In the letters, researchers led by first author Gregory M. Erickson, a paleobiologist at The Florida State University, concluded that massive dinos grew fast — for example, a 5.5 ton T-Rex could reach skeletal maturity in just two decades. However, when Nathan Myhrvold tried to reanalyze the data, he couldn’t replicate the results. The authors have issued corrections to address the small mistakes unearthed by Myhrvold’s analysis, but argue he couldn’t replicate their results because they hadn’t fully explained their methodology.
After Myhrvold attempted to replicate the findings of maximum size and growth rate for several papers, he found issues in many, including the two Nature letters, according to a press release on Myhrvold’s website:
Astonishingly, the examination of 11 species contained within two studies reported in Nature...revealed that each of the 11 species included multiple serious errors in a key result or graph.
Myrhvold also published his reanalysis in “Revisiting the Estimation of Dinosaur Growth Rates” in PLOS One — in 2013.
Two years later, in December, 2015, the authors have issued corrections to their letters.
First, let’s look at “Gigantism and comparative life-history parameters of tyrannosaurid dinosaurs,” which has been cited 136 times since it was published in 2004, according to Thomson Scientific’s Web of Knowledge. Here’s the correction note:
Questions have been raised about the methods used and conclusions reached in this Letter. In revisiting the work, we realized that we did not provide sufficient methodological details regarding the many steps that went into our growth curve analysis, although the main conclusions of the paper were not affected. We regret any misunderstanding that might have resulted. A detailed rationale is available in the Supplementary Methods and Discussion of this Corrigendum and the source data are provided as Supplementary Data. We thank N. Myhrvold for bringing these issues to our attention.
In our reanalysis we found a minor translational mistake affecting the reported growth for Tyrannosaurus, which does not appear to have contributed to Myhrvold’s concerns (details can be found in the Supplementary Methods and Discussion to this Corrigendum.) The correct equation is Mass=(5,649/[1+e−0.55(Age−16.2)])+5. This produces a maximal growth rate of 758 kg yr−1 using points closely bounding the inflection point and 774kgyr−1 using the instantaneous equation. The reported value was 767kgyr−1 . This slight discrepancy (see the corrected Fig. 2 in the Supplementary Methods and Discussion to this Corrigendum) does not compromise our conclusion that Tyrannosaurus primarily achieved gigantism through evolutionary acceleration.
And here’s the note for a 2001 letter, “Dinosaurian growth patterns and rapid avian growth rates,” which has been cited 143 times:
Questions have been raised about the methods used in the construction of dinosaurian growth curves in this Letter. These were caused by ambiguity with regard to how curve-fitting functions were utilized, and insufficient explanation for how maximum growth rates were calculated. Taken together, these omissions gave the impression that we were able to fit very specific curves even in cases where data were seemingly too scarce to justify them. We apologise for the confusion. However, the main conclusions of the paper were not affected. A detailed rationale is available in the Supplementary Methods and Supplementary Discussion of this Corrigendum and the source data are provided as Supplementary Data. We thank N. Myhrvold for bringing these issues to our attention.
In our reanalysis we found the following translational mistakes, which do not appear to have contributed to Myhrvold’s concerns; however, we take this opportunity to rectify them. The growth rates for Psittacosaurus mongoliensis were incorrectly reported as 5.82kg yr−1 versus 5.28kg yr−1 in Fig. 2 and 12.5 gd−1 in the legend to Fig. 3. Fortunately, the correct value of 14.1 gd−1 was used in the comparative regression calculations. Finally, the mass estimate used for one of the Apatosaurus specimens was incorrectly transcribed. This modestly affected the growth curve parameters in Fig. 2. Details can be found in the Supplementary Methods and Discussion to this Corrigendum along with the corrected Fig. 2. The change causes a negligible shift in the overall dinosaur regression line slope (see the Supplementary Data to this Corrigendum) and does not compromise our conclusion that dinosaurs grew like endotherms.
Myhrvold’s concerns about the letters caught the attention of the New York Times, which wrote about the debate in 2013:
Dr. Myhrvold, a physicist, said he was not accusing Dr. Erickson or his collaborators of deliberately falsifying or manipulating data, because he could not know how the errors occurred. But in a letter to Nature, Science, PLOS One and other journals that published Dr. Erickson’s work, he raised the possibility.
“At the very least these problems are serious errors that merit correction in the literature,” he wrote. “The problems also appear to be consistent with scientific misconduct, which may factor into any resulting investigation.”
Last week, Dr. Myhrvold emailed the scientists who had collaborated with Dr. Erickson on the papers to alert them. “I tried very hard to reproduce the results of these papers,” he told them, “and I failed to do so.” In exhaustively describing what he thought were mistakes in the papers, Dr. Myhrvold wrote, “This includes cases where the data set appears to have been altered or fabricated.”
We asked Myhrvold — who said he has been researching dinosaurs “off and on since the early 1990s” — if these corrections addressed his concerns. He told us:
In the latest Nature correction, [Erickson] at least admits that there were problems. So in a sense that is progress.
But in Myhrvold’s opinion, the papers still contain fatal flaws, and “violates every standard of statistical ethics:”
[Erickson] still tries to justify using 3-parameter curves fit to just 3 data points. That is just absurd! He offers the justification that the dinosaur Shuvuuia is “rare”. Well of course it is, but the fact that data are hard to come by does not mean it is valid to proceed!
As another example, you cannot fit 3-parameter curves to 3 data points. Most statistical methods require at least 2 more data points than parameters to have any validity at all.
Here is the most amazing part. Erickson does not explain even now how he got the numbers that he published in enough detail that one could reproduce them. He makes vague claims that he used “averaging” but the claims don’t hold up. There is no justification to averaging data prior to curve fitting….In addition to this, he has lots of incredibly sloppy things. I don’t think that there is a single numerical result in the 2001 paper that is correct.
Another unfortunate thing is that he claims that it does not change his conclusions. This is also false.
Another question we had: After Myhrvold raised concerns about the papers, why did it take Nature two years to decide to correct them? A journal spokesperson told us:
We take all concerns raised about papers we publish seriously and look into them carefully. As a result, it can take time for authors and/or institutions to undertake and report on investigations and for corrections and other responses to be developed and published. In this case extensive reanalysis was undertaken and the submitted correction underwent further peer review.
The other authors of the dinosaur growth papers have been more receptive to his critiques, said Myhrvold:
Other authors in the field, like Holly Woodward, Andrew Lee, Sarah Werning, Jack Horner had papers which were critiqued in my PLOS paper. They have accepted the results of mywork. In fact, Werning and Lee were at various points were referees of my paper.
John Hutchinson was the author of a paper I critiqued in the PLOS paper – he promptly published a correction and was great about the whole thing.
Indeed, in May, 2014, John Hutchinson at the University of London issued a correction to his PLOS paper, “A Computational Analysis of Limb and Body Dimensions in Tyrannosaurus rex with Implications for Locomotion, Ontogeny, and Growth,” which notes that some of the conclusions were affected:
After reviewing these mistakes and sources of uncertainty, we now judge that the data in our paper do not support our published conclusions regarding the accuracy of DME models. We no longer consider our data sufficient to permit an evaluation of how accurate this method may be, and we wish to withdraw our earlier statements on this issue (p9: the last paragraph of the results section headed ‘Growth’, p13: the three paragraphs in the discussion headed ‘Implications for growth rates?’; and Figure 6).
We’ve reached out to Erickson, and will update this post with anything else we learn.
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