12 replies to this topic

[Bonedigger]

One of the most fundamental arguments for evolution is the argument from homology, where morphological similarity is used as proof of phyletic relationship due to inheritance from a common ancestor. Classically, symplesiomorphic (shared primitive form) characters were used to group taxa. With the rise of cladistics, however, the focus has shifted to synapomorphic (shared derived form) characters in the determination of phyletic relationships. One of the consequences of that shift is that derived characters that before would be ignored except when dealing with the diagnosis for a particular taxon are now an integral part of the phyletic analysis. This gives a more comprehensive view of the character distributions within a group of taxa.
Homoplasy-correspondence between parts or organs acquired as the result of parallel evolution or convergence. (http://www.merriam-w...onary/homoplasy) Homoplasy is a flat contradiction to the principle of using morphological similarity to prove relationship, because you cannot attribute such similarity to inheritance, but rather it would have had to originate independently. In reality, it is nothing more than an ad hoc explanation as to why the principle of homology doesn't work in a particular instance.

During the 1980's and 1990's several workers including, but not limited to, Richard C. Hulbert Jr., Bruce J. MacFadden, and Thomas S. Kelly, did a comprehensive revision of the mesodont (middle-crowned) and hypsodont (high-crowned) grazing horses. While a college student in the '90s, I mapped out the character distributions in several of their cladistic analyses, and the first of these I am presenting here. In 1989, Hulbert published an analysis that included the 13 well established genera of hypsodont horses, and 10 "Merychippus" grade mesodont horses, with "Parahippus" leonensis as the outgroup (Hulbert, Richard C. Jr., 1989. Phylogenetic Interrelationships and Evolution of North American Late Neogene Equidae. In "The Evolution of Perissodactyls", Prothero, D. R. and Schoch, R. M. (eds.)). He used 45 characters, 7 of which have multiple states (3 with differently derived states, and 4 with sequentially derived states), for a total of 52 derived characters.

Below is Hulbert's fig 11.2 cladogram with all of the characters mapped and color-coded as follows: Yellow= unreversed synapomorphies, i.e. characters that can be unequivocally attributed to shared inheritance. Green= synapomorphies that are subsequently reversed in one or more taxa and are therefore equivocal in there use as proof of relationship. Pink= reversals of the above green characters. Blue= parallelisms where the character would have to have been acquired independently more than once, i.e. homoplasy. Gray= autapomorphic characters unique to a single taxon and therefore useless for determining phyletic relationship.



17 of the characters prove to be unreversed synapomorphies and therefore can be used as unequivocal evidence of phyletic descent. I have 18 mapped as yellow, but character 44--tridactyl to monodactyl feet--is actually a parallelism in the Equinae. Hulbert used Pliohippus mirabilis, a tridactyl form, to score the characters for Pliohippus. But the more derived Pliohippus pernix and Pliohippus nobilis are monodactyl (see, for example, Kelly http://www.nhm.org/s...ience/CS473.pdf), so one-toed feet would have had to originate independently twice-once in the Pliohippus clade, and again in the Astrohippus-Dinohippus-Equus-Onohippidium-Hippidion clade.
12 of the characters are synapomorphic but get reversed, and so are equivocal in their use in establishing phyletic relationship.
6 of the characters are autapomorphic (unique to a single taxon) and therefore useless for determining interrelationships.
17 of the characters are parallelisms, or, in other words, homoplastic, and therefore contradict the principle of homology.
A count of the total number of instances where a character state has been changed yields 29 synapomorphies, 27 reversals, and 44 parallelisms (some parallelisms occur more than twice). Now, I'm no mathematical genius, but when the ratio of the number of occurrences that support a method (29 synapomorphies) to the number of occurrences that contradict a method (44 parallelisms) is about 2:3, there is something seriously flawed with the method. If you include the reversals with the parallelisms, it gets even worse, about 2:5.

My question for evolutionists is this: if the practice of using morphological similarity to prove phyletic relationship due to inheritance from a common ancestor performs so poorly and is so equivocal in such a closely (and truly) related group like the Equinae, why should it carry any credibility when dealing with such widely disparate forms like a human, a bat, and a whale? The only way I can see to maintain such an argument is if you engage in extreme "cherry picking" in your selection of characters that "prove" relationship.

