Megalodon size

[elosha11]

^Also that bass is not nearly twice the gator's size, in fact it's probably a little smaller/lighter than the gator. A bass twice the size of a small gator would be more of a threat to the gator than vice versa. Probably couldn't kill the gator, but could drive it off and perhaps injure it. Also would like context of the pic, is the gator actually preying on the gator or trying to drive it off? If it just sneaked up and grabbed the fish's tail, we don't really know what would have happened next. It's still an interesting picture, but I don't really know how we can make a good analogy from such drastically different sized animals.

[Grey]

Jul 14, 2016 23:21:03 GMT 5 coherentsheaf said:

Hm the pliosaurs can take pachycormid twice its size claim... Really? How would they kill it efficiently? Crocs sometimes manage to kill similar sized animals (mostly by drowning) but it is quite some effort for them. I dont think that pliosaurs with the kind of jaws present in the largest species so far would easily prey on giant pachycormids.

McHenry said me that but I wonder if he wasn't contradicting what he said in his thesis.

Don't we have a metriorhynchid tooth embedded in a piece of Leedsichthys? I suppose that Simolestes, Liopleurodon, or the bigger metriorhynchids would all have been capable.I would have thought a big pliosaur could handle something twice its own size. Crocs can, and the skull construction ain't that different

[coherentsheaf]

Well I dont doubt that they would have been capable to do so on occasion, but not consistently with little risk, which you wanna do. Megalodon surely would be effective at attacking <10m whales with little risk.

[theropod]

So here’s the thing, following a recent discussion I wanted to replicate the jaw-perimeter-based regression used by Kent on P. benedenii, using the data from Mollet et al. 1996.

He apparently did so by first plotting jaw perimeter to the y-axis and total length to the x-axis and fitting a model to this, at least the figure in the paper looks somewhat like this:

read.table(file="gwdata.csv", header=T)->gwmorph
lm(gwmorph$UJP~gwmorph$TL)


plot(gwmorph$UJP~gwmorph$TL, col="blue", pch=8, ylab="Upper Jaw perimeter (mm)", xlab="Total length (mm)", xlim=c(0,8000), ylim=c(0,1800))
curve(41.7793+0.1949*x, col="grey", add=T)
text(3000, 1500, expression(y == 41.779+0.195*x), col="grey")

I get a very similar result to him by inversing the regression:
y=41.7793+0.1949*x
(y-41.7793)/0.1949=x
-214.363+5.131*y=x


plot(gwmorph$TL~gwmorph$UJP, col="blue", pch=8, xlab="Upper Jaw perimeter (mm)", ylab="Total length (mm)", ylim=c(0,8000), xlim=c(0,1800))
curve(-214.363+5.131*x, col="grey", add=T)> abline(v=1533)
text(600, 7000, expression(y == -214.363+5.131*x), col="grey")
abline(v=1533, col="grey")
text(1700, 7651.46, "7651mm TL", col="grey")

However, the result is different when I directly fit the model this way around, with Jaw perimeter as the independent variable:




lm(gwmorph$TL~gwmorph$UJP)
curve(390.481+4.466*x, col="black", add=T)
text(600, 6500, expression(y == 390.481+4.466*x), col="black")
text(1700, 7236.859, "7237mm TL")

So the question, why is there a difference (that’s not immediately clear to me), why was it done like that in the paper and is there a reason to do it, which one is, consequently, the proper method to use (or should I take the mean between both lines?), what implication does this have for other cases where the same is done, and what is the "actual" correlation between these variables (I would have thought that from the actual relationship of jaw size to body size, one should be able to unequivocally calculate the relationship of body size to jaw size by inversing the function). 
Does it have to do with least squares only measuring the distance on the y-axis? If so, that still leaves open the other questions. I’ve already asked other people, including a math student, but without success. I’m hoping coherentsheaf might be able to explain it to me.


For replication, here is my dataset, taken from the appendix in Mollet et al. 1996:

TL UJP
1975 385
1975 410
2195 433
2420 487
2560 547
2675 533
2715 530
2795 570
3140 618
3310 685
3710 785
3790 790
4075 815
4572 1120
4712 1230
4788 805
4825 978
4885 938
5110 985
5300 1022
5360 1104
5368 1160
5370 1055
5474 1200
5486 980
5537 1120
5537 1265
5633 1270
5740 1128
5944 1300
6096 1430
7010 1120
7010 1250

Attachments:

[coherentsheaf]

Reversing the regression is suboptimal, the direct regression should explain more variance and is preferable. You are correct in saying that OLS minizes distances on the y axis alone, but this is whgat you want for a predictive model: The deviation for the estimated value (y) should be minimal.

[theropod]

So if I’m only given an equation for predicting x from y, what if I want to predict y from x?, and why would a study (e.g. Kent 1999, Lowry et al. 2009) do it that way around?

[coherentsheaf]

So if I’m only given an equation for predicting x from y, what if I want to predict y from x?

