Theory of the growth and evolution of feather shape

We present the first explicit theory of the growth of feather shape, defined as the outline of a pennaceous feather vane. Based on a reanalysis of data from the literature, we propose that the absolute growth rate of the barbs and rachis ridges, not the vertical growth rate, is uniform throughout the follicle. The growth of feathers is simulated with a mathematical model based on six growth parameters: (1) absolute barb and rachis ridge growth rate, (2) angle of helical growth of barb ridges, (3) initial barb ridge number, (4) new barb ridge addition rate, (5) barb ridge diameter, and (6) the angle of barb ramus expansion following emergence from the sheath. The model simulates growth by cell division in the follicle collar and, except for the sixth parameter, does not account for growth by differentiation in cell size and shape during later keratinization. The model can simulate a diversity of feather shapes that correspond closely in shape to real feathers, including various contour feathers, asymmetrical feathers, and even emarginate primaries. Simulations of feather growth under different parameter values demonstrate that each parameter can have substantial, independent effects on feather shape. Many parameters also have complex and redundant effects on feather shape through their influence on the diameter of the follicle, the barb ridge fusion rate, and the internodal distance. Simulated isochrones-the loci, or sets, of feather cells of the same age-have the same oblique chevron-shaped position in the mature feather as fault bars, which are isochronic defects in the barbules created by a disruptions during development. Accurate simulation of fault bar shape and position confirms the uniform absolute growth rate hypothesis and the general realism of the model. The theory defines a six-parameter feather morphospace, and provides many predictions about the developmental determination of feather shape that can be tested with detailed observations and experiments on developing feathers. This theory also provides testable predictions about the changes in developmental mechanisms required to evolve different feather shapes to accomplish various functions.