Prum, R.O.*; Williamson, S.: Models of the developmental determination of feather shape and pigmentation pattern.

We present the first explicit theories of the growth of feather shape (the outline of a pennaceous vane) and the determination of within feather pigmentation pattern. 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 spread following emergence from the sheath. The growth model simulates a diversity of shapes that correspond closely to real feathers, including various contour feather shapes, asymmetrical feathers, and even emarginate primaries. Each parameter can have substantial independent effects on feather shape. The 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. Accurate simulation of the shape and position of feather fault bars strongly confirms the uniform absolute growth rate hypothesis and the realism of the model. Within feather pigmentation patterning is simulated by activator-inhibitor models during feather growth. Simple activator inhibitor models successfully simulate most common feather pigmentation patterns, including horizontal bars, stripes, and chevrons. More complex patterns, such as alternating rows of spots, can be simulated by including additional parameters. The pigmentation pattern models can simulate many of the complex transitions in feather patterning observed in complex avian plumages. Together, the two models provide numerous testable predictions about the developmental determination and evolution of feather shape and pigmentation patterning.