A priori you cant (afaik). However if you know the standard deviations or the amount of variance explained you can simply use the fact that the slope is equal to s_y/s_x*r where r² is the explained variance and the slope in the other direction is s_x/s_y*r. To find the constant you just use the fact that in standardized terms x-mean(x)=s_x/s_y*r (y- mean(y)) if you know the means.

and why would a study (e.g. Kent 1999, Lowry et al. 2009) do it that way around?

I dont know.

[Grey]

More to come for soon.

UJP is measurable in GWS but not in Megalodon.

Summed tooth width is measurable in both.

For practical purpose, I favor the later. There are too much of not hard data to assume for the former. I m curious to know if the new work will give similar results. From my prior tests it doesn't seem so.


A suggestion, maybe the larger sharks in the scatterplot were reported with actually inaccurate body length measurements, which would make the regression somewhat erroneous?

[theropod]

^Was this a suggestion regarding the question I asked or something unrelated? I don’t see what it would have to do with the subject.
Otherwise, is there any reason to presume the regression is "erraneous" in the first place, leading you to seek for reasons why it would be?
Of course we could question the validity of any great white shark measurement (including the ones of the specimens you work with), the idea is that if you’ve got enough of them the errors should even out. However I agree that some of these could be questionable (specifically the two largest specimens should be excluded, considering they are the questionable specimen the paper was all about checking, and obviously weren’t included by Mollet et al. either), my attempt was merely to replicate Kent’s regression (and he appears to have used all of them) not to imply anything about the validity of the specimens.

Coming to that now though; except for the possibility faulty measurements in this sample, which is always a possibility, including other, comparable datasets, what reasons are there to presume the regression is erraneous, let alone, as you suggested, that it is significantly biased to produce underestimates?

In case you just don’t trust the equation for some reason, use mean jaw perimeter and mean total length for scaling and you get 6.8m for Parotodus (but 7.5m with the two dubious specimens included). That’s also lower than Kent’s figure, all the more so with the most obvious questionable specimens omitted, so where is the implication that the latter is an underestimate?

Summed tooth width is nice, but is nowhere near as frequently measured or reported for great white sharks. As you expressed to me, you doubt the validity of these methods. You might have a point with Lowry et al. 2009, based on what was discussed above. However, if anything, it would appear to give results that are too high if the data on jaw perimeter are anything to go by, and at least that’s based on a sample of 31 (33 if you consider "Kanga" and "Malta"), from a published work.

coherentsheaf: Where would that leave me if I, say, wanted to calculate jaw perimeters for given total lengths that are consistent with length estimates based on given jaw perimeters?
Or a different question, though not directly shark-related, you can do the same with the sperm whale dataset from Lambert et al. and depending on what is chosen as an independent variable (I think it was lenght) there ends up being either a slight positive, or a slight negative allometry of skull length with regard to total length. How do I find out which is actually the case? It can hardly be both at the same time, just as an animal can hardly have a different expected jaw size for its total length than the one used to calculate that total length in the first place…

[theropod]

In any case, the two 7m specimens omitted, the difference between total length~jaw perimeter and the inverse of jaw perimeter~total length ends up being a single millimetre.

[elosha11]

Theropod,

I have had earlier communications with Henry Mollet, and he was usually very quick to respond. Of course, my questions were with regard to certain specimen sharks on his website, elasmomollet, and were not as complex as yours. But I can put you in contact with him if you want to pose any questions to him. It sounds like you may have more questions for Kent's study than for Mollet's underlying data, but if you think it helpful, Mollet may be willing to communicate with you. I believe he found both the Malta and Kanga shark length estimates to be plausible and supported somewhat by the physical remains and photographs. I'm sure you've already read his paper on that inquiry, but he might be able to provide more detail in one on one communications.

Also, I know Grey has communicated regularly with Kent, and perhaps could refer you to Kent. Perhaps Kent would be willing to discuss the results you found when using the jaw perimeter as an independent variable.

[theropod]

I’ve already had contact with both Kent and Mollet years ago, but thanks. There aren’t really any unclarities about the dataset though. Yes, I know the paper and I know they didn’t rule out the measurements being accurate completely, since their measurements still (narrowly) fell within the 95% confidence band (except for the jaw perimeter of Malta, i.e. 97.5% of 7m sharks would be expected to have a bigger jaw perimeter than it), but it was borderline (check figure 1).
That only means, as they put it, that these specimens "could" be 7m TL, not the same as saying they were (only that they could theiretically be with a fair bit of variation accounted for) or how good the measurements actually are. Grey proposed that some of the measurements in the dataset may be questionable, and considering that there were whole papers on the matter these two certainly qualify.

Especially in terms of jaw perimeter (as you’ll notice the jaw perimeters of those supposed 7m individuals are closer to those of other individuals measured at ~5.5m).

[Grey]

Jul 19, 2016 18:58:04 GMT 5 theropod said:

^Was this a suggestion regarding the question I asked or something unrelated? I don’t see what it would have to do with the subject.

