reference below (Bapst 2013). It is a paper on the limits of resolution using theoretical cladograms. Frankly, it is over my head. Apologies, Neil. I stand by my large reptile tree cladogram as an reflection of actual evolutionary events. The tree is a practical application, not a theoretical one. However, let me offer some theory below (It probably duplicates something that has been published before that I am unaware of. If so, don’t turn me in!)

Some workers,
perhaps most current workers, follow the paradigm that you need at least 3x as many characters in order to attempt to resolve a list of taxa in phylogenetic analyses. In counterpoint, the large reptile tree currently employs only 228 characters versus a current total of 640 taxa with full resolution.

So what’s going on? 
‘In practice’ does not seem to be following ‘in theory.’ Of course, all the theoretical problems go away when you employ subsets of the large reptile tree, using only 12 to 50 taxa instead of the whole list. These subsets also employ 228 characters (most of them, I hope, parsimony informative), and that raises the ratio of those analyses above 3x. But that’s not even necessary.

Here’s a simplified solution that seems to help explain this issue.
You might think 1 character dichotomy should split 2 taxa, and it does. But one character dichotomy also lumps two taxa on each sides of that split. Ratio: 1 character/4 taxa.

Figure 1. Characters vs. taxa in analyses. Note one character lumps and splits 4 taxa. Two characters lumps and splits 8 taxa. Three characters lumps and splits 12 taxa given the present list of traits.

Figure 1. Characters vs. taxa in analyses. Note one character lumps and splits 4 taxa. Two characters lumps and splits 8 taxa. Three characters lumps and splits 12 taxa given the present list of traits.

I’ve only extended this example
to three character dichotomies splitting and lumping 12 taxa with complete resolution using a 1:4 character:taxon ratio.

Now imagine
having a trait trichotomy (like fins, feet AND flippers) or four trait options (add limbless to this list) and you can see the possibilities for nesting more taxa with complete resolution increase greatly with relatively few characters. Of course, we’ll never completely fill in the large grids. It gets complicated fast with missing taxa and incomplete taxa and evolution going the way it wants to go without regard for the order of the matrix.

This then
is how the large reptile tree is able to keep adding taxa without adding characters. I don’t think I’ve even come close to hitting the limit for taxa yet. The 3x rule does not appear to hold true here. Rather the maximum number of taxa looks to be several multiples of the number of characters in theory, a smaller number in practice.

If one can define a new species
by a set of traits that no other species has, one should be able to split that taxon apart from all other taxa in phylogenetic analysis. Right? That’s all we’re trying to do here. So far, the large reptile tree is succeeding — and it does better (more robust bootstrap scores) as mistakes are corrected. If anyone has an old matrix, they should ask for for the latest update here.

Bapst DW 2013. When Can Clades Be Potentially Resolved with Morphology?



12 thoughts on “A cladogram issue illustrated

  1. Ummmmmm…. This is all wrong. To an embarrassing degree. It beggars belief I should need to explain it

    The entire idea is based on “one character dichotomy also lumps two taxa on each sides of that split”. But it doesn’t!
    Take your example of feet/find with four taxa. The whale and dolphin are united by fins, yes, but the feet are not a shared derived characteristic of the fox and dog. They a plesiomorphic. Therefore you cannot tell whether the relationships are
    ((dog, fox)(whale, dolphin))

    The same goes when you add the jaw character and the lepidoasaurs. The cladogram you show as being the only mpt, has the lizards defined by their multiple jaw bones and the fins evolving independently twice in whales and mosasaurs. But It is equally parsimonious that whales and mosasaurs group together based on fins and the single jaw bone evolved twice. Both of these involve the same number of character state transformations. Count them yourself. You need another character to unite the mosasaurs with lizards

    The whole point of parsimony, literally the entire driving force behind the method, is that every node needs a unique shared DERIVED character to define it! Barest minimum is one character state per node, number of nodes bring no of taxa -1 in a fully resolved tree.

    I’ve made a slightly less specific reply to your comment on the other post

  2. Common plesiomorphic trait for dog, fox, whale, dolphin = single jaw bone in this example. I could have used traits A, B, C, but I thought it would be more informative this way.

    With regard to ‘every node needs a unique share DERIVED character to define it — I have not found that to be true… exactly. I have found a unique SET of derived characters define a clade, and a minimum of three to give it a 50+ rating in Bootstrap analysis. That set more often than not includes traits found in other nodes. It’s like DNA, both in theory and in practice, in which the set or combination of traits makes each left and node unique, but most individuals / clades share the vast majority of DNA.

    It’s called “pulling a Larry Marin” when you attempt to define a clade by one single trait, because Larry would always find another unrelated clade that would share that trait. Amnion is one good single trait. So are mammary glands. I can think of few others.

    • “Common plesiomorphic trait for dog, fox, whale, dolphin = single jaw bone in this example.”

      But common plesiomorphic traits don’t define a clade! Parsimony just doesn’t work like that! Parsimony counts changes in traits, therefore a trait has to change to define a clade. This is seriously the most basic principle in parsimony, it astonishes me you can be so ignorant of a method you use so much.

      You don’t even need to take my word for it. You can count the changes yourself.
      If the tree is the one you gave, and just using the two characters you gave, there is one change from multiple to single jaw bones in the mammals, and two changes from feet to fins, one in whales and one in mosasaurs. Total: three changes.

      Now change it so that the relationships are

      (((Dog,fox),(horned lizard,iguana)),((mosasaurus, tylosaurus),(whale,dolphin))).

