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Post by Grey on Jun 12, 2015 20:57:23 GMT 5
Really I still think assuming Livy's holotype to be representative of the average size of its species to be too much arbitrary to really represent anything.
Or basically we assume that Livy got larger on average than both meg and the male sperm whale on average but meg and the sperm whale got a larger maximum size based on the current data.
But I keep thinking that without being an particularly large individual, the holotype is unlikely to represent an average, medium sized individual of its species.
I'm in contact with Chilean researchers, they do have casts and pictures of previously collected Livy's teeth from Chile formations and they're just similar in size to those in the holotype with some being noticeably smaller despite similar in shape to the larger ones in the holotype.
Not that being a mean average individual it's implausible at all but systematically assuming this is far less rigorous than the comparative data for meg and the modern sperm whale.
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Post by theropod on Jun 13, 2015 13:39:52 GMT 5
There are currently no data on Livyatan’s maximum size. We have no alternatives as I see it. Future findings will help (at least with establishing a more reliable average figure), but they have a certain inherent problem that makes them very hard to consider…
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Post by Grey on Jun 13, 2015 14:21:29 GMT 5
We have no data regarding mean average either.
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Post by theropod on Jun 13, 2015 17:27:23 GMT 5
What data we have are still more likely to correspond to average than to maximum or minimum. As you would put it, we have to go with the least bad option. What else could we do?
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Post by Grey on Jun 14, 2015 13:20:35 GMT 5
In the absence of any data about intraspecific variation or any evidence for larger individuals individuals yet, I dont think it is justifiable to say the holotype is a mean average individual. It could as well correspond to a 16-17 m bull sperm whale individual.
But the comparison by blaze still is valuable to use.
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Post by theropod on Jun 14, 2015 13:55:56 GMT 5
In the absence of any data about intraspecific variation or any evidence for larger individuals individuals yet, I dont think it is justifiable to say the holotype is a mean average individual. It could as well correspond to a 16-17 m bull sperm whale individual. But the comparison by blaze still is valuable to use. But you think corresponding to a very small part of the population is justifyable without any data supporting it? That is not at all more justifyable than that it was a female, for example, even if you assume it must have lived out its whole life (which as I remarked, other top-predators, even those without competitors, such as Tyrannosaurus, don't tend to do).
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Post by Grey on Jun 14, 2015 14:13:24 GMT 5
I can roll with comparing Livyatan either with a 10 m meg or with a 18 m one at this point.
I suspect Livy to have been most likely a full grown individual for the reasons mentionned earlier so I just have a real problem with the assumption that the holotype corresponds necessarily with the average sized adult meg. Again not saying it's wrong but I see no reason to conclude at this because the next step after this is too speculate the maximum size of Livyatan based on Physeter average. I wont try to theorize a 20-21 m Livy if one assume that a 14-16 m individual is an average not full grown individual.
I dont think I ll change my mind on this.
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Post by theropod on Jun 15, 2015 14:39:03 GMT 5
Well, speculating on maximum size is not what I'm asking you to do. We should just not be afraid to say that we simply do not know it.
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Post by Grey on Jun 15, 2015 16:04:34 GMT 5
Indeed, but I stay on the opinion that saying the holotype represents an average, not fully grown individual is not the most likely option, albeit not impossible either. The describers of the specimen say it is comparable to the modern sperm whale in size. Using the assumption it is an average sized individual would imply it is likely quite larger than the average modern sperm whale, which is very conflicting with the other assumptions. All what we can say is that it's a really big physeteroid which likely grew somewhere between 14 and a bit more than 17.5m.
But again I certainly can roll with this comparison, just like the others.
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Post by theropod on Jun 16, 2015 1:13:24 GMT 5
They likely mostly compared it to males. The Livyatan holotype is comparable to the large males in their dataset.
If you don't think you'll change your opinion I won't try to dissuade you. This is simply what I am going to assume for now. Maybe future data will prove me wrong one or the other way, maybe this assumption will turn out to be right or close to it. Either way, in the absence of better data I'm sticking to the mean.
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Post by Grey on Jun 16, 2015 2:53:43 GMT 5
Of course they compared it to the males, I guess they are more representative of the size we usually have in mind for the sperm whales.
Maybe if you want you could determine the average size for sexually adult males in Physeter so that you verify if the holotype is bigger. But I really think premature to say the species in on average larger than the modern sperm whale and in the absence of data for premature death, I see it as a full grown adult.
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Post by coherentsheaf on Jun 16, 2015 3:04:55 GMT 5
theropodIf you find a single individual that is comparable in size to a large male sperm whale, in general the best bet is that the average size is lower. The reason for this is that the probability distribution of mean size of a unknown species is decreasing with large sizes. A given individual I has the following relationship with the average size M P(M=y|I=x)=P(I=x|M=y)*P(M=y)/P(I=x) TRhis relationship is known as bayes theorem (I am being somewhat simplisitc here, the actual probability calculus would be somewhat more complicated) The expression P(A|B) means Probability of A given B happened. So what does it tell us? The a priori probabilities P(M=y) and P(I=x) decrese with x and y. We assume x to be a constant, namely the measured size of Lyviatan. This means P(I=x) is constant. P(M=y) decreases the larger you get. I will further assume that the distribution in size is peaked around its mean and symmetric. This means P(I=x|M=y) increases until M=x and then decreases. We try to find for what values of y the expression is maximal. Differenting in y gives something like P(I=x|M=y)'*P(M=y)/P(I=x)+ P(I=x|M=y)*P(M=y)'/P(I=x). For all y>=x the first term is smaller equal 0 and the second term smaller than zero. This implies they cannot be maximum, which further implies that the highest probability for the mean is attained at some lower value for y.
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Post by theropod on Jun 16, 2015 3:32:25 GMT 5
Grey: I'm also fine with assuming it to be equivalent in size to the modern sperm whale and megalodon for now, given the variables. I'm not agreed to try and use such speculations to establish the largest known predator, anyway. coherentsheaf:I got lost somewhere in the last part. What can't be a maximum? And am I getting the meaning og the bars right as conditional probability? Isn't it basically its absolute size and the resulting rarity of animals even bigger than it that implies the likelyhood of any given average size to be smaller than an animal as huge as Livyatan?
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Post by coherentsheaf on Jun 16, 2015 15:22:38 GMT 5
Grey: I'm also fine with assuming it to be equivalent in size to the modern sperm whale and megalodon for now, given the variables. I'm not agreed to try and use such speculations to establish the largest known predator, anyway. coherentsheaf:I got lost somewhere in the last part. What can't be a maximum? And am I getting the meaning og the bars right as conditional probability? Isn't it basically its absolute size and the resulting rarity of animals even bigger than it that implies the likelyhood of any given average size to be smaller than an animal as huge as Livyatan? Values where y is larger than x. "Isn't it basically its absolute size and the resulting rarity of animals even bigger than it that implies the likelyhood of any given average size to be smaller than an animal as huge as Livyatan?" You are right this is kind of the stattement, but in all generality you can plausibly find counterexamples, so I just used peaked symetric distributions, which is enough for our intuition (symmetry because we do not know either way in which direction the thing is skewed a priori).
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Post by theropod on Jun 16, 2015 21:11:12 GMT 5
Hmm, in a symmetric distribution of describing a population, isn’t the mean right in the middle, the value at which the probability function has its maximum? Doesn’t that make it equally likely that the mean is lower and that it is higher than the size of any given individual? I mean that I understand the reasoning from absolute size, I just don't spot where it figures into the distribution.
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