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Post by Verdugo on Sept 17, 2019 19:44:42 GMT 5
theropod Good catch! . If i recall correctly, Erickson et al (the paper that has the original data) also used Mean measurements too. Look at Fig 3A, you can clearly tell that they used the Mean BM and BF for their regression and not from the actual measured value of the specimens. I have an idea. In table 1 of Erickson et al, they did provide the figures for Min, Max Bite force and Body mass. I think the Min and Max figures must have come from the actual smallest and largest Crocodilians that they measured. Hence, those figures would have been actual in vivo figures and not distorted by Mean calculations. Perhaps you try log-transforming those figures and then run a regression. Try to run the BF against TL and BM to see which dimensions would have been the actual best predictor for BF. I also have another suggestion. Erickson et al pointed that Gavialis gangeticus and Tomistoma schlegelii have BF lower than expected for their size. I figure if you are to generate a regression to estimate the BF on an extinct species who is very unlikely to have BF lower than expected (says Purussaurus) then i think the data of these two species should be excluded from the regression (so that the BF of the extinct species like Purussaurus would be less likely to be underestimated) EDIT: I just realised that if you use both Min and Max figures, you may run into the problem of ontogeny (where the increase in BF can also be attributed to ontogeny and not just size factor). Maybe it's best that you only use the Max figures.
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Post by theropod on Sept 17, 2019 20:09:50 GMT 5
All very good points, I am definitely going to look into that. So that alone doesn’t explain the differences between those studies. I think we can confidently dismiss that regression, especially for anything outside of the size range they studied. However the regression for the ontogenetic series of salties they used (you know, the one that was actually log transformed, the one with the highest results) probably didn’t use any sort of mean values.
I should add that what really matters is the interpretation of the figures in question. The bite force estimate simply isn’t the bite force estimate for an 8.whatever ton Purussaurus specimen (or any of the other values we plugged in), it’s the hypothetical mean bite force for a taxon with that mean body mass–both merely aren’t the same specimens. So it’s not so much that this is entirely useless, as that it is misinterpreted, even by the studies themselves (Aureliano et al. even specifically stated their estimate to be for that specific specimen…well, nope).
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Post by theropod on Sept 18, 2019 14:53:45 GMT 5
Regarding Verdugo ’s suggestion, here we go: > data.frame(bf=c(4355,6276,1863,2736,4399,3172,5938,7295,16414,3127,4577,2447,2509,9452,1357,1303,2420,1192,4310,1125,1125), bm=c(164,182,43,69,110,87,186,207,531,65,87,95,34,297,15,25,45,23,103,14,28), tl=c(318,340,215,244,284,261,315,332,459,246,263,262,183,372,155,166,177,162,304,133,156))->crocbf > crocbf bf bm tl 1 4355 164 318 2 6276 182 340 3 1863 43 215 4 2736 69 244 5 4399 110 284 6 3172 87 261 7 5938 186 315 8 7295 207 332 9 16414 531 459 10 3127 65 246 11 4577 87 263 12 2447 95 262 13 2509 34 183 14 9452 297 372 15 1357 15 155 16 1303 25 166 17 2420 45 177 18 1192 23 162 19 4310 103 304 20 1125 14 133 21 1125 28 156 > attach(crocbf) > lm(log(bf)~log(bm))->logbfbm > lm(log(bf)~log(tl))->logbfbm > lm(log(bf)~log(bm))->logbfbm > lm(log(bf)~log(tl))->logbftl > summary(logbfbm)
Call: lm(formula = log(bf) ~ log(bm))
Residuals: Min 1Q Median 3Q Max -0.44411 -0.12107 0.03653 0.08573 0.32301
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.95783 0.20701 23.95 1.18e-15 *** log(bm) 0.72222 0.04703 15.36 3.64e-12 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2078 on 19 degrees of freedom Multiple R-squared: 0.9254, Adjusted R-squared: 0.9215 F-statistic: 235.8 on 1 and 19 DF, p-value: 3.639e-12
> summary(logbftl)
Call: lm(formula = log(bf) ~ log(tl))
Residuals: Min 1Q Median 3Q Max -0.42867 -0.16118 -0.03154 0.18955 0.38006
