A long tail of truth and beauty: A zigzag pattern of feather formation explains the symmetry, complexity, and beauty of the peacock’s tail

One hundred and fifty years after the publication of Darwin’s sexual selection theory, the problem of the peacock’s train remains unsolved. Darwin assumed that the peacock’s long train was maladaptive and was the indirect effect of selection by female mate choice based on the train’s beauty. While a relationship between the feathers’ elaborate features and mating success has been shown, the concept of eyespots as the basis of female choice remains controversial. We examined the anatomical plan underlying feather development using museum specimens and observed a zigzag pattern of feather follicles that determined both the number and the hexagonal arrangement of eyespots on the train as well as, strikingly, the individual eyespots’ color rings. While the zigzag pattern explains the symmetry, complexity, and structural beauty of the peacock’s train, it also precludes individual eyespot variation. The only available variation in eyespot number is expected to be due to annual addition of new rows of 10/11 feathers as a function of age, giving rise to an inherently determined eyespot number. New insights show that eyespot number and feather length are developmentally correlated and an asymptotic function of a male’s age, that their effects on female choice would be confounded and inseparable, and that male vigor would be a crucial factor affecting male fitness. Females may not always choose males with the largest number of eyespots, as older males may lack vigor. We propose a multimodal model of female choice based on male size, vigor, and beauty where females see eyespot and train size not as separate traits but as one complex trait combining both. The new model may be able to explain conflicting results and why eyespot number alone may not be sufficient to explain female choice. Beauty is truth, truth beauty. Keats


57
The Indian blue peacock's, Pavo cristatus, elaborate and long tail (we use tail and train 58 interchangeably, as appropriate-former to signify the long horizontal tail, the latter in expanded 59 vertical position) has long represented a paradigmatic case for the theory of sexual selection by 60 female choice. However, even after 150 years, the problem of the evolution of the peacock's 61 long tail remains unsolved-we still do not know the basis (target) of female choice in peafowl. 62 Darwin (1859) recognized the peacock's long tail as a problem for his theory of evolution by 63 natural selection as he conjectured it was too long to be of adaptive use to the animal; therefore, 64 it was maladaptive. Unlike in other animals, where a sexually selected trait may be directly under may prefer to mate with males who possess more beautiful and elaborate tails (Darwin, 1871). It 70 was thought that this reproductive advantage enjoyed by males with more elaborate tails would 71 compensate for any loss of male fitness such as reduced survivorship due to predation. This 72 explanation sets the stage for research to focus on elucidating how females assess "beauty" or 73 attractive traits (in peacocks and other birds) in their choice of mates (Andersson, 1994). 74 Two key requisites for evolutionary theory, be it via natural or sexual selection, are variation and 75 heritability. If the peacock's train is a target of female choice, then there must be genetic or 76 phenotypic variation in female preference that would directly or indirectly depend on variation in 77 the peacock's train morphology (size, shape, and/or coloration). Although female choice is 78 widely assumed to be responsible for the evolution of the peacock's tail, research on this matter  While much work has been done to investigate the basis of female choice, less work has 96 addressed the structure of the trait, i.e., the train itself. The peacock's train is a complex 97 structure, with the upper train coverts comprising a diverse variety of feather types, each varying 98 in structure, iridescence level, color pattern and symmetry (see Lillie, 1942 and Manning and 99 Hartley, 1991 for details). The complexity and the bilateral symmetry of the train (Figure 1) can 100 be appreciated by connecting the eyespots in any direction (see Figure 2A). To achieve this 101 remarkable symmetry in a fan formation, the feather follicles must develop in a specific 102 arrangement at their origin, i.e., on the uropygium. Upon failing to find significant variation peacock's upper-tail covert feathers or train feathers) would preclude genetic variation in the 114 number of individual eyespots. Accordingly, the only source of intrinsic variation in feather and 115 eyespot number would be between age classes, arising from the age-dependent addition of new 116 rows of feathers. On the other hand, feather length-being a quantitative trait-is expected to 117 show variation within as well as between age classes. Thus, all intrinsic between-individual 118 variation in eyespots may be related to animal age, which may reach a developmentally pre-

