The formation of periodic patterns is of fundamental importance in embryonic development. One of the simplest and most frequently observed patterns is the maintenance of a minimum distance between neighbouring elements, for example between teeth, hair, feathers, digits etc. Theoretical models describing these phenomena have been proposed for feather patterning. However, there has been no detailed quantitative analysis of the relationship between cell population density and feather spacing. To

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... fine the relation between these quantities and specifically to test the prediction of a mathematical model, we have examined the formation of the feather pattern after varying proportions of the dermal cells have been killed by X-irradiation. It is known that the development of a feather primordium is normally associated with an increase in cell population density in the dermis. Using X-ray irradiation of the skin in vivo and in vitro, we show that the relation between cell population density and spacing of feather primordia indicates the importance of a threshold number of cells for feather patterning. Moreover, there is a prima facie case for supposing that X-rays act on feather spacing system, reducing the ability of dermal cells to prevent spreading of the pattern. Thus, X-irradiation may have a secondary effect on the spacing of primordia rather than, or as well as, affecting the mechanisms that determine their primary positions.