Allometry of the duration of flight feather molt in birds

We used allometric scaling to explain why the regular replacement of the primary flight feathers requires disproportionately more time for large birds. Primary growth rate scales to mass (M) as M(0.171), whereas the summed length of the primaries scales almost twice as fast (M(0.316)). The ratio of length (mm) to rate (mm/day), which would be the time needed to replace all the primaries one by one, increases as the 0.14 power of mass (M(0.316)/M(0.171) = M(0.145)), illustrating why the time required to replace the primaries is so important to life history evolution in large birds. Smaller birds generally replace all their flight feathers annually, but larger birds that fly while renewing their primaries often extend the primary molt over two or more years. Most flying birds exhibit one of three fundamentally different modes of primary replacement, and the size distributions of birds associated with these replacement modes suggest that birds that replace their primaries in a single wave of molt cannot approach the size of the largest flying birds without first transitioning to a more complex mode of primary replacement. Finally, we propose two models that could account for the 1/6 power allometry between feather growth rate and body mass, both based on a length-to-surface relationship that transforms the linear, cylindrical growing region responsible for producing feather tissue into an essentially two-dimensional structure. These allometric relationships offer a general explanation for flight feather replacement requiring disproportionately more time for large birds.