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Post by theropod on Jun 5, 2015 11:59:50 GMT 5
Exactly, finally a paper that didn't just search out the biggest tooth they could find and then produced one single estimate.
Therefore this gives us some data about the whole of C.megalodon's population, and very importantly as well, throughout a long time span.
I think there are better estimation methods available for single specimens, but systematic biases depending on tooth position will tend to cancel each other out in such a large sample.
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Post by Grey on Jun 5, 2015 12:35:24 GMT 5
Yeah, I still tend to think the best theoretical method is based on jaws circumference, sadly it has not been used for C. megalodon in peer review works yet. Siverson usually says the largest individuals yeilded by this method are in the 18-20m range, so maybe the difference with maximum size in this study (about 18m) isn't that great even if the two methods generally won't yieild absolutely similar results for the same specimen. And yes, Pimiento and Balk did not focuse on maximum size.
Regardless, I think 18m TL is now almost definitely a reasonnable figure for this species, with a body mass in the 50-70 metric tons range.
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Post by theropod on Jun 5, 2015 13:04:18 GMT 5
I think we can all agree that, within the degree of uncertainty inherent to estimating any animal's size solely from teeth (regardless of these, I would always support using the most likely figure, even though quantifying the error bars would be a good idea), some of the known specimens reaching 18m is probable. I also think such specimens could have been present in their data set, after all some come very close and Shimada's method is likely to produce underestimates for some tooth positions.
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Post by Grey on Jun 7, 2015 1:19:52 GMT 5
A question, in this body-size distribution, I remark that the curve is reaching the 1.3 Log Body Size each time. 10^1.3 corresponds to 19.9m TL. Am I right it is reaching it but has not been counted because being outlier or am misreading something ?  |
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Post by theropod on Jun 7, 2015 1:40:22 GMT 5
The sampled specimens ranged from 2.2 to 17.9m. There is no reason the authors would exclude such individuals if they had them in their sample, they stated themselves that they didn’t exclude any size range. There is even less reason for them to exclude them from everything except one figure. The frequency of body sizes is presented in discrete steps here, representing intervals (10^0.4-10^0.5, 10^0.5-10^0.6…and so forth…10^1.2-10^1.3), each bar shows the number of individuals within a certain size range, not at any precise size. The largest size interval isn’t composed of individuals that were 10^1.3m long, it’s composed of individuals that were between 10^1.2 and 10^1.3m long, and since we know the largest individuals were 17.9m, more precisely between 10^1.2 and 10^1.253. Those density curves do not mean every specific size was present in the sample (otherwise there would have to be an infinite number of specimens, which is precisely what the curve approximates, which is also why it extends beyond the data range), those are just probability functions fitted to the data. In fact, the likelihood of finding any one precise value is always zero, the likelyhood of a specific size range is given by the integral of the function in that interval. The probability of such an interval of the same width gradually declines towards the tails, but in a normal distribution never reaches it 0 (although for all practical purposes, it does). coherentsheaf can give you a more accurate and concise explanation than that, but I think the principle should be clear. |
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Post by Grey on Jun 7, 2015 2:16:23 GMT 5
In short, individuals at 10^1.3m long are not reflected by any direct data but are theoretically existing according to the curve, right ?
What misleads me is that the curve reaching 1.3 is still representing individuals precisely between 0 and 10 individuals, which seemed to indicate it is based on direct material. The fact they say they didn't intend to focuse on maximum size let me think they didn't account sizes topping 1.3 I would have more envisionned the curve ending at around 1.25 in the table.
Remark also that the line englobing from 0.4 to 1.2 seems to willingly exclude the range between 1.2 and 1.3. I guess that's nothing but a bit misleading.
But in other words, does this distribution curve can be considered a way to reasonnably predict the maximum size of C. megalodon ?
