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linear dimensions vs. body mass

I assume the data given on non-avian dinosaurs are linear measurements.  If
we take a linear measurement, such as total length, and see how living
crocodilians fall, we will get the following distribution:

0-0.5m:  0
0.5-1.0m:  0
1.0-1.5m:  4
1.5-2.0m:  5
2.0-2.5m:  1
2.5-3.0m:  5
3.0-3.5m:  4
3.5-4.0m:  4

This is roughly similar to the distribution given for non-avian dinosaurs.
Similarly, the body mass distribution corresponding to the length
distribution given for non-avian dinosaurs will approximate a negative
exponential.  This is because body mass varies as the cube of any linear
dimension.  Which brings up the point that people often use linear
measurements as indicators of body size, usually because linear
measurements are not as variable as body mass or volume.  The problem is
that an animal twice is long is not twice as large in most biologically
meaningful ways.  It is about 8 times as large.

I will close my remarks about body size by saying that size distributions
within taxa, including dinosaurs, do not match a negative exponential
distribution exactly.  They tend to cluster around their means, suggesting
that there is indeed something at work to keep body size within a certain
range within a given taxon.

Best regards,