It would seem to me that the more reasonable hypothesis, at least with regard to the Equidae, is that all these characters are "subroutines" that were built into the equid genome from the start. And that allowed them to be mosaically expressed in different combinations as the horses spread out and diversified in the rapidly changing early post flood world. Of course, that presents an even bigger problem for an evolutionary origin of these characters. How do you select for and preserve a character that hasn't even been expressed yet?

(For those interested, I do have a pdf of the Excel workbook I created mapping the characters, with a separate page for each character description and distribution, if I can ever figure out a way to upload it. Is there a way to upload files to this site, or would I need to upload it to a file sharing site and link to it instead?)

[gilbo12345]

Great work Bonedigger

I'm not much of a geology person, however it seems that you've exposed the problem with the details of this issue. This is more evidence for the arising theme that when one looks closely into the details of evolution there are many contradictions to be found.

[herebedragons]

Hi Bonedigger ...

I commend you on you work here. I must say it is the best argument against evolution that I have seen yet on this forum (not that I have seen every argument on the entire forum).

I do have a couple of concerns that I would like to address regarding your work before I accept it as a valid argument. I have only a basic understanding of phylogenetic tree construction and part of what I hope to gain from this discussion is a better understanding of the process (you can't argue for or against something unless you understand the thing you are arguing for or against).

1. This work seems a bit dated, however, I have been unable to locate anything newer. My Evolution (Futuyma, Douglas) textbook has a slightly different treatment of this Hypsodont group but it seems the biggest difference is he left out many of the Merychippus spp. MacFadden has a newer book (1994) which I would presume he has revised the phylogeny somewhat. I haven't got access to this book yet, but I will try to get it.

2. Cavanaugh, Wood and Wise have done a baraminological study of the Equidae and have concluded that Equidae is a monobaramin, and interpret it as rapid, post-flood interbaraminic diversification. It seems strange that the discontinuities that you characterize have been overlooked by other creationists / IDists. This isn't evidence against your findings (I am not really sold on the science of baraminology), but it does make me ask - why didn't Cavanaugh, Wood and Wise notice these issues?

source: http://scholar.googl...t=0,23&as_vis=1

3.

The only way I can see to maintain such an argument is if you engage in extreme "cherry picking" in your selection of characters that "prove" relationship.

Are you saying that is what the authors did in here? Do you have the original cladogram where they list the symapomorphies on the nodes that they used to characterize the clades? Did they not include some of the characters in their treatment?

4. I am confused by your usage of homology and homoplasy. From Wikipedia http://en.wikipedia....ology_(biology)

"A homologous trait may be homoplasious – that is, it has evolved independently, but from the same ancestral structure – plesiomorphic – that is, present in a common ancestor but secondarily lost in some of its descendants – or (syn)apomorphic – present in an ancestor and all of its descendants"

So, if the trait evolved from the same ancestral structure it is homologous. Why do you say that parallelism (homoplasy) is contradictory to homology?

Agreed that the number of expected homoplasious traits should be minimal and this cladogram has, what seem to be, a significant number.

5. In determining your ratio of 2:3, why do you count each instance of parallelism but only the first instance of synapomorphy? For example: Trait # 39 is one instance of parallelism. (I am not sure how to treat trait # 4 since it occurred in several lineages). But if you number each instance of parallelism, then shouldn't you also number each instance of synapomorphy since a synapomorphy is present in an ancestor and in the descendants? As an example: trait # 27 is a synapomorphy at every node except the outlier group. Seems inconsistent. Can you justify this approach?

Keep in mind, I freely admit i may be arguing from ignorance. Maybe you can help me understand this better. I would also be interested in the dataset you have. I have no idea how to upload to this site. If you have access to a file sharing site, that should work.

It would seem to me that the more reasonable hypothesis, at least with regard to the Equidae, is that all these characters are "subroutines" that were built into the equid genome from the start. And that allowed them to be mosaically expressed in different combinations as the horses spread out and diversified in the rapidly changing early post flood world.

Do I understand this correctly; you are accepting that this cladogram is correct (or at least close) but are proposing a mechanism that explains the apparent inconsistencies (especially the parallelisms)?


Thanks

HBD

[Bonedigger]

Hello herbedragons
Thanks for the questions. One of the reasons I made this post was to get other eyes on my arguments and critically examine them for weaknesses and deficiencies.

1. This work seems a bit dated, however, I have been unable to locate anything newer. My Evolution (Futuyma, Douglas) textbook has a slightly different treatment of this Hypsodont group but it seems the biggest difference is he left out many of the Merychippus spp. MacFadden has a newer book (1994) which I would presume he has revised the phylogeny somewhat. I haven't got access to this book yet, but I will try to get it.

