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Theory of the Growth and Evolution of Feather Shape

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30JOURNAL R.O. PRUMOF EXPERIMENTAL AND S. WILLIAMSON ZOOLOGY (MOL DEV EVOL) 291:30–57 (2001) Theory of the Growth and Evolution of Feather Shape RICHARD O. PRUM* AND SCOTT WILLIAMSON Department of Ecology and Evolutionary Biology, and Natural History Museum, University of Kansas, Lawrence, Kansas 66045 ABSTRACT 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 pro- pose 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 heli- cal 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 param- eter, does not account for growth by differentiation in cell size and shape during later keratiniza- tion. 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 prima- ries. Simulations of feather growth under different parameter values demonstrate that each pa- rameter 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 ma- ture 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 determi- nation 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 mecha- nisms required to evolve different feather shapes to accomplish various functions. J. Exp. Zool. (Mol. Dev. Evol.) 291:30–57, 2001. © 2001 Wiley-Liss, Inc. A basic principle of developmental biology is that The evolution of molluscan diversity involved the complex shapes and spatial patterns are not speci- exploration of this potential shell morphospace. fied in precise detail (Thompson, ’42; Ball, ’98). Feathers are extraordinarily diverse and com- Rather, complex forms are created by fundamen- plex structures. Feathers are the most complex tal physical, chemical, and cellular interactions epidermal appendages found in animals (Lucas whose precise outcome is specified by relatively and Stettenheim, ’72). They are uniquely charac- few critical parameters. Thus, the growth of terized by their complex branched structure and many diverse biological forms can be understood striking diversity in size, shape, color, and tex- in terms of similar general developmental mod- ture (Lucas and Stettenheim, ’72; Brush, ’93, ’96; els and basic parameters (Thompson, ’42; Ball, Prum, ’99). Feathers are branched like plants, but, ’98). However, some biological forms grow by such unlike typical plants, feathers do not grow from distinct mechanisms that they require unique ex- bifurcating shoots. Rather, feathers grow from planatory models that incorporate specific pa- their bases like hairs. Feathers grow from a rameters. For example, the diversity in shape of mollusk shells can be described by a unique de- velopmental model based on the shape of the growing surface, the growth in size of the grow- *Correspondence to: Richard O. Prum, Natural History Museum, Dyche Hall, University of Kansas, Lawrence, KS 66045-2454. ing surface, and the angle of its rotation during E-mail: [email protected] growth around an axis (Raup and Michelson, ’65). Received 31 March 2000; Accepted 27 October 2000 © 2001 WILEY-LISS, INC. GROWTH OF FEATHER SHAPE 31 unique organ—the feather follicle—which is char- shape determination was simplistic and incom- acterized by a cylindrical invagination of a epi- plete. In their exhaustive survey of the morphol- dermal tissue (Lucas and Stettenheim, ’72; Prum, ogy and development of feathers, Lucas and ’99). Feather follicles have evolved a unique de- Stettenheim (’72: 371) wrote only that, “Variations velopmental mechanism—the helical growth of in the rates at which [barb] ridges form and grow barb ridges—in order to grow a branched epider- affect the final lengths of the barbs and hence the mal appendage from its base (Lucas and Stet- shape of the vanes.” This brief statement incor- tenheim, ’72; Prum, ’99). Feathers are amazingly porated the erroneous differential barb ridge diverse in shape, and they range over five orders growth rate hypothesis of Lillie and Juhn (’32), of magnitude in size from less than 1 mm to over but it explicitly hypothesized for the first time that 10 m in certain captive-bred fowl (Young, ’99). the rate of new barb ridge addition is a critical Feathers can function in flight, swimming, ther- determinant of feather shape. Some authors have moregulation, physical protection, visual and tac- noted the role of deciduous barbs in the produc- tile communication, sound production, tactile and ing the racket-tipped rectrices of motmots (Motmo- auditory sensation, foraging, water repellency, and tidae; Beebe, ’10; Wagner, ’59; Bleiweiss, ’87), but even water transport (Stettenheim, ’76). A prelimi- these feather shape changes occur after feather nary conceptual model of the evolution of this mor- growth is completed. Bleiweiss (’87) described the phological and functional diversity requires an morphology of barbs and barbules in a diversity explicit developmental theory of the mechanisms of racket-shaped feathers that lack deciduous by which feather shape is determined. barbs, and are thus determined by follicular The growth and evolution of feather shape di- growth mechanisms. Bleiweiss (’87) proposed that versity have so far eluded any general theory or the reduced barb lengths that create the constric- explicit modeling. The growth of different feather tions in vane width characteristic of these racket- shapes must be understood in terms of the