Simpson’ ratio diagrams
Simpson’s ratio diagrams (Simpson 1941, Large pleistocene felines of North America. American Museum Novitates, 1136, p.1-27, 11 fig., New York) provide rapid and easy comparaisons, both of size and shape, for a single bone or a group of bones.
The reference is provided by a single bone (or a group of bones), or means of a bone sample, the dimensions of which are converted into decimal logarithms. By convention, logarithms of these dimensions are placed on the "0" line of the graph. In most cases I used an extant equid, E. hemionus onager, as reference.
Dimensions of the material under study are also converted into decimal logarithms.
Arithmetic diifferences between the reference logarithms and the logarithms of the studied dimensions are placed above the "0" line if they are positive (larger dimensions), or below if they are negative (smaller dimensions).
In such a logarithmic diagram, proportions remain unchanged whatever the absolute dimensions: diagrams of two bones differing by their size but identical by their proportions will appear one above the other but on parallel lines.
The diagram interpretation is easier when couples of dimensions describing main proportions are placed side by side. For instance, "gracile-robust" proportions appear immediately when "widths" are placed beside "lengths". It may also be convenient to group the dimensions of anatomical parts (diaphysis, proximal end, distal end). When data are often missing for some dimensions (for example when a particular part of the bone is often badly preserved), I recommend to place them at the begining or at the end of the diagram.
See the "Systems of measurements" for the measurements numerotations.
1. Skull comparisons
A small skull from Longueuil Sainte-Marie, ca. 50 years BC, could have been referred to a Donkey in reason of its small size. The Simpson’s ratio diagram shows, however, that by its proportions it is close to a Pony, not a Donkey.
2. Limb bones proportions
Limb bones proportions give some information on the more or less cursorial adaptations and, inside a group of closely related species, on the quality of the ground in their environment.
The most cursorial forms have short proximal bones, (Humerus, Femur) relative to distal bones (MC III et MT III).
When the ground is hard, Ph III are more narrow.
On the illustrated ratio diagram, E. przewalskii is most cursorial and runs on the hardest ground. The Late Pleistocene European E. gallicus is quite different, in particular by the greater length of its Ph I.