concept

Scaling exponent

The exponent in the power law Y = a·Mᵇ that describes how a biological measure (Y) changes with body mass (M). The exponent b is the heart of the whole calculation: b = 1 means the measure grows in lockstep with mass (isometry); b < 1 means it grows slower; b > 1 means it grows faster. Plot the data on log-log axes and the straight line you get has a slope of exactly b. These exponents are not arbitrary - they expose deep physical regularities, like the 3/4 exponent of Kleiber's metabolic law, or the exponents that make the power flight demands outrun the power muscles can supply in giant flyers.