The observation that the growth rate of primaries follows allometric scaling may have a simpler explanation than Rohwer et al. suggest here.

They observed that growth rate scales as the 0.17 power of body mass, close to the 0.19 power found by Hedenstrom. The explanation offered is that “The growth zone, within which the barbs of the feather vane also grow, is essentially a linear structure that produces a two-dimensional feather. If the growth zone were to scale in proportion to the length of the grown feather, then the rate of growth would be inversely proportional to the square root (allometric scaling factor 0.5) of feather length.” Hence, it is suggested that growth rate scales as body size to the power 1/6 (= 0.1667).

An alternative, in my opinion simpler explanation is that the 3-dimensional feather grows through a 2-dimensional surface –the surface of the follicle. Thus, growth rate measured as feather mass or volume would scale as the 2/3 power of body mass, and measured as length as M^(2/3)^(1^3) = M^(2/9). That is well in line with Hedenström’s results, and the data in table 1 do not reject 2/9 (= 0.222) power scaling either.