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -3.4084 0.8242 -4.135 0.000562 *** log(tl) 2.0903 0.1500 13.939 1.99e-11 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2271 on 19 degrees of freedom Multiple R-squared: 0.9109, Adjusted R-squared: 0.9062 F-statistic: 194.3 on 1 and 19 DF, p-value: 1.985e-11
So as you can see the correlation is a bit better for the body mass data, although it isn’t a huge difference. so with this in mind, some bite force predictions based on this formula (all results in Newtons) > exp(predict.lm(logbfbm, data.frame(bm=c(1000,2000,3000,4000,5000,6000,7000,8000,8423.9,12113,14976,19291,31590,54588)), interval="prediction", level=.50)) fit lwr upr 1 20883.98 17638.42 24726.74 2 34452.65 28743.90 41295.20 3 46174.15 38214.86 55791.17 4 56837.10 46756.76 69090.66 5 66776.25 54667.18 81567.55 6 76174.24 62107.70 93426.66 7 85144.84 69178.59 104796.06 8 93765.09 75947.51 115762.74 9 97327.51 78738.02 120305.85 10 126519.42 101472.66 157748.54 11 147470.56 117664.73 184826.56 12 177059.66 140386.39 223313.13 13 252822.10 197948.43 322907.39 14 375297.91 289641.37 486285.91 1: C. porosus 1000 kg 2-8: various giant extinct crocodilians 2 000-8 000 kg 9: Purussaurus brasiliansis UFAC 1403, (probably inflated) estimate as per Aureliano et al. 8 423.9 kg 10: Kronosaurus queenslandicus (Harvard) max based on reconstructions by McHenry 12 113 kg 11: Aramberri pliosaur mean mass based on vertebral width 14 976 kg 12: Pliosaurus macromerus (Cumnor mandible) 12 726 m estimate by McHenry (based on unreliable reconstructed mandible) 19 291 kg 13: Entirely hypothetical 15 m pliosaur based on macromerus 31 590 kg 14: Entirely hypothetical 18 m pliosaur based on macromerus 54 588 kg As always, of course note that this is based on in vivo and peak bite forces, and this is massively extrapolated (though not as massively as some other people seem to think is fine to do, so I guess it should be fine for our purposes). So this would predict ~14.7 t (50% PI 11.8-18.5) for Aramberri and about 12.7 t (50% PI 10.1-15.8) for a big K. queenslandicus, which I think actually sounds fairly reasonable. Also a Purussaurus the size Aureliano et al. estimated would presumably bite harder than they calculated, at 9.7 t (50% PI 7.9-12.0), although of course actual Purussaurus doesn’t seem to have grown that big, but at 6 t it would still bite with 7.6 t and at 5 t with 6.7 t, roughly equivalent to their figure (6.9 t). The 15 and 18 m would, based on this, bite with an enormous 25 and 38 t respectively, so almost certainly the highest bite force estimated for anything if such a pliosaur had actually existed.
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Post by maxime13 on Sept 18, 2019 15:18:20 GMT 5
In the book "Dinosaurs and other reptiles from the Mesozoic of Mexico", the author wrote about the monster of aramberri and the animal that killed him. The length of the crown of the teeth that caused the bite marks on the pterygoid is arround 30 cm and 6 cm near the tip of the crown. The monster of aramberri, based on the old photo of the lost parts of the skull, would have teeth that measured 5.5 cm at the base of the crown, and biggest tooth crown of kronosaurus measure around 12 cm in length. So if one pliosaur could have grown to 15-18 m, that's probably this one
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Post by Verdugo on Sept 18, 2019 16:22:33 GMT 5
Thanks theropod, that's pretty awesome. Though i still have some questions. Does the regression software you use allow you to detect which input data falls below 95% CI? The thing is in my previous post i suggested you to exclude Gharial and False gharial because Erickson et al suggested so (as these two species fall below the 95% CI in their regression, however we now know that Erickson's regression is rather problematic). I wonder if these two species still fall below the 95% CI in the new regression here. Could try running the regression again but this time includes data from Gharial and False gharial? Also, are there any other Crocodilians that fall 95% CI? If there are any, i think we could also exclude those taxons especially since we're trying to predict the Bite force of extant taxons who are extremely unlikely to bite weaker than expected (such as Purussaurus)
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Post by theropod on Sept 18, 2019 17:18:20 GMT 5