devel- shaped feathers are a consequence of the position opmental mechanisms operating within the fol- in the follicle at which new barb ridges are added, licle collar—the layer of cells at the base of the and their angle of growth toward the dorsal mar- internal epidermal layer of the tubular feather fol- gin. Bleiweiss (’87) correctly identified the role of licle. The anatomical details of feather growth the angle of helical growth of barb ridges in the have been well described (Davies, 1889; Strong, growth of feather shape. However, the hypothesis ’02; Greite, ’34; Hosker, ’36; ’Espinasse, ’39; Lucas that barb length is controlled by the position of and Stettenheim, ’72), and a new generation of new barb ridge addition in the follicle is based on studies is beginning to examine the molecular ba- the inaccurate notion that the follicle has a fixed sis of many features of feather development (e.g., diameter that that can sometimes be greater in Chuong et al., ’90; Chuong, ’93; Nohno et al., ’95; size than the barb and rachis ridges it contains Ting-Berreth and Chuong, ’96a, b; Chuong and (Bleiweiss, ’87). Histological cross-sections of grow- Widelitz, ’98). However, little research has been ing feathers document that follicle diameter is de- done explicitly on the growth of feather shape termined by the barb and rachis ridges it contains, (Lucas and Stettenheim, ’72; Spearman, ’73; Saw- and that new barb ridge addition takes place at a yer et al., ’86; Edelman, ’88; Brush, ’93, ’96). single posterior new barb locus, or, if there is an We have found only a few previous hypotheses aftershaft, at two laterally displaced new barb loci in the literature about the effect of cell growth in (e.g., Strong, ’02; Hosker, ’36; ’Espinasse, ’39; the follicle collar on feather shape. Lillie and Juhn Lucas and Stettenheim, ’72). (’32) proposed that differential growth rates Currently, there is no generalized theory or ex- among barb ridges of the follicle produced the plicit model of the determination of the feather variations in feather shape and symmetry. This shape based on the known mechanisms of devel- hypothesis was quickly falsified (’Espinasse, ’34, opment in the feather follicle. Fortunately, the re- ’39; Hosker, ’36), but has remained surprisingly lationship between developmental mechanisms of influential (e.g., Lucas and Stettenheim, ’72: 371). the follicle and feather shape is amenable to math- Subsequently, ’Espinasse (’39: 281) hypothesized ematical modeling. In this article, we review the that the shape of the feather vane “is clearly de- basic details of feather morphology and growth. termined by (a) the length of the barbs and (b) Next, we discuss the previous literature on feather the angle they take up, when dry, with the ra- barb and rachis ridge growth rates, an under- chis.” ’Espinasse was correct to reject differential standing of which is critical to creating a realistic barb ridge growth rates, but his model of feather theory of feather shape determination. Based on 32 R.O. PRUM AND S. WILLIAMSON our reanalysis of this literature, we propose that cylindrical feather follicle—called the collar the absolute growth rate of the barb and rachis (feather growth is thoroughly reviewed in Lucas ridges, independent of direction, is uniform and Stettenheim, ’72; Prum, ’99). Most of the fol- throughout the follicle collar. We then present a licles that produce all the feathers in a bird’s life six-parameter mathematical model of the growth develop during the first 12 days of life in the egg of pennaceous feathers that is based on known (Lucas and Stettenheim, ’72).
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    COMMENT BOOKS & ARTS topics. To name a few: the mathematical laws that relate growth, flight and locomotion to mass and size (a topic currently experiencing a renaissance); the shapes of cells, bubbles and soap films; geometrical compartmen- talization and honeycombs; corals; banded minerals; the intricate shells of molluscs and of the minuscule protozoan radiolar- ians; antlers and horns; plant shapes; bone microstructure; skeletal mechanics; and the UNLIMITED/SPL TAYLOR/VISUALS GEORGE morphological comparison of species. The book’s central motif is the logarithmic spiral, which appears on the plaque com- memorating Thompson’s former residence in St Andrews. He saw it first in foramini- fera, and again in seashells, horns and claws, insect flight paths and the arrangement of leaves in some plants. This, to Thompson, was evidence of the universality of form and the reduction of diverse phenomena to a few mathematical governing principles. How much influence did On Growth and Form have? Evolutionary and developmen- tal biologists often genuflect to Thompson’s breadth and imagination while remaining sceptical that he told us much of lasting value. Thompson was reacting against the Dar- winism of his age, whereby, in its first flush IN RETROSPECT of enthusiasm, it seemed adequate to account for every feature with a plea to adaptation. Thompson’s insistence that biological form had to make sense in engineering terms was On Growth and Form a necessary reminder. But it did not challenge the idea that natural selection was evolution’s Philip Ball celebrates a classic work on the mathematics scalpel — it merely imposed constraints on the forms that might emerge.