It is a little dated. In 1991 Hulbert and MacFadden continued the analysis (in "Morphological transformation and cladogenesis at the base of the adaptive radiation of Miocene hypsodont horses." Am. Mus. Novitates 3000:1-61 available as a free pdf download here (http://digitallibrar...andle/2246/5083)). In that study they left out the more hypsodont genera and focused only on the "Merychippus" grade taxa with the addition of a couple more species. I am currently transferring the character map for that analysis to an Excel workbook (I mapped these out by hand on paper with a multi-color pen while I was in school). They also switched to favoring multi-state characters, some with as many as six states per character. It didn't help Here's a screenshot of what I have transferred so far.
In 1995 Thomas S. Kelly continued the analysis with the addition of new material (New Miocene horses from the Caliente Formation, Cuyama Valley Badlands, California. Contributions in Science 455: 1-33 available as a free pdf download here (http://www.nhm.org/s...ience/CS455.pdf)). He also erected three new genera-Acritohippus, Heteropliohippus, and Parapliohippus, for some of the taxa.
In 1998 Kelly continued the analysis with the addition of more material (New Middle Miocene equid crania from California and their implications for the phylogeny of the equini. Contributions in Science 473: 1-44 available as a free pdf download here (http://www.nhm.org/s...ience/CS473.pdf)). As far as I know Kelly's 1998 paper is the most recent analysis of hypsodont/mesodont horse relationships. The common complaint in the discussion section of all four papers was the abundance of homoplasy.
When I decided to make my OP, I debated whether to use Kelly's 1998 analysis with it being the most recent, or Hulbert's 1989 analysis with it being the logical starting point on which the other analyses were based. I opted for Hulbert's for several reasons. Hulbert mapped out the reversals and parallelisms on his figure, which is unusual. Normally you are just given the most parsimonious cladogram(s) and a list of the nodes where the synapomorphies (yellow and green characters in my picture) are presumed to have arisen. The only indication you usually have for the amount of homoplasy is the consistency index, which doesn't give you the graphic picture you get with mapping characters. With Hulbert having mapped them (although he did miss a couple), there could be no appearance of me having misinterpreted or misrepresented the data. He also included all of the hypsodont taxa in his cladistic analysis. The subsequent papers left out some of the taxa like Hippidion and Onohippidium from their analysis because their phyletic position was presumably established. Also, the subsequent papers were an extension of Hulbert's analysis, so it made the best starting point. And finally, Hulbert tried to make as many as possible of his characters with only two states, which gives a less cluttered picture when all of the characters are mapped.

2. Cavanaugh, Wood and Wise have done a baraminological study of the Equidae and have concluded that Equidae is a monobaramin, and interpret it as rapid, post-flood interbaraminic diversification. It seems strange that the discontinuities that you characterize have been overlooked by other creationists / IDists. This isn't evidence against your findings (I am not really sold on the science of baraminology), but it does make me ask - why didn't Cavanaugh, Wood and Wise notice these issues?

source: http://scholar.googl...t=0,23&as_vis=1

Cavanaugh, et. al. based their study on Robert L. Evander's character matrix in his "Phylogeny of the Equidae", also published in the same volume as Hulbert's analysis. I assume they did so because it includes all equids, not just Neogene ones. Many of Evander's characters are basic characters for horses in general, and many of Hulbert's characters are more specialized and inapplicable for non-grazing horses, so the two would not necessarily mesh. I wouldn't call my illustration discontinuities, but rather inconsistencies in the application of homology to determine phyletic relationship. As far as why other creationists haven't noticed what I'm illustrating, your guess is as good as mine. I must confess that I am more "schooled" in evolutionary cladistics than I am in Baraminolgy, although I am looking to rectify the latter.

3. Are you saying that is what the authors did in here? Do you have the original cladogram where they list the symapomorphies on the nodes that they used to characterize the clades? Did they not include some of the characters in their treatment?

No. In fact, it is because Hulbert did not engage in cherry picking that you see the abundant homoplasy pattern above. As I mentioned earlier, Hulbert did map all of the characters, although he didn't designate which characters were parallelisms (he did indicate reversals), and he missed adding a couple of placements.

