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Hind limb proportions do not support the validity of Nanotyrannus

While it was not the main focus of their paper, Persons and Currie (2016), in a recent paper in Scientific Reports hinted at the possibility of Nanotyrannus lancensis being a valid taxon distinct from Tyrannosaurus rex, using deviations from a regression model of lower leg length on femur length.

Similar to encephalisation quotients, Persons and Currie devised a score (cursorial-limb-proportion; CLP) based on the difference between the observed lower leg length and the predicted lower leg length (from a regression model) expressed as a percentage of the observed value. The idea behind this is pretty simple in that if the observed lower leg length value is higher than that predicted for its size (femur length), then that taxon gets a high CLP score. I don't particularly like this sort of data characterisation (a straightforward regression [albeit with phylogeny, e.g. pGLS] would do the job well), but nonetheless, Persons and Currie found that when applied to Nanotyrannus, its CLP score was unexpectedly high for a tyrannosaur of its size - and well removed from any of the known ontogenetic stages of Tyrannosaurus. Thus, the authors remark:
"Comparisons between the CLP scores of Tyrannosaurus and specimens referred to the controversial genus Nanotyrannus indicate a strong discrepancy in cursorial adaptations, which supports the legitimacy of Nanotyrannus and the previous suggestions of ecological partitioning between Nanotyrannus and the contemporaneous Tyrannosaurus."
This is a bit of a bold statement to make from the data they present.
It's not that clear from their paper so I got the data from their tables and I played around with them.

First the 53-taxon data set plotted after log10 transformation:
Log-transformed lower leg length against log-transformed femur length for the 53-taxon dataset
The (non-phylogenetic) regression line, 95% confidence intervals (CI) and 95% prediction intervals (PI) are shown in red. Looks like a pretty strong relationship.

Since this dataset is composed of specimens with maximum values, I added the additional multiple-specimen dataset to this plot:
Log-transformed lower leg length against log-transformed femur length for the 53-taxon dataset plus additional specimens
Taxa with multiple specimens are coloured: red, Allosaurus fragilis; orange, Coelophysis bauri; green, Herrerasaurus ischigualastensis; lightblue, Albertosaurus sarcophagus; lightblue2, Gorgosaurus libratus; blue, Tyrannosaurus rex; turquoise, Nanotyrannus lancensis. The lines are for the 53-taxon regression model.

What's immediately obvious is that both Nanotyrannus specimens fall above the 95% PI from the 53-taxon regression model, indicating that they are substantial outliers. However, what is striking, is that while CLP scores indicate a "strong discrepancy" between Nanotyrannus and Tyrannosaurus (here in blue), it is not so apparent from the above plot. With the eye of faith you can easily extend the Tyrannosaurus ontogenetic series back towards Nanotyrannus.
Log-transformed lower leg length against log-transformed femur length with regression line fitted through Nanotyrannus and T. rex specimens
The above plot is showing a regression line (along with 95%CI and 95%PI) fitted for a subset of the data comprising only of Nanotyrannus and Tyrannosaurus specimens. The smallest definitive Tyrannosaurus specimen in the dataset falls below the line but within the 95% PI. If this is not clear, here is the same plot but only the relevant Nanotyrannus and Tyrannosaurus specimens shown.
The bivariate plot and regression line for Nanotyrannus and T. rex specimens
With such a small sample size, we can't be certain; this regression definitely suffers from small sample size - just look at the 95% CI. It's not even worth fitting a model just for the Tyrannosaurus specimens and comparing the coefficients with the Nanotyrannus+Tyrannosaurus regression!

Having said that, just for this simple plot, I don't think this dataset presents a strong evidence for the validity of Nanotyrannus as a separate taxon from Tyrannosaurus, but a not-very strong but probable hypothesis for an ontogenetic limb proportion allometry in Tyrannosaurs with the Nanotyrannus specimens being very young individuals. By all means, this plot is not definitive evidence for Nanotyrannus being juvenile Tyrannosaurus, but illustrates more importantly that it equally does not support a distinct generic status for Nanotyrannus.

As a side note, if you look at Fig 2 from Persons and Currie (2016), it should be clear why log-transforming data before fitting a regression model is so important. Hint: look at how the confidence intervals fan out...

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