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# The Evolution of the Horse Face

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From Melvin Konner's The Evolution of Childhood:
In horse evolution, the face lengthened faster than the body size increased because face length is determined by the area of tooth surface needed for chewing, which, since it tracks the amount eaten, depends on body mass.  Body mass increases roughly as the cube of body length, and tooth surface as the square of face length, so face length must increase faster than body length, a prediction confirmed by the fossil record and interspecies comparisons.
The whole book's full of interesting empirical work I was barely aware existed, especially trait regressions where each species is a data point.

writes:
Body mass increases roughly as the cube of body length...

This raises a question that has been bugging me for years: Why is body mass index defined as the ratio of body mass to the square of your height, and not the cube?

david writes:

@Andy Wood

Take a look. The BMI is simpler to calculate in your head, though, which probably accounts for its appeal.

MikeP writes:

Body mass increases roughly as the cube of body length, and tooth surface as the square of face length...

"As the square...?" Horses have rows and columns of teeth?

tk writes:

Why didn't this happen with other animals?

writes:

I thought amount eaten increases more slowly than body mass with increasing size.

MikeP writes:

You may be thinking of Kleiber's Law...

Kleiber's law, named after Max Kleiber's biological work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the ¾ power of the animal's mass. Symbolically: if q0 is the animal's metabolic rate, and M the animal's mass, then Kleiber's law states that q0 ~ M¾. Thus a cat, having a mass 100 times that of a mouse, will have a metabolism roughly 31 times greater than that of a mouse. In plants, the exponent is close to 1.

But, since they already screwed up the fact that the chewing surface for a horse is directly proportional to the length of its mouth, not the square of that length, we can forgive the fact that the amount that it eats is proportional to the 9/4 power of the body length, not the cube of that length.

In fact, your recollection solves a problem raised by my noticing that chewing surface is not proportional to the square of mouth length. Since the exponential ratio 9/4 : 1 is almost the same as 3 : 2, the empirically observed proportions of body length to mouth length are maintained. So it's only the analytical explanation that is mistaken, not the measurements.

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