4. I am confused by your usage of homology and homoplasy. From Wikipedia http://en.wikipedia....ology_(biology)

"A homologous trait may be homoplasious – that is, it has evolved independently, but from the same ancestral structure – plesiomorphic – that is, present in a common ancestor but secondarily lost in some of its descendants – or (syn)apomorphic – present in an ancestor and all of its descendants"

So, if the trait evolved from the same ancestral structure it is homologous. Why do you say that parallelism (homoplasy) is contradictory to homology?

Agreed that the number of expected homoplasious traits should be minimal and this cladogram has, what seem to be, a significant number.

Leave it to wikipedia to obfuscate a definition. I would suggest, if you haven't already, look at the merriam-webster definition of homoplasy I posted above. Or, better yet, let me illustrate with a hypothetical scenario. Let's call the normal condition of a human having three bones in their index finger (not including the metacarpal) the primitive (plesiomorphic) condition. Now let's say John Doe is born with an extra bone in his index finger, giving him four instead of three. He grows up, has two children, and both those children inherit that "derived" (apomorphic) condition of having four bones in the index finger. If you were to compare the two children with their unusual index fingers, you would be correct in assuming that they inherited that derived condition from the same father. That's homology. Now let's say we have another man, Joe Smith, who also happens to be born with four bones in his index finger. He grows up, has two children, and they inherit the "derived" (apomorphic) condition of four bones in the index finger from him. If you compare his two children, you would also be correct in attributing their "derived" condition to inheritance from a common ancestor, i.e. homology. However, if you compare one of John Doe's children to one of Joe Smith's children, you would be tempted to jump to the same conclusion, but you would be wrong, because that similar derived condition of four fingers in the index finger was independently acquired, and cannot be used to prove relationship by the assumption that the derived state was inherited from a common ancestor. That's homoplasy. It's contradictory because the basic assumption of any evolutionary phyletic arrangement is that you can use shared derived characters to prove relationship due to inheritance of that derived character from the common ancestor that acquired it. When that assumption only works part of the time as illustrated in my character map, it's time the assumption was called into question. I hope that helped to clear it up a little and didn't just muddy the water.

5. In determining your ratio of 2:3, why do you count each instance of parallelism but only the first instance of synapomorphy? For example: Trait # 39 is one instance of parallelism. (I am not sure how to treat trait # 4 since it occurred in several lineages). But if you number each instance of parallelism, then shouldn't you also number each instance of synapomorphy since a synapomorphy is present in an ancestor and in the descendants? As an example: trait # 27 is a synapomorphy at every node except the outlier group. Seems inconsistent. Can you justify this approach?

Keep in mind, I freely admit i may be arguing from ignorance. Maybe you can help me understand this better. I would also be interested in the dataset you have. I have no idea how to upload to this site. If you have access to a file sharing site, that should work.

Wow! You just multiplied the counting exponentially with what you are suggesting. As I mentioned in my OP, the count is of the number of instances where a character state would have to have changed. And that is a minimum. If you move them farther up the cladogram, that does increase the count. Yes, you could recount the synapomorphies at each node, or, more accurately, just between the end members (the actual taxa). However, you would also have to do the same for parallelisms and reversals. Take, for example, character 39 which you mentioned and which occurs at five different nodes. In Nannipus it is synapomorphic with regard to Cormohipparion. However, in Nannipus and Cormohipparion, it is parallel with regard to Neohipparion, Pseudhipparion, "M." coloradense, Calippus, Protohippus, Astrohippus, "Dinohippus", Equus, Onohippidium, and Hippidion. You could also do the same with the other nested groups and get similar results. Personally, I wouldn't even want to try to keep track of that count.
I'll have to see what I can do. With so many file sharing sites going down, I'm leery of joining any of them and free uploads usually don't last very long. Maybe I'll convert all the sheets to png's and link to an album on photobucket.

Do I understand this correctly; you are accepting that this cladogram is correct (or at least close) but are proposing a mechanism that explains the apparent inconsistencies (especially the parallelisms)?

Well, not really. As noted by Hulbert in the text for his figure 11.2, the cladogram he presents is just "one of five equally most parsimonious cladograms". In other words, there are four other ways to arrange it that have the same number of steps, parallelisms, reversals, etc. What I am saying is that we will never be able to accurately describe the pattern in nature by imposing a phyletic pattern on nature with it's concomitant assumption of acquired characters. The origin of those characters must go deeper than simple chance acquisition and inheritance.
I hope I have answered your questions adequately and thanks again for the input.

