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Post by coherentsheaf on May 3, 2013 2:03:28 GMT 5
Here is the regression analysis I did back then (I removed some typos and unnecessary statements) Some time ago, theropod noted large variance in the sperm whale measurements used to construct the regression equation that in turn was used to estimate livyatan body length. In this post I will try to quantify the consequences of this variance. At first I fitted the same linear model that the authors of the paper did. Here are the corresponding qq - plot and tukey anscombe plot: qq -plot  This indicates that the errors are normally distributed. Tukey Anscombe plot  This indicates that there is constant variance and the expected value of the errors is 0. Since the the errors are uncorrelated, this means we can statistically analyze the regression equation beyond just giving a point prediction. We can now predict in what range of measurements Livyatan falls with what probability (under the assumption that it is similar to a sperm whale). The results are: Livyatan falls into the range range of 1141 cm to 1557cm with a probability of 95%. Livyatan falls into the range range of 1219cm to 1479cm with a probability of 80%. However further inspection of the data tells us that one of the points has a very large cooks distance:  I decided to redo the analysis without this data point as well. The results were: The point estimate of Livyatan becomes: 1416 cm The 95% prediction interval is: 1254 -1577 cm The 80% prediction interval is: 1315 -1516 cm So excluding one unusual data point gives us larger estimates for Livyatan. As always here is my R-code:
livyatan <- read.table("livyatan.txt", header=TRUE)
attach (livyatan)
fit <- lm(BL.CBL ~BZW)
plot(fit)
summary(fit)
livyatan.BZW = dataframe (BZW=197)
predict(fit, livyatan.BZW, interval="predict", level=0.95)+294
predict(fit, livyatan.BZW, interval="predict", level=0.8)+294
predict(fit, livyatan.BZW, interval="predict", level=0.4)+294
fit2 <- lm(BL.CBL[-2]~BZW[-2])
plot(fit2)
summary(fit2)
predict(fit2, livyatan.BZW, interval="predict", level=0.95)+294
predict(fit2, livyatan.BZW, interval="predict", level=0.8)+294You have to save the sperm whale measurents as livyatan.txt file to load them with R-studio: Sex BL CBL BL-CBL BZW M 1630 490 1140 170 M 1440 470 970 220 M 1560 450 1110 200 M 1460 415 1045 190 M 1000 255 745 125 M 1400 430 970 180 M 1280 310 970 160 M 1150 320 830 130 M 1360 365 995 165 M 1220 340 880 165 F 970 260 710 130 F 890 230 660 110 F 950 247 703 126 F 930 243 687 115 F 880 210 670 120 |
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Post by Grey on May 3, 2013 6:38:05 GMT 5
You should send this to Lambert, it would be interesting to know his opinion.
But I don't get if you achieve here a highest possibility for Livyatan size ? As you know, maths have always been my weak point in these subjects.
The point estimate of 14,16 m is the most likely to you ?
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Post by creature386 on May 3, 2013 11:18:22 GMT 5
About the weight, I made some calculations based on a 18 m long 45 t Physeter.
For a 13,5 t Livyatan I got ~20 t and for a 17,5 m one ~40 t.
I know, square cube law calculations are rather meaningless, but you can use them as an upper range, because due to size allometry, larger Sperm Whales get bulkier (for example a 20,5 m Physeter weighs 88 t and not 66 t).
So, I think Elosha's suggested range is too high.
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Post by coherentsheaf on May 3, 2013 17:28:15 GMT 5
You should send this to Lambert, it would be interesting to know his opinion. But I don't get if you achieve here a highest possibility for Livyatan size ? As you know, maths have always been my weak point in these subjects. The point estimate of 14,16 m is the most likely to you ? None of these estimates is any good. Livyatan has had very different ecology than Physeter. Since ecology will determine morphology to a far greater degree than phylogeny, modern sperm whales are a very poor analogy. However assuming similar proportions to a sperm hale, the second estimate is superior to the one by Lambert, since he failed to exclude an untypical data point that lowered the regression line. I don't think confirmation is needed: mathematics stands on it own. |
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Post by Grey on May 3, 2013 17:52:06 GMT 5
You should send this to Lambert, it would be interesting to know his opinion. But I don't get if you achieve here a highest possibility for Livyatan size ? As you know, maths have always been my weak point in these subjects. The point estimate of 14,16 m is the most likely to you ? None of these estimates is likely. Livyatan has had very different ecology than Physeter. Since ecology will determine morphology to a far greater degree than phylogeny, modern sperm whales are a very poor analogy. Definitely interesting. However, body size is only one part of the morphology, so in my view it does not reject Livyatan as possibly within these sizes range. It could be that large without possess a morphology totally similar to the sperm whale. Same for Zygophyseter, which has a different morphology than the others raptorial physeteroids. Looking at the the comparison I posted with Physeter skull, I have a hard time to envision Livyatan being more than 17 m being as heavy as a 17 m+ sperm whale, which becomes heavier and stockier when growing, with an important skull. I'm thus interested at your personnal view of Livyatan morphology, size and proportion. |
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Post by coherentsheaf on May 3, 2013 17:56:35 GMT 5
None of these estimates is likely. Livyatan has had very different ecology than Physeter. Since ecology will determine morphology to a far greater degree than phylogeny, modern sperm whales are a very poor analogy. Definitely interesting. However, body size is only one part of the morphology, so in my view it does not reject Livyatan as possibly within these sizes range. It could be that large without possess a morphology totally similar to the sperm whale. Same for Zygophyseter, which has a different morphology than the others raptorial physeteroids. Looking at the the comparison I posted with Physeter skull, I have a hard time to envision Livyatan being more than 17 m being as heavy as a 17 m+ sperm whale, which becomes heavier and stockier when growing, with an important skull. I'm thus interested at your personnal view of Livyatan morphology, size and proportion. I do not know how large Lyviathan got. It seems we donot have any fossil or extant analogues. Any attempt to estimate its size is likely error prone. I would say that a plausible size ange is anyhere beteen 10 and 20 metres. |
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Post by Grey on May 3, 2013 18:02:18 GMT 5
That's why I will still rely on the actual propositions by Lambert et al.