122
In this report based on observations on museum specimens of peacock tails, we show that a 123 simple zigzag pattern of feather formation giving rise to hexagonal arrangement of eyespots 124 uniquely determines the symmetry, complexity, and beauty of the peacock's tail. Hexagonal 125 arrangement of identical circles is the most efficient form of packing, and it was shown to apply 126 to the origin of feathers in birds (Sengel, 1976). By beauty, in this manuscript, we only mean the 127 complexity of the eyespot distribution and the color patterns and do not want to confuse with 128 everyday and wider meaning of the word beauty. Second, we show that eyespot feathers 129 originate in alternate, zigzagging rows of 10/11 annually, making the total number of eyespots an 130 intrinsically determined trait. Third, we argue that both feather number (Manning, 1989) and 131 feather growth are asymptotic functions of age that-when considered with the male vigor which    158 We counted the number of eyespots, eyespot feathers, and fishtail feathers displayed by the 159 included specimens (Figure 3). In the cases where an eyespot was missing due to damage, we 160 counted it as if it were present to estimate the total number of eyespots. Very few of the samples 161 had a uropygium that was in good condition. Of the museum specimens six had intact uropygia 162 in P. cristatus and one in P. muticus. Wherever we were certain that the integrity of the sample   To simulate and illustrate the train's eyespot distribution, we used the following observations 174 and/or assumptions: (1) Based on our overall observations (7 P. cristatus, and 1 P. muticus), we 175 concluded that each cell on the uropygium ( Figure 1B) represents the base of a corresponding 176 feather (attempting to determine direct one-to-one correspondence would have required 177 damaging the specimens); (2) we used a row of 10 or 11 dots in the shape of the (oval) 178 uropygium to represent train feathers but we used a flat and not a convex surface as the latter was 179 not possible. In the result section we discuss why using a convex surface in the simulation would      Second, the zigzag arrangement of feathers appeared as an invariant trait in our sample (Table 1). 226 While this one-to-one correspondence between clearly visible follicle insertion patterns and train 227 morphology may be expected, our data suggest that the developmental plan does not permit 228 random (one feather at a time) variation in eyespot number (Table 1).   Fifth, number of eyespot feathers and feather length are independent traits that vary 239 asymptotically as a function of age (data not shown). This is consistent with Manning's (1989) 240 finding that eyespot number increases during the first 4 to 7 years of the animal's life and 241 thereafter increases more slowly or remains effectively constant. 242 3.3. Interspecies variation: P. cristatus vs. P. muticus 243 We also had access to a small number of P. muticus (green peacock) specimens (N = 7) from 244 Southeast Asia (Table 1; Figure 4) for comparative analyses, which could provide clues as to

Speciation in-silico:
The origin of the train's symmetry and complexity 263 We investigated the significance of the arrangement of feathers in rows of 10/11 and their 264 "zigzag" alignment (see Figure 2). To achieve this, we used graphic design software to

283
This is what we would see from a distance.

285
We further explored what the eyespots distribution pattern would be like if the feathers were 286 arranged in 10/11 parallel rows instead of the zigzag arrangement that we observed in this study.

287
Notably, the train eyespot pattern that we obtained is remarkably different from the 10/11 zigzag 288 pattern. Our reconstruction of a parallel arrangement yielded a palm-leaf-like pattern that fanned 289 out in parallel rows of eyespots rather than the pattern observed in a peacock's train on display 290 ( Figure 5B). While both patterns are striking, the 10/11 zigzag arrangement yields a denser and 291 uniformly symmetrical arrangement of eyespots, as seen in the animal.

292
Because the above results raised the question of why 10 or 11 rows were observed, we simulated    rows on the uropygium shown in Figure 3, but many of them would be too small to be visible 383 through photography or to be effective to illicit female response. The idea that the maximum 384 eyespot number in adult animals is invariant within and across populations is consistent with the 385 annual addition of new rows of feathers, which occurs rapidly at a younger age (~4-7 years), 386 while slowed growth or complete cessation of new feather development occurs after a certain age 387 (Manning, 1989). It is important to point out that the lack of variation in eyespot number applies 388 to the lifetime total number and not to the population, which may contain eyespot variation 389 arising from different age classes.  which feather number may increase at a slower rate (Manning, 1989).   beauty, and vigor and suggest that it is not the number of eyespots but the size of the eyespot-