[Clice]

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[Bonedigger]

Hey I would recommand using SkyDrive for sharing office documents. I've been using it for years and it works great. You get 7 GB of free storage, and it very cheap to upgrade: http://windows.micro...S/skydrive/home

That was easy. Thanks for the tip. Here is a SKyDrive link to the Hulbert-89 pdf (http://sdrv.ms/S8MyY7). It can be downloaded from there. The pages of the pdf are bookmarked with the character number (e.g. CH-01 = character 1).

[herebedragons]

That was easy. Thanks for the tip. Here is a SKyDrive link to the Hulbert-89 pdf (http://sdrv.ms/S8MyY7). It can be downloaded from there. The pages of the pdf are bookmarked with the character number (e.g. CH-01 = character 1).

Thanks Bonedigger. I haven't had much time to work on this lately, but hopefully I will have a response later this week. I have looked at some updated phylogenies but I don't think they solve the problem, they just shift it around.

One of the major strengths that the ToE presumably has is in its predictive power, particularly in the ability to group organisms into a nested hierarchy. I think your work does challenge that predictive power. I'm not ready to draw a conclusion yet, but this is worth exploring deeper.

Good work. I have always said that if you want to challenge the ToE you have to first understand it and then use the same tools to take it apart.

HBD

[GoneAstray]

One of the most fundamental arguments for evolution is the argument from homology, where morphological similarity is used as proof of phyletic relationship due to inheritance from a common ancestor.

I think you've perhaps overstated this even though in essence it is correct. The way I understand it, IF there is a common ancestor, homologous structures can be found in their offspring. There are homologous structures and there is no other theory known of that can explain them.

Homoplasy is a flat contradiction to the principle of using morphological similarity to prove relationship, because you cannot attribute such similarity to inheritance, but rather it would have had to originate independently. In reality, it is nothing more than an ad hoc explanation as to why the principle of homology doesn't work in a particular instance.

I'm afraid this is just flat out wrong. Just so we are clear, in convergent evolution, species can share traits/organs. This is called homoplasy. Just to show you why the above is wrong you need to know a bit about convergent evolution. Here's an example, a comparison between Thylacine (Thylacinius cynocephalus) and Grey Wolf (Canis lupus) skulls.


Although the skulls look very similar, there are some distinct differences. If you look at the third picture in the large one, the left skull has openings (maxillary palatal vacuity), while the wolf does not. There are also ways to distinguish between their teeth. You can also see the comparison of the skulls here.

So, as the example shows it is possible to tell the difference between convergent evolution and close ancestry.

There is some great further reading you can do on the subject here

I'm now struggling to go any further because I don't have access to the book you use or Hulbert's analysis, plus that diagram isn't like anything I have seen before. But hopefully I've given enough to show you where you have gone wrong in your initial point.

[Bonedigger]

Well, for starters, I am well familiar with convergent evolution, and I am intimately familiar with the skulls and dentition of a thylacine as compared to a placental wolf (yes I did learn a few things in all those classes I took in paleontology, mammalogy, comparative vertebrate anatomy, etc.). In fact, I even posted pictures comparing BoneClones replicas of a thylacine and a red wolf from my own collection here (http://evolutionfair...indpost&p=85442).
In reading your post it becomes immediately apparent that my argument went completely over your head due to a misconception on your part. You obviously don't realize that the term homoplasy is used for more than just convergent evolution (widely disparate taxa converging on a similar morphology, like the thylacine and a placental wolf). The term homoplasy is also used for parallelism (closely related taxa independently acquiring the same characters), which, by no coincidence, is the main subject of my post--the ubiquitous occurrence of parallelism in mesodont/hypsodont horses. Lest you think that this usage is something I've come up with on my own, I'll give you examples from the first three articles I cite above in my OP and my response to herebedragons.
Hulbert 1989, p.189
"...many of the characters used in the study showed homoplasy. Even so, the inferred high degree of parallelism probably reflects the true evolutionary history of the group."
Hulbert and MacFadden 1991, p. 56.
"The exact phylogenetic relationships among these 12 merychippines remain to some extent poorly resolved. Reasons for the poor resolution include a high degree of homoplasy in the acquisition of certain character states,..."
Kelly 1995, p. 25.
"...it is well documented that many of the morphological character states of the late Neogene hypsodont horses are homoplasous; that is, they exhibit a high degree of parallelism, convergence, and reversal..."