In one mail, Lambert said me he personnally believed something around 15 m.
I think a new paper is in preparation, revisiting its physiology. I think the size issue will be then again discussed.
Hopefully, new material will be found and described...
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Post by theropod on May 3, 2013 22:17:06 GMT 5
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Post by Grey on May 3, 2013 22:57:16 GMT 5
The truth lies probably somewhere between. I presume that's why many of the official informations (from the exhibits by the describers themselves) use 15-16 m.
If I remember right, McHenry listed the body mass of Zygo at something seemingly less bulky at parity than the modern sperm whale.
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Post by creature386 on May 4, 2013 0:48:04 GMT 5
I have a question regarding Zygophyseter.
The abstract of the first description stated Zygophyseter to be almost complete. But Darren Naish gave a size range of 6-7 m, so it sounds like they estimated sizes. Because this is important for the overall size of Livyatan (when we use the scaling method), can anyone tell me if these are estimated and if yes how? Because if the lower size for Zygophyseter is correct, than 15 m for Livyatan is also likely correct, when scaling.
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Post by coherentsheaf on May 4, 2013 1:08:14 GMT 5
4.2. Estimate based on the fossil physeteroid Zygophyseter varolai Body length of Zygophyseter varolai is estimated between 650 to 700 cm4, on the basis of the preserved skeleton of the holotype (complete skull with mandible and significant portion of postcranial skeleton, including 29 vertebrae). Thanks to the good relation between BL –CBL and BZW evidenced in the extant Physeter macrocephalus (see Supplementary Fig. 7), we used the ratio of these measurements in Z. varolai to obtain an estimation of the body size of Leviathan melvillei. Considering the smallest estimation of Z. varolai BL (650 cm): BL–CLB = 650 cm – 148 cm = 502 cm (BL –CBL)/BZW = 502/74.5 = 6.738 Estimated body length of L. melvillei: BL = 6.738 (BZW) + CBL = 6.738x197 cm + 294 cm = 1621 cm Considering the largest estimation of Z. varolai BL (700 cm): BL–CLB = 700 cm – 148 cm = 552 cm (BL –CBL)/BZW = 552/74.5 = 7.41 Estimated body length of L. melvillei: BL = 7.41 (BZW) + CBL = 7.41x197 cm + 294 cm = 1753 cm From here: www.nature.com/nature/journal/v466/n7302/extref/nature09067-s1.pdf |
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Post by theropod on May 18, 2013 2:11:11 GMT 5
It would be interesting to see a skeletal reconstruction of a stem physeteroid like Zygophyseter or Brygmophyseter. This could help asess whether comparing the skull bulk with extant Physeter is a reliable method of gauging overall bulk. I suspect it is not, due to strong morphological and ecological divergence, but this way we could have some certainity. also, I found this nice comparison of stem physeteroid skulls with Orcinus orca: img6.imageshack.us/img6/2474/acroi.jpgin this context it is important to note M. masseter is only one of the muscles used for biting, hence what you see here might paint a wrong image, but the skull morphology is interesting. Livyatan seems to most closely resemble the much smaller Acrophyseter in general shape (strongly curved, about equally robust upper and lower jaws), while Orcinus has a more robust mandibula, Brygmophyseter a more robust rostrum, and Zygophyseter straight and comparatively gracile jaws (of course still very robust but I can see why it is suspected to have had a dolphin-like snout). In terms of the posterior part fo the jaw Acrophyseter resembles the Orca most closely, it has a tall protruding frontal area and deepened cranium compared to the others. |
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Post by Grey on May 18, 2013 12:49:26 GMT 5
I had asked to Lambert if Acrophyseter could be a more likely analogue but he recalled that we know almost nothing of this one either in terms of body size and body length.
Also, Acrophyseter is much smaller in scale than Livyatan so the proportions for both animals are probably not that similar in any case. I would still more rely on Physeter and Zygophyseter instead of this one.
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Post by theropod on May 18, 2013 13:32:33 GMT 5
Not really a matter of debate as we don't know the figures of Acrophyseter, but morphologically it is closest.
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Post by Life on May 18, 2013 14:47:57 GMT 5
It would be interesting to see a skeletal reconstruction of a stem physeteroid like Zygophyseter or Brygmophyseter. This is B. Shigensis holotype:  |
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