Dinosaurs May Have Been Smaller Than We Thought

PraedSt · #1 (**permalink**) 25-June-2009, 08:00 PM

Sorry, this is a few days old. I just found it. I'm gutted!

From Science Daily

Quote:

Scientists have discovered that the original statistical model used to calculate dinosaur mass is flawed, suggesting dinosaurs have been oversized.
...
"Paleontologists have for 25 years used a published statistical model to estimate body weight of giant dinosaurs and other extraordinarily large animals in extinct lineages. By re-examining data in the original reference sample, we show that the statistical model is seriously flawed and that the giant dinosaurs probably were only about half as heavy as is generally believed" says Gary Packard from Colorado State University.

"The original equation used by scientists produces fairly accurate results when determining the mass of smaller animals, but when used on larger animals our research shows that many errors have occurred," says Geoffrey Birchard, associate professor of environmental science and policy at George Mason University who was involved with the research. "The new equation shows that dinosaurs are much smaller than we thought, but there is no mistaking that they were indeed huge animals."

And in case, like me, you were wondering if their fossilized bones had expanded:

Quote:

According to Birchard, this new research suggests that some dinosaurs were much more slender than had been thought.

PraedSt · #2 (**permalink**) 25-June-2009, 08:03 PM

I can't access the actual paper in the Journal of Zoology, but for those who can, it's here. The abstract:

Quote:

We use data from the literature to compare two statistical procedures for estimating mass (or size) of quadrupedal dinosaurs and other extraordinarily large animals in extinct lineages. Both methods entail extrapolation from allometric equations fitted to data for a reference group of contemporary animals having a body form similar to that of the dinosaurs.

The first method is the familiar one of fitting a straight line to logarithmic transformations, followed by back-transformation of the resulting equation to a two-parameter power function in the arithmetic scale. The second procedure entails fitting a two-parameter power function directly to arithmetic data for the extant forms by nonlinear regression.

In the example presented here, the summed circumferences for humerus plus femur for 33 species of quadrupedal mammals was the predictor variable in the reference sample and body mass was the response variable. The allometric equation obtained by back-transformation from logarithms was not a good fit to the largest species in the reference sample and presumably led to grossly inaccurate estimates for body mass of several large dinosaurs. In contrast, the allometric equation obtained by nonlinear regression described data in the reference sample quite well, and it presumably resulted in better estimates for body mass of the dinosaurs.

The problem with the traditional analysis can be traced to change in the relationship between predictor and response variables attending transformation, thereby causing measurements for large animals not to be weighted appropriately in fitting models by least squares regression. Extrapolations from statistical models obtained by back-transformation from lines fitted to logarithms are unlikely to yield reliable predictions for body size in extinct animals.

Numerous reports on the biology of dinosaurs, including recent studies of growth, may need to be reconsidered in light of our findings.

Celestial Mechanic · #3 (**permalink**) 25-June-2009, 08:16 PM

Even Miss Anne Elk has revised her theory about the dinosaurs in light of these findings:

Quote:

My theory about the dinosaurs, {Cough} {Ah-henh!} {Cough}

By Miss Anne Elk {Cough} {Cough} {Ah-henh!}

{Ah-henh!} {Eeee-henh!}

{Cough} {Ah-henh!}

Dinosaurs were real small at one end, real skinny in the middle, and real small at the other end.

{Ah-henh!}

mike alexander · #4 (**permalink**) 26-June-2009, 12:21 AM

Never liked the idea of linear regression on log-transformed data. Too many people assume linearity with no good reason except it's easy do do and understand.

But, this could also help explain how those lumbering, heavy buggers could move around so well. They weren't all that heavy.

PraedSt · #5 (**permalink**) 26-June-2009, 01:09 AM

Quote:

Originally Posted by mike alexander

Never liked the idea of linear regression on log-transformed data. Too many people assume linearity with no good reason except it's easy do do and understand.

I do that.

Thing is (as with their small animals), it works quite well for the "next few points". I've even extrapolated much further; but I'm not an academic. I'm surprised that it took the field so long to test an alternate model- if that indeed is the case here. I wish I could read the whole paper...

HenrikOlsen · #6 (**permalink**) 26-June-2009, 01:32 AM

Quote:

Originally Posted by mike alexander

Never liked the idea of linear regression on log-transformed data. Too many people assume linearity with no good reason except it's easy do do and understand.

I think it's because when you have weight based on volume and strength based on muscle cross section it's not only easy to assume some sort of power relationship but it also makes some sort of sense.

mugaliens · #7 (**permalink**) 26-June-2009, 02:38 AM

Quote:

Originally Posted by mike alexander

But, this could also help explain how those lumbering, heavy buggers could move around so well. They weren't all that heavy.

Evidently not. In fact, light as a bird!

...waitaminute...

Ara Pacis · #8 (**permalink**) 26-June-2009, 02:52 AM

Don't we have a few instances of dino fossils that preserve the external shape?

mike alexander · #9 (**permalink**) 26-June-2009, 02:57 AM

There was also that recent fossil from Argentina (?) that appears to show at least some dinos had an avian pulmonary system.

Going from 40 to 20 tons would make a big difference.

Henrik wrote:

Quote:

I think it's because when you have weight based on volume and strength based on muscle cross section it's not only easy to assume some sort of power relationship but it also makes some sort of sense.

Of course, but lots of bad things can happen when you extrapolate assuming the same function. I like to fit curves using untransformed data and see what the fitted function is telling me.

Ah.

Quote:

The problem with the traditional analysis can be traced to change in the relationship between predictor and response variables attending transformation, thereby causing measurements for large animals not to be weighted appropriately in fitting models by least squares regression. Extrapolations from statistical models obtained by back-transformation from lines fitted to logarithms are unlikely to yield reliable predictions for body size in extinct animals.

Without seeing the details of the actual method used, I can say that applying weighting to log-transformed data must be done very carefully. If you just log-transform your data first and run a simple linear regression, the weighting (whatever you're using: 1/x, 1/x^2) won't work right.

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