The fact that you're presenting the thylacine and placental wolf as proof that it's easy to distinguish homoplasy from homology tells me you have no clue what I'm talking about, so let me illustrate. Here is a portion of a classic picture of horse evolution, the original for which can be found here (http://www.geolocati...lution.jpg/-/en).


Notice the monodactyl (one-toed) foot in both Pliohippus and Equus. Tell me, did they inherit that character from a common ancestor (homologous), or did they acquire it independently (homoplastic-the historically correct adjectival form of homoplasy)? And what do you base your conclusion on? According to all four cladistic analyses cited above, they acquired it independently and it tells you nothing about their relationship to each other.
Next time read and understand an argument before you post.

[drwho]

number of occurrences that contradict a method (44 parallelisms)

I don't understand why you say this is a contradiction. It's difficult to comment without knowing what the individual traits in question are, but if something is heavily advantageous, wouldn't you expect there to be a reasonable likelihood of it arising and propagating in two or more closely related species? Especially if is a trait that can develop easily due to any number of mutations?

My question for evolutionists is this: if the practice of using morphological similarity to prove phyletic relationship due to inheritance from a common ancestor performs so poorly

The "poor performance" claim, I don't believe has been substantiated yet. I could be wrong, but I assuming that this is based on your earlier assumption that the concept of parallel evolution contradicts evolution?

and is so equivocal in such a closely (and truly) related group like the Equinae, why should it carry any credibility when dealing with such widely disparate forms like a human, a bat, and a whale? The only way I can see to maintain such an argument is if you engage in extreme "cherry picking" in your selection of characters that "prove" relationship.

It would seem to me that the more reasonable hypothesis, at least with regard to the Equidae, is that all these characters are "subroutines" that were built into the equid genome from the start. And that allowed them to be mosaically expressed in different combinations as the horses spread out and diversified in the rapidly changing early post flood world. Of course, that presents an even bigger problem for an evolutionary origin of these characters. How do you select for and preserve a character that hasn't even been expressed yet?

Well, the idea is that if evolution is correct, then you should be able to arrange animals and groups into a "family tree" of sorts. If not, then there should be no identifiable pattern of inheritance, and traits should be more or less randomly dispersed amongst different groups. The fact that a tree like the one above is possible is consistent with evolutionary theory. While you can do this with morphological characteristics, sometimes there is some uncertainty within closely related groups regarding the precise branching pattern. But if you "zoom out" and look at the big picture, there is greater certainty regarding the divergence pattern of distantly related groups. That's basically the answer to your question regarding closely related vs distantly related groups.

Having said all this, morphological analysis can be difficult due to convergent evolution and the relatively few traits which are not necessarily always identical. For reasons such as these, when dealing with closely related species, there are sometimes a number of potential branching patterns that are theorized.

The unequivocal proof lies in the use of molecular genetics to derive phylogenetic trees. This offers billions of base pairs to analyze as opposed to a few dozen traits. As well, it offers complete objectivity.
You would hypothesize that if we are correct in our thinking, that a tree without any anomolies can be derived by comparing DNA sequences and that this tree should resemble those derived from analyzing morphological features. And that this should hold true whether you analyze the entire genome or any given gene. As it turns out, this is the case.

[MarkForbes]

I don't understand why you say this is a contradiction. It's difficult to comment without knowing what the individual traits in question are, but if something is heavily advantageous, wouldn't you expect there to be a reasonable likelihood of it arising and propagating in two or more closely related species? Especially if is a trait that can develop easily due to any number of mutations? The "poor performance" claim, I don't believe has been substantiated yet. I could be wrong, but I assuming that this is based on your earlier assumption that the concept of parallel evolution contradicts evolution?...

That's were the logical and empirical mistake comes in. Traits don't ARISE because they are advantageous, they PERSIST, because they are.
Even if taken as just a thought model, complex traits do not arise easily. There is just to much of a survivability gap in between to "evolve" from one sustainable life form to another.

[drwho]

Traits don't ARISE because they are advantageous, they PERSIST, because they are.

Indeed. You emphasize an important point.
Although, you ended the bold font change two words too early. This is why I said: "...arising and propagating" (as opposed to "arising and disappearing.")

Even if taken as just a thought model, complex traits do not arise easily. There is just to much of a survivability gap in between to "evolve" from one sustainable life form to another.