      Here the character changes are:
      One change from feet to fins in the mosasaur/whale clade, and two changes from multiple jaw bones to single jaw bone, one in dogs, one in whales. Total: three changes again.

      Now let’s try making one of these clades paraphyletic

      (Horned lizard,(iguana,((tylosaurus,mosasaurus),((dog,fox),(whale,dolphin)))))

      Here the changes are: two changes from feet to fins, one in the mosasaurs, one in whales, and one change from multiple jaw bones to single in mammals. Total: three changes

      Now let’s make the tree really wrong:

      (Whale,(dolphin,(mosasaurus,(tylosaurus,(horned lizard,(iguana,(dog,(fox)))))))).

      Here the changes are: fins to feet at the base of the dog/lizard clade; transition from single jaw bone to multiple at the mosasaur/lizard/dog clade; reversal back to single jaw bone in dogs. Total: three changes

      I frankly could go on all day, there are a lot more equally parsimonious combinations. But for now I will simply say how stupified I am that you even made this mistake. You can have all the anatomy knowledge you like, but you don’t even know the most basic principles of cladistics! I’m staggered!

  3. “Common plesiomorphic trait for dog, fox, whale, dolphin = single jaw bone in this example.”

    Parsimony doesn’t work that way! Parsimony counts character *changes*. A plesiomorphic trait has not changed from the primitive condition. Therefore parsimony will not use a plesiomorphic trait to define a clade. This the most basic principle of parsimony, and I am astonished that you can be so ignorant of it. The method of parsimony was specifically created to avoid the creation of clades defined by plesiomorphies!

    You don’t even have to take my word for it. Lets take your own example and do exactly what PAUP does: count the character changes.

    You gave two characters: 1 – Feet or fins; 2 – single jaw bone or multiple

    The tree you gave is:
    (((mosasaurus, tylosaurus),(Iguana, horned lizard)),((dog,fox),(whale,dolphin)))
    Character changes are: 1 – change from multiple jaw bones to single jaw bone in mammals; 2 – change from feet to fins in mosasaurs; 3 – change fromfeet to fins in cetaceans.
    Total: three changes

    Now lets shift things a bit.
    (((mosasaurus, tylosaurus),(whale, dolphin)),((dog,fox),(iguana,horned lizard)))
    Character changes here are: 1 – change from feet to flippers in whale/mosasaur clade; 2 – change from multiple to single jaw bones in cetaceans; 3 – change from multiple to single jaw bones in dogs.
    Total: three changes. Equally parsimonious

    Lets make lizards paraphyletic
    (iguana,(horned lizard,((mosaurus,tylosaurus),((whale,dolphin),(dog,fox)))))
    Character changes are: 1 – feet to fins in mosasaurs; 2 – feet to fins in cetaceans; 3 – change from multiple to single jaw bones in mammals.
    Total: three changes. Another equally parsimonious tree

    Now, just for fun, lets make this really wrong.
    (iguana,(horned lizard,(dog,(fox,(whale,(dolphin,(mosasaurus,tylosaurus)))))))
    Character changes are:1 – feet to fins in the whale/mosasaur clade; 2 – tranition from multiple to single jaw bones in mammal/mosasaur clade; 3 – reversal back to multiple jaw bones in mosasaurs
    So, completely idiotic tree, but still: three changes. Just as parsimonious

    I could go on, there are many more equally parsimonious trees . For now I will simply say that this is what happens when you try to use a method as a black box.

      • How am I going off the deep end? I’m using your own illustration as an example! You tried to show how you could get one most parsimonious tree with 8 taxa and only two characters. I showed, using your own 8 taxa and your own two characters, that there is considerably more than one most parsimonious tree. This really is not as hard as you’re making it

    • I know that is the point you’re making. But your own examples show that fewer characters CAN’T handle more taxa. None of your examples produce one most parsimonious tree.

      If you had actually bothered to read my post you would see that using the same characters and taxa in your own simple examples there are many many more equally parsimonious trees.

  4. Neil, it does not matter how many MPTs are produced in this example. A single MPT is not what I’m looking for here. Just that fewer characters can handle more taxa. That’s all. And I do read your replies. It’s not a problem, as long as we keep this civil. This is just the nature of argument. One almost never sees the other’s point of view. If you’ve had siblings or a spouse, and I imagine that you have, then you already know what I’m talking about. Thanks for your notes.

  5. Hello, I was trying to find one of my own papers and happened to stumble on this. As the Bapst in Bapst (2013), I just wanted to add that if you found it over your head, perhaps this semi-silly, semi-serious version of the results (using a beloved group of theoretical monsters) which I presented at A Real Conference (Evolution 2012, Ottawa) will help:

    It has very little to do with the substance of this post however; I think Neil originally pointed to my paper as a description of why saying things about ancestors is a challenging issue in morphological phylogenetics.

    • Hello, Dr. Bapst. Thank you for sharing your beloved group of theoretical monsters. Very informative and entertaining. However, I have to disagree with you in slides 14 and 16 and for your use of fewer than a dozen character traits. I realize yours is just an illustration, as was mine. In the real world of phylogenetics we’re both going to need upwards of 150 character traits to establish relationships to a high degree of certainty. Thereafter only incremental advances can be expected. That 150 number likely provides 100+ synapomorphies that lump basal taxa (even if unknown) and only a few dozen to only a few traits that split derived taxa. At least, that has been my experience in the large reptile tree. Fewer characters, and far fewer characters, as you point out, may provide the appearance of relationships when convergence is mucking up the works. And, worse case scenario, one tries to nest actual sisters in which only a skull is known for one and only post-cranio is known for another. These things happen.

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