The fractal dimension of a conspicuous ornament varies with mating status and shows assortative mating in wild red-legged partridges (Alectoris rufa)

Complex body designs, such as plumage ornaments in birds, can be described by fractal geometry. These complex patterns could have a role as visual signals during courtship and social interactions, but an empirical validation in the wild is currently lacking. Here, we investigated whether the fractal dimension (FD) of a complex plumage pattern displayed by red-legged partridges Alectoris rufa could function as a potential sexual signal. We captured wild birds early in the breeding season and tested if mated and unmated birds differed in the FD of their conspicuous melanin-based black bib. We also tested if the FD of the black bib was correlated within the pair, looking for evidence of assortative mating based on the expression of this trait. We simultaneously assessed similar effects in other ornamental traits (black bib size, white throat patch and black flank band surface, redness of the eye rings and bill). Mated birds showed higher black bib FD values than unmated ones. Mated males, but not females, also displayed a larger black bib. Moreover, the black bib FD (but not the trait size) and the white throat patch surface showed assortative mating. Finally, females with higher black bib FD showed smaller black flank band surface, suggesting a trade-off in the expression of the two melanin-pigmented plumage traits. This provides unique and novel indication for the shape complexity of a pigmented trait, here described by its fractal dimension, to be potentially under sexual selection in a wild animal.A.C. was funded by a Juan de la Cierva-formación postdoctoral grant (FJCI-2015-23536; Ministerio de Economía, Industria y Competitividad, MINECO). Financial support was obtained from the projects PII1I09-0271-5037, PII1C09-0128-4724 and SBPLY/17/180501/000468 from the JCCM and CGL2009-10883-C02-02 from Ministerio de Ciencia e Innovación (Spain). F.C. was supported by the University of Maryland.Peer Reviewe