An Approach to the Functional Analysis of Bill Shape

paper I wish to outline several methods that are useful in clarifying the correlations of these several factors with the size and shape of the bill, with special emphasis being placed upon the question of bill shape.Because the avian bill is a three-dimensional structure, functional investigations must eventually include all dimensions.Yet for the present, a good foundation for future functional studies can be established by considering the bill as a two-dimensional feature.Thus, for the purposes of this paper, the silhouette of the bill may be taken as its shape and will serve as the object under analysis.The shape of the silhouette of the bill may be described in terms of a number of different measures.One commonly used measure is the curvature of the culmen and of the tomium for the upper jaw and the curvature of the tomium and of the gonys for the lower jaw.It is possible to reduce the analysis of bill shape to that set of factors influencing the curvatures of the culmen, tomlure, and gonys.Such a simplification has many decided advantages, but it also obscures certain aspects of bill shape.Another set of useful measures is the moment arms of the force vectors and the angle between the force vector and a set of x-y axes at the center of rotation of the jaw; this set of measures will be used in the analysis of the magnitude of the forces acting on the bill.All the factors influencing bill shape may be classified into historical and nonhistorical factors.All historical factors, whether these are accidental or not, will be excluded from this study.Inclusion of these factors would simply make the analysis inordinately complex without achieving significant gains at this time.The major nonhistorical factors affecting the shape of the bill are: (a) the demands for a specific structure because of the particular feeding method and other uses of the bill, (b) the forces acting on the bill, (c) the necessary size of the bill, and (d) the weight of the bill.These factors are not independent of one another, but are all closely interrelated.The first factor, that of the necessary shape of the bill for the particular feeding method, places definite limitations on the other factors.The remaining factors, in turn, restrict the possible influence of the first.Moreover, the factors of force, size, and weight are so closely interrelated that it is scarcely possible to consider one without the others.This interrelationship between these factors will be come increasingly clear throughout the paper.Much of the previous work has concentrated on the influence of the particular mode of feeding; the general correlation between bill shape and feeding method is reasonably well established.I would like, in this paper, to concentrate attention on the factors of force, size, and weight which are still little understood.Jan.