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Post by theropod on Jun 7, 2015 3:32:31 GMT 5
As the curve never reaches zero (it never actually ends), "theoretically" even individuals at 10^2m would exist, if the population is only large enough. In an infinitely large population, everything is possible. But their probability is so incredibly low that they are non-existing for all practical purposes, because real populations aren’t infinite and a non-zero probability doesn’t automatically mean that something exists. I’ll leave you to figure out the probability of specimens at 10^1.3m or more. It’s low, low enough to not be represented in a dataset of over 500, but obviously there are some specimens in the world that could potentially be this big (we are talking about probabilities in the order of small fractions of a percent tough). It is misleading because isn’t. The curve and the bars are two different things. As I explained, the bar refers to all specimens above 10^1.2m (and below 10^1.3m) in length (even if the largest sampled specimens in this interval are actually only 17.9m long), not specimens that actually reach 10^1.3m (such specimens are not known). It’s about all the specimens in that interval, just because that interval is represented by a handful of specimens that doesn’t mean the upper end of the interval is too (this is purely a theoretical consideration of course, in this case we already know for sure that no specimen in the sample was bigger than 10^1.253, so the probability of specimens that are bigger is less than 0.2%. If you make categories for a range of data, each spanning the same interval, inevitably the upper and lower bound of the categories are not precisely (at best approximately, but obviously not necessarily even that, depending on how wide the intervals are) reached by the actual specimens in the sample. The fact that they also say they didn’t exclude any size though makes me think that they didn’t arbitrarily exclude any specimens just for their size. That would definitely defy the purpose of the study.  Since the equation isn’t given, no, it can’t. Even if it were though, you’d have to make up a probability in order to define maximum size (I.e. how exceptional the specimen you consider "maximum-size" is). |
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Post by Grey on Jun 7, 2015 3:51:54 GMT 5
Hmm to me the curves ends at zero in all distributions outside of 1.3 except for the Middle Miocene one. But I get what you mean.
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Post by coherentsheaf on Jun 7, 2015 3:59:28 GMT 5
Very well explained theropod, I guess the zentralmatura was not particularly hard for you  |
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Post by theropod on Jun 7, 2015 4:14:30 GMT 5
Very well explained theropod, I guess the zentralmatura was not particularly hard for you It was ok  , I got a B, but without having studied a lot or slept a lot the night before... Grey: It looks that way because it is already very close to 0, i.e. the probability of sizes in this region is very low (not surprising of course). |
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Post by creature386 on Jun 7, 2015 13:46:37 GMT 5
As the curve never reaches zero (it never actually ends), "theoretically" even individuals at 10^2m would exist, if the population is only large enough. In an infinitely large population, everything is posssible. But their probability is so incredibly low that they are non-existing for all practical purposes. Are you sure? I mean, it is not just about probability, it is also about the possibility of such an animal to exist in the first place. Even when assuming infinite food, the anatomy of a Megalodon also has its limits. It is questionable if it could even swim at such a size. |
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Post by theropod on Jun 7, 2015 15:38:13 GMT 5
That’s why I wrote "non-existing for all practical purposes", as in "walking straight through a solid wall-improbable". In real life, such an animal certainly never existed (and in real life, you certainly can’t walk straight through solid walls), but in a theoretical, infinite sample, it could (and so could you). Hence why the mere extent of the upper tail of a distribution curve doesn’t give us the animal’s maximum size, it gives us the relative probabilities of individuals of these sizes (in this case for example, the highest probability is for sizes slightly above 10m, but the probabilities decline more steeply for higher sizes than for smaller ones) and whether they can be assumed to exist depends on the size of the sample.
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Post by Grey on Jun 7, 2015 16:31:22 GMT 5
Of course I have not interest into the absurd infinitely small size of 10^2 (hello Megashark) but the curve exceeding the 10^1.3 and still corresponding to few specimens just made me wonder if it was suggesting (rather than indicating) individuals at ~20m TL.
But I'm not wishing it, I was suspecting the actual largest specimens in the sample were going to be ~18m, which is reasonnable (and still hard to envision).
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Post by coherentsheaf on Jun 7, 2015 18:06:24 GMT 5
Of course I have not interest into the absurd infinitely small size of 10^2 (hello Megashark) but the curve exceeding the 10^1.3 and still corresponding to few specimens just made me wonder if it was suggesting (rather than indicating) individuals at ~20m TL. But I'm not wishing it, I was suspecting the actual largest specimens in the sample were going to be ~18m, which is reasonnable (and still hard to envision). The curve does suggest that there is a not completely low probability for there being larger individuals than those in the sample. What is usually done to get such estimates for the probability density is to take a small distance around the value you want to calculate and then make out the average of the specimens in this small area (sometimes a little more complicated the contributions will be multiplied with a function that decreases as the distance increases). So when you see a distribution like the one above, it means that there were relatively many individuals at the top end, which indicates that it was not that extremely unusual to have been that large which further indicates that there could be even larger individuals. |
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Post by Grey on Jun 7, 2015 18:16:25 GMT 5
And basically, one of the purpose of the studies indicate that if we were cruising on Mio-Pliocene oceans, most of the time we'd to cross the path of 10-12 m megs.
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, I got a B, but without having studied a lot or slept a lot the night before...