We don't know what the traits are; whether they are complex or not. If I'm not mistaken, one of these was a change from tridactyly to monodactyly, which isn't a complex change by any stretch.
And obviously, the traits in question here (such as monodactyly) are not hazardous to survival, as they are present in one or more species in the above figure.

Most importantly though, to reiterate and elaborate on what I stated earlier: similar characteristics can arise from a number of mutations. This is evidenced by the countless instances of novel mutations in humans that have given rise to the same morphological trait, congenital deformity or disease. Indeed, different naturally ocurring mutations in different species (i.e. humans and dogs) can also manifest themselves in the same way or in comparable ways.
Moreover, in instances in which two species share a nearly identical genome, mutations within a given gene are more likely to cause the same phenotypic change.

Keep in mind too, that the hypothesized branching patterns with respect to extant species are all corroborated through phylogenetics using molecular genetics. These illustrate the specific genetic mutations following the divergence of two species.

[Bonedigger]

Sorry for the delayed response, but I was out of town on vacation and only now have found the time to sit down and write an in-depth reply.

I don't understand why you say this is a contradiction.

Frankly, I don't understand why you don't realize that it is a contradiction. The whole basis on which such cladograms are built is the premise that morphological similarity can be used to determine phyletic relationship as the result of inheritance from a common ancestor that possessed said character. Characters that prove to require independent derivation (not inheritance) in different taxa in any such analysis contradict that first basic premise. In other words, it's a case of wanting to "have your cake and eat it too." Characters that "prove" to be attributable to inheritance are used as proof of evolutionary relationship, and characters that don't fit the presented evolutionary pattern are explained away with secondary ad hoc rationalizations like parallel evolution or reversals. The only basis on which you can claim that a character trait is the result of parallel evolution or reversal is the fact that it doesn't coincide with the currently accepted evolutionary scheme!! In other words, all such descriptions are nothing more than post hoc allocations, not pre-analysis predictions. If, while developing different phylogenies, one character that proves to be parallel in one phylogeny, then proves to be synapomorphic in another, no problem!! Evolution "'splains it all!!" It doesn't matter what the evidence itself presents, you've got a wealth of ad hoc secondary explanations to cover it.

Let me illustrate with an analogy. Suppose you were to flip a coin a hundred times. Your main starting premise is that you have a two-headed coin. Any results that are consistent with that premise (i.e. heads results) are gathered in and presented as proof of your premise. Any results that are not consistent with your premise (i.e. tails results) are dismissed and explained away as invalid regarding your first premise due to secondary factors (miscall, misflip, the wind blew it off, or whatever silly story you can invent as to why the results don't match your premise). If you were then to argue that you have a two-headed coin, you would be ridiculed out the door because of your "cherry-picking" methodology. Yet, that's exactly the methodology that cladograms like I illustrated above require you to employ in order to maintain evolutionary acquisition and inheritance as an explanation for homology. Characters that are consistent with the cladogram are used as proof of such evolutionary inheritance, but a relatively equal number of characters that are inconsistent with it are explained away.

It's difficult to comment without knowing what the individual traits in question are, but if something is heavily advantageous, wouldn't you expect there to be a reasonable likelihood of it arising and propagating in two or more closely related species? Especially if is a trait that can develop easily due to any number of mutations?

I think Mark Forbes addressed this part adequately but I will add my own response.

It's difficult to comment without knowing what the individual traits in question are,

That is a misrepresentation. I posted the pdf with full character descriptions and distributions here. If you don't understand the characters, or can't be bothered to, then admit it. Don't pretend like you're working in the dark. They are all well established characters, many of which have been used to diagnose equid genera and species for more than a hundred years.

but if something is heavily advantageous, wouldn't you expect there to be a reasonable likelihood of it arising and propagating in two or more closely related species? Especially if is a trait that can develop easily due to any number of mutations?

Careful, you're bordering on teleology !! Arguing that a trait is advantageous doesn't explain how it arises in the first place. No, I wouldn't expect it to arise in closely related species, because you have yet to demonstrate how an advantageous character can arise to begin with, much less multiple times, and many of the taxa in Hulbert's analysis that display homoplasy are not "closely related" species. Arguing that such a "trait can develop easily due to any number of mutations" just puts the burden of proof on you. Tell me, for example, how does a trait like a deeply pocketed dorsal preorbital fossa (character 4--not present in any extant taxa but scattered throughout the extinct taxa) "develop easily?" Is your assertion based on a knowledge of equid morphology and genetics, or just a blind faith in the omnipotent ability of evolution?