Well, as per your suggestion I omitted the gharial and false gharial before running the regression, so do you mean the 95% CI for the regression run with these taxa, or the one run without them? Here is my original regression, with 95% confidence (blue) and prediction (green) intervals. As you can see, there are lots of crocodilians that fall outside the 95% CI, both above and below it. That’s not surprising, the CI is where the mean is expected to fall in 95% of samples, not where 95% of all individual observations are expected to fall (that would be the prediction interval). It wouldn’t make sense to exclude everything above or below the 95% CI, because it becomes more precise at the lower sizes where there are more data. However, only Gavialis would fall outside the 95 % prediction interval, and Tomistoma is right at the edge of the 95% confidence interval. Here is the regression run again, this time with Tomistoma and Gavialis included:
data.frame(bf=c(4355,6276,1863,2736,4399,3172,5938,7295,16414,3127,4577,2447,2509,9452,1357,1303,2420,1192,4310,1125,1125,2006,6450),bm=c(164,182,43,69,110,87,186,207,531,65,87,95,34,297,15,25,45,23,103,14,28,121,255), tl=c(318,340,215,244,284,261,315,332,459,246,263,262,183,372,155,166,177,162,304,133,156,334,405))->crocbf2 attach(crocbf2) lm(log(bf)~log(bm))->logbfbm2 summary(logbfbm2)
Call: lm(formula = log(bf) ~ log(bm))
Residuals: Min 1Q Median 3Q Max -0.76244 -0.11491 0.08908 0.15714 0.34411
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.03118 0.25673 19.60 5.63e-15 *** log(bm) 0.69543 0.05737 12.12 6.05e-11 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2641 on 21 degrees of freedom Multiple R-squared: 0.8749, Adjusted R-squared: 0.869 F-statistic: 146.9 on 1 and 21 DF, p-value: 6.045e-11
As you see, this would put Tomistoma firmly inside the 95% CI, but would put C. porosus outside of it. Either way, Gavialis remains firmly below the 95% PI. The same bite force predictions as before, but using this model: > exp(predict.lm(logbfbm2, data.frame(bm=c(1000,2000,3000,4000,5000,6000,7000,8000,8423.9,12113,14976,19291,31590,54588)), interval="prediction", level=.50)) fit lwr upr 1 18677.34 15133.40 23051.19 2 30245.55 24159.92 37864.10 3 40097.88 31729.89 50672.73 4 48978.80 38483.43 62336.51 5 57200.88 44687.25 73218.65 6 64933.39 50484.95 83516.87 7 72281.16 55965.02 93354.14 8 79314.89 61186.91 102813.70 9 82214.54 63333.29 106724.75 10 105838.92 80699.42 138809.87 11 122666.39 92955.34 161873.89 12 146283.31 110023.72 194492.66 13 206135.72 152728.60 278218.58 14 301544.89 219604.11 414060.19
I would say the difference is there, but it’s not enormous. If we exclude Gavialis, but include Tomistoma, we’d get this: data.frame(bf=c(4355,6276,1863,2736,4399,3172,5938,7295,16414,3127,4577,2447,2509,9452,1357,1303,2420,1192,4310,1125,1125,6450),bm=c(164,182,43,69,110,87,186,207,531,65,87,95,34,297,15,25,45,23,103,14,28,255), tl=c(318,340,215,244,284,261,315,332,459,246,263,262,183,372,155,166,177,162,304,133,156,405))->crocbf3 attach(crocbf3) > lm(log(bf)~log(bm))->logbfbm3 > summary(logbfbm3)
Call: lm(formula = log(bf) ~ log(bm))
Residuals: Min 1Q Median 3Q Max -0.43340 -0.13494 0.04732 0.10634 0.32276
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.99563 0.20081 24.88 < 2e-16 *** log(bm) 0.71157 0.04503 15.80 9.16e-13 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2064 on 20 degrees of freedom Multiple R-squared: 0.9259, Adjusted R-squared: 0.9221 F-statistic: 249.7 on 1 and 20 DF, p-value: 9.165e-13
exp(predict.lm(logbfbm3, > exp(predict.lm(logbfbm3, data.frame(bm=c(1000,2000,3000,4000,5000,6000,7000,8000,8423.9,12113,14976,19291,31590,54588)), interval="prediction", level=.50)) fit lwr upr 1 20150.12 17083.20 23767.64 2 32997.49 27661.51 39362.80 3 44033.35 36639.30 52919.56 4 54036.11 44711.20 65305.82 5 63334.76 52169.08 76890.20 6 72108.24 59171.04 87874.05 7 80467.79 65814.96 98382.88 8 88488.59 72166.82 108501.80 9 91800.05 74783.20 112689.06 10 118873.36 96057.39 147108.67 11 138245.59 111170.17 171915.21 12 165536.77 132332.02 207073.26 13 235130.32 185754.70 297630.51 14 347008.23 270447.09 445243.14 I think we don’t really need to exclude Tomistoma, based on this. In fact, the correlation is almost the same whether we exclude it or not. Gavialis however I would exclude, since it’s outside the 95% PI, a clear outlier, and decreases the correlation significantly (and doesn’t really represent what we want to estimate in most cases, taxa with relatively powerful jaws and large prey).