The suggestion is regarding the subject of the thread, the subject of the thread is not your question, I've not quoted your question while posting. I'm not enoughly educated in these maths to discuss this.

Jul 19, 2016 18:58:04 GMT 5 theropod said:

Otherwise, is there any reason to presume the regression is "erraneous" in the first place, leading you to seek for reasons why it would be?
Of course we could question the validity of any great white shark measurement (including the ones of the specimens you work with), the idea is that if you’ve got enough of them the errors should even out. However I agree that some of these could be questionable (specifically the two largest specimens should be excluded, considering they are the questionable specimen the paper was all about checking, and obviously weren’t included by Mollet et al. either), my attempt was merely to replicate Kent’s regression (and he appears to have used all of them) not to imply anything about the validity of the specimens.

Coming to that now though; except for the possibility faulty measurements in this sample, which is always a possibility, including other, comparable datasets, what reasons are there to presume the regression is erraneous, let alone, as you suggested, that it is significantly biased to produce underestimates?

In case you just don’t trust the equation for some reason, use mean jaw perimeter and mean total length for scaling and you get 6.8m for Parotodus (but 7.5m with the two dubious specimens included). That’s also lower than Kent’s figure, all the more so with the most obvious questionable specimens omitted, so where is the implication that the latter is an underestimate?

You might have a point with Lowry et al. 2009, based on what was discussed above. However, if anything, it would appear to give results that are too high if the data on jaw perimeter are anything to go by, and at least that’s based on a sample of 31 (33 if you consider "Kanga" and "Malta"), from a published work.

It appears that the larger specimens are usually harder to accurately measure, perhaps some more of them were mismeasured, which could induce some issues on the regression. That's more a question than a suggestion.

Regarding the initial data regarding summed CW, I don't say it is correct yet but it is true the relative constancy of the results, even over large scaling, and the fact they are sensibly larger is intriguing enough.


But who knows, maybe additional sample will clear all that and make the final results nearer to those you can extract from Kent.

Summed tooth width is nice, but is nowhere near as frequently measured or reported for great white sharks.

It is as we talk.

As you expressed to me, you doubt the validity of these methods.

I don't doubt their validity yet but the discrepancy can make them questionable. I concur that a whole new method directly made for the Carcharocles genus is of greater interest to me as of now.

[theropod]

Well, obviously you’ve responded to my post, so the question is justify, a simple yes or no would have been fine…

It appears that the larger specimens are usually harder to accurately measure

Presumably correct, that doesn’t mean every specimen below 5m is beyond doubt and every specimen above can be dismissed arbitrarily. The point stands that shark measurements are somewhat prone to being reported correctly and there’s often no way to know when they are, and in every case were we base our observations on measurements reported from the literature there is this possibility. That’s important to be kept in mind, but I think we are already all aware of it.
Also smaller sharks are even further from the relevant size range, so in exchange for possibly better measurements you get even poorer predictive value if you limit your observations to small sharks. For the same reason we’re not using porbeagle sharks.

Regarding the initial data regarding summed CW, I don't say it is correct yet but it is true the relative constancy of the results, even over large scaling, and the fact they are sensibly larger is intriguing enough.

I think you’re misunderstanding me, there’s no point in defending your work if there’s nobody actually attacking it.

It is as we talk.

Well it wasn’t available for previous researchers without access to a major collection of shark specimens to measure, so no point in criticising their choice of alternatives every time they are brought up.

I don't doubt their validity yet but the discrepancy can make them questionable.

You basically just wrote that you don’t doubt their validity yet, but you doubt their validity.
A discrepancy between two results makes both of them questionable by default. If there really is a discrepancy, which should first of all be verified properly (e.g. by making an estimate for the same Parotodus specimen based on its crown widths).

I concur that a whole new method directly made for the Carcharocles genus is of greater interest to me as of now.

A method that has the same relation to Carcharocles in all other respects doesn’t become of greater interest for Carcharocles just because someone calls it a method "made for Carcharocles". Your data and approach are very interesting, they just don’t automatically mean there has to be some error in everything else.

[Grey]

I don't imply there is some error in everything else and certainly my method is at work and I don't have the best tools in my hands, nor the material to argue anything about it. At the same time, questioning estimates from Kent is legit as well if initial CW measurements don't correlate with his figure. Although I'd be less reluctant to do this with a comparable sample. but that's not criticism, I don't need to recall I respect Kent's works. I don't defend my work either, I present it.

What I mean by 'greater interest' is a method directly taken from Carcharocles direct measurements, not assuming virtual data such as tooth free space, spacing..., and compare it with a sample of related sharks (including makos actually).

I would advise to not take Parotodus summed CW only since the root is substantially larger in this species, like in makos and contrary to GWS. Taking only the CW would result in most likely overestimates. And the estimate I got from one mako dentition on elasmo for the Yorktown meg dentition was already large enough (about 20m) though still near to the larger GWS based estimates.