The "poor performance" claim, I don't believe has been substantiated yet. I could be wrong, but I assuming that this is based on your earlier assumption that the concept of parallel evolution contradicts evolution?

As I argued earlier, parallel evolution is contradictory to any phylogeny based on inheritance because it requires secondary ad hoc explanations that are not consistent with the premise on which such phylogenies are constructed.

Well, the idea is that if evolution is correct, then you should be able to arrange animals and groups into a "family tree" of sorts. If not, then there should be no identifiable pattern of inheritance, and traits should be more or less randomly dispersed amongst different groups.

This is nothing more than a classic straw man argument, with a false dichotomy where any perceived nested hierarchy (no matter how much data you have to ignore in the process) is supposed to be proof of evolution, while creation, on the other hand, supposedly predicts that the distribution of characters should be completely random (arbitrary), and have no discernable (functional) pattern. Woodmorappe and many others have amply demonstrated that created objects fit easily into nested hierarchies.

The fact that a tree like the one above is possible is consistent with evolutionary theory.

(The straw man is continued) On the contrary, the fact that a tree like the one above is possible is proof that, rather than being a logical deduction from the data, evolutionary trees are imposed on the data in "cookie-cutter" fashion, regardless of how well it fits with the actual data itself. And then, anything that doesn't coincide with that imposed evolutionary tree, like the blue and pink characters in the cladogram above, is explained away with secondary ad hoc rationalizations like parallel evolution and reversal.

While you can do this with morphological characteristics, sometimes there is some uncertainty within closely related groups regarding the precise branching pattern.

This just begs the question of evolution all together.

But if you "zoom out" and look at the big picture, there is greater certainty regarding the divergence pattern of distantly related groups. That's basically the answer to your question regarding closely related vs distantly related groups.

The greater certainty that you refer to comes from the fact that as you "zoom out", the characters used become more and more abstract, more distant from the actual taxa, and therefore less likely to be contradicted by the nitty gritty details that actually make up a taxon. Or, in other words, the characters used become more and more "cherry-picked."

But, just for kicks, let's zoom out a level and include the browsing horses and see where that gets us. Characters 3 through 9 are all related to the presence and degree of development of the dorsal preorbital fossa (DPOF). My current avatar is a tracing of Pliohippus pernix. The dark cavity in front of the orbit (eye socket) is a deep DPOF. Hulbert, et. al. used "Parahippus" leonensis as the outgroup because, dentally, it represents an ideal intermediate between the browsing and grazing horses (relatively low crowned cheek teeth but with thin cement present on the permanent teeth, a well developed crochet, etc.). However, it has an incipient to nonexistent DPOF. This polarizes the DPOF as a derived character within the grazing horses. However, numerous browsing horses possess a well developed, deep DPOF (e.g. Megahippus and here). On this taxanomic level then, that makes the presence of a DPOF in both grazing and browsing horses...you guessed it...homoplastic. Zooming out just increases the homoplasy, rather than eliminating it, as long as you're not just looking at selected characters.

Having said all this, morphological analysis can be difficult due to convergent evolution and the relatively few traits which are not necessarily always identical. For reasons such as these, when dealing with closely related species, there are sometimes a number of potential branching patterns that are theorized.

The unequivocal proof lies in the use of molecular genetics to derive phylogenetic trees. This offers billions of base pairs to analyze as opposed to a few dozen traits. As well, it offers complete objectivity.
You would hypothesize that if we are correct in our thinking, that a tree without any anomolies can be derived by comparing DNA sequences and that this tree should resemble those derived from analyzing morphological features. And that this should hold true whether you analyze the entire genome or any given gene. As it turns out, this is the case.

Tell me, what are the base pair sequences for, for example, Pliohippus mirabilis, which possesses a nasal notch dorsal to P2; a deep dorsal preorbital fossa; a posteriorly pocketed DPOF; a broad preorbital bar; a malar fossa; an early connection of the protocone with the hypocone; a hypoconal groove that closes rapidly; tridactyl podials; etc. etc., all of which are characters not possessed by any extant equid. While it is true that phenotype (what you can observe in fossil forms) is a product of genotype (what you can't observe in fossil forms), this is just the classic evolutionist dodge where the "real" evidence is somewhere else in some other discipline. I daresay that if the subject of this thread was equid genetics rather than equid fossils, you would be appealing to the fossil record as offering the "unequivocal" proof regarding horse evolution.