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Post by theropod on Sept 18, 2019 17:44:36 GMT 5
Oh btw, all the above are molariform bite forces, of course, in case it wasn’t obvious. Caniniform bfs will follow.
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Post by theropod on Sept 18, 2019 18:07:22 GMT 5
Caniniform bite forces:
> data.frame(bfc=c(2830,4283,856,NA,3069,2023,4310,4194,11216,2035,2891,NA,1588,3985,6162,963,894,1672,900,3112,711,720),bfm=c(4355,6276,1863,2736,4399,3172,5938,7295,16414,3127,4577,2447,2509,6450,9452,1357,1303,2420,1192,4310,1125,1125),bm=c(164,182,43,69,110,87,186,207,531,65,87,95,34,255,297,15,25,45,23,103,14,28), tl=c(318,340,215,244,284,261,315,332,459,246,263,262,183,405,372,155,166,177,162,304,133,156))->crocbf > attach(crocbf) > lm(log(bfc)~log(bm))->logbfcbm > summary(logbfcbm)
Call: lm(formula = log(bfc) ~ log(bm))
Residuals: Min 1Q Median 3Q Max -0.51893 -0.10667 0.05636 0.12557 0.35100
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.58498 0.22575 20.31 7.38e-14 *** log(bm) 0.71419 0.05055 14.13 3.49e-11 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2314 on 18 degrees of freedom (2 observations deleted due to missingness) Multiple R-squared: 0.9173, Adjusted R-squared: 0.9127 F-statistic: 199.6 on 1 and 18 DF, p-value: 3.493e-11
> exp(predict.lm(logbfcbm,data.frame(bm=c(1000,2000,3000,4000,5000,6000,7000,8000,8423.9,12113,14976,19291,31590,54588)), interval="prediction", level=.50)) fit lwr upr 1 13608.50 11299.51 16389.31 2 22325.63 18303.85 27231.09 3 29824.07 24247.77 36682.76 4 36626.66 29591.34 45334.64 5 42954.62 34527.95 53437.85 6 48928.35 39162.35 61129.71 7 54622.74 43559.44 68495.92 8 60088.45 47762.94 75594.62 9 62345.55 49494.31 78533.64 10 80809.29 63570.70 102722.49 11 94030.77 73568.68 120184.09 12 112668.34 87566.47 144965.94 13 160242.77 122894.76 208940.94 14 236828.15 178881.07 313546.73
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Post by Verdugo on Sept 18, 2019 18:12:21 GMT 5
^ Yeah, when i said CI i really meant Prediction Interval, sorry got mixed up a bit (it has been quite a while since i last touched Statistics). Anyway, so the last regression that includes Tomistoma but not Gavialis would be the most accurate right?
Btw, i did not expect you to the regression this way. Normally, i would do linear regression (assuming the logBF = y and logBM = x and then run a linear regression y = Ax + b). But i guess it does not matter which way you want to do it.
I'm not sure if running a regression for Caniniform BF would be appropriate due to the rather large variations in out-level arm length (some Crocs have short snout while others have long snout). Not to mention that Pliosaur also appears to be rather long snouted as well (when scaled to similar volume). If you want to predict the Caniniform BF for Pliosaur then you'll have to use longer snouted Crocodilians as input while exclude shorter snouted ones (if you use shorter snouted one, you might overestimate the Caniniform BF of species that have long out level). On the other hand, if you want to predict shorter snouted species like Purussaurus then you'll have to exclude longer snouted Crocodilians from your input data. Since we have to exclude so many species for either cases, the regression might not be meaningful. Not to mention the fact that you'll have to do quantitative judgements on your own to decide which species would be long or short snouted (some Crocodilians such as Orinoco croc are somewhat in between, which makes it rather difficult to put it in either cases).
EDIT: Turn out correlation of the regression is actually rather good. I guess the variations in out-level arm at the Caniniform is not as much as i assumed?
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Post by theropod on Sept 18, 2019 18:41:50 GMT 5
Yeah, well you didn’t get anything wrong, Erickson et al. do call what they did a confidence interval. Perhaps they actually mean a prediction interval though, as the interval does look pretty broad. But I don’t really want to re-run their analysis, it’s somewhat besides the point. And yes, I think so. But that’s what the prediction intervals are for. 50% of observations would be expected to fall in that range, so that gives us an idea of the variation. That for caniniform bite force is not that much wider than that for molariform bite force (upper end is 32% higher than mean, 28% higher for molariform bite force). Orinoco crocodiles have actually been suggested as the closest extant analogue for pliosaur skull proportions, so we could always try scaling pliosaurs up from that isometrically: bfc bfm 1 13336.25 19541.99 2 21169.98 31020.97 3 27740.52 40648.97 4 33605.25 49242.72 5 38995.44 57141.11 6 44035.34 64526.21 7 48801.43 71510.10 8 53345.01 78167.94 9 55213.16 80905.39 10 70339.88 103071.00 11 81027.24 118731.48 12 95926.14 140563.27 13 133270.36 195284.79 14 191910.44 281211.75
We can do the same based on Alligator: bfc bfm 1 13842.59 21233.39 2 21973.74 33705.91 3 28793.75 44167.24 4 34881.14 53504.80 5 40475.98 62086.82 6 45707.23 70111.12 7 50654.27 77699.48 8 55370.36 84933.58 9 57309.44 87907.96 10 73010.48 111992.06 11 84103.61 129008.00 12 99568.18 152729.37 13 138330.24 212187.19 14 199196.72 305551.35
Of course both are only scaling from single specimens, but there doesn’t actually seem to be a very big difference here, despite one being mesorostrine and the other brevirostrine. I think Erickson et al. noted that too, bite force in crocodiles tends to scale with body size fairly well, and is fairly independent of skull shape (save for some extremes, like gharials). Yes, pretty much. Or perhaps more longirostrine crocodilians make up with longer in-levers and/or proportionately larger skulls.
Anyway, I also prefer to focus on posterior bite forces, but I wanted this for the purpose of comparison, because we have the 17 m and 20.3 m megalodon estimates partly based on in vivo data, with anterior bite forces of 123 876 and 179 219 N respectively.
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Post by Grey on Sept 18, 2019 19:31:14 GMT 5
In the book "Dinosaurs and other reptiles from the Mesozoic of Mexico", the author wrote about the monster of aramberri and the animal that killed him. The length of the crown of the teeth that caused the bite marks on the pterygoid is arround 30 cm and 6 cm near the tip of the crown. The monster of aramberri, based on the old photo of the lost parts of the skull, would have teeth that measured 5.5 cm at the base of the crown, and biggest tooth crown of kronosaurus measure around 12 cm in length. So if one pliosaur could have grown to 15-18 m, that's probably this one Wheter this tooth size estimate is tenable is not clear. The problem being that no real material so far suggests the existence of such a tooth.
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Post by Grey on Sept 19, 2019 0:13:28 GMT 5
Theropod, this further shows how much pliosaurs should not be underestimated despite their relatively shorter length. Even the real larger ones would have peak bite forces comparable to a large Carcharocles.
I tend to think that, in a theorical fiction contest, a 20 tonnes pliosaur would have at least be able to fairly intimidate a 20 tonnes Carcharocles.
The bite force, endothermy and unparalleled maneuvrability at such a size would have been fearsome advantages to the reptile.
I tend to think Carcharocles may be the "apex predator of all time" (with only Livyatan a potential good alternative) but this may be mainly linked to its gigantic size, body or feeding apparatus.
Pliosaurs may have represented a different type of pinacle in macropredation.
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Post by dinosauria101 on Sept 19, 2019 0:57:51 GMT 5
GreyI agree! Pliosaurs seem to have been taking the biggest bites of any predator relative to weight
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Post by theropod on Sept 19, 2019 1:20:42 GMT 5
Bite force on its own doesn’t make a bite more damaging. Komodo dragons and great white sharks have low to average bite forces for their size, yet their bites are both among the most potent in the extant world.
Comparison between pliosaurs and Carcharocles is pretty similar to that between tyrannosaurs and allosaurs, they are using their jaws very differently, and have very different teeth in those jaws.
Pliosaurs do have huge jaws for their size, especially in length, but for pliosaurs and crocodiles, the jaw length probably plays an important factor for increasing the anterior gape sufficiently to handle large animals, as well as for making use of the neck flexibility these taxa retain for giving them better reach. The huge jaws of pliosaurs may simply be for facilitating the biting of large prey. Taxa with shorter jaws (like sharks) went the route of increasing the gape angle at the joint to achieve that instead, for a shark with macrophagous morphology, longer jaws would be detrimental, not beneficial, because they need to achieve a sawing motion.
I would tend to think the presumed superior maneuverability over an axial swimmer at these sizes would be a pliosaur’s main advantage (one that is very hard to quantify, even though there seems to be a consensus that their unique locomotion would make them very agile). And one I would not underestimate in a 3-dimensional, marine environment.
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Post by dinosauria101 on Sept 19, 2019 1:23:07 GMT 5
theropodI meant jaw size, not bite force. Sorry if that was unclear
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