Fractal geometry of a complex plumage trait reveals bird's quality

Animal coloration is key in natural and sexual selection, playing significant roles in intra- and interspecific communication because of its linkage to individual behaviour, genetics and physiology. Simple animal traits such as the area or the colour intensity of homogeneous patches have been profusely studied. More complex patterns are widespread in nature, but they escape our understanding because their variation is difficult to capture effectively by standard, simple measures. Here, we used fractal geometry to quantify inter-individual variation in the expression of a complex plumage trait, the heterogeneous black bib of the red-legged partridge (Alectoris rufa). We show that a higher bib fractal dimension (FD) predicted better individual body condition, as well as immune responsiveness, which is condition-dependent in our study species. Moreover, when food intake was experimentally reduced during moult as a means to reduce body condition, the bib's FD significantly decreased. Fractal geometry therefore provides new opportunities for the study of complex animal colour patterns and their roles in animal communication.

[1]  John A. Endler,et al.  A framework for analysing colour pattern geometry: adjacent colours , 2012 .

[2]  John A. Bissonette,et al.  Wildlife and Landscape Ecology: Effects Of Pattern And Scale , 2012 .

[3]  C. Cela-Conde,et al.  Predicting beauty: fractal dimension and visual complexity in art. , 2011, British journal of psychology.

[4]  M. Stevens,et al.  Pattern mimicry of host eggs by the common cuckoo, as seen through a bird's eye , 2010, Proceedings of the Royal Society B: Biological Sciences.

[5]  I. Galván,et al.  The expression of melanin-based plumage is separately modulated by exogenous oxidative stress and a melanocortin , 2009, Proceedings of the Royal Society B: Biological Sciences.

[6]  T. Gluckman,et al.  A method to quantify the regularity of barred plumage patterns , 2009, Behavioral Ecology and Sociobiology.

[7]  L. Barmuta,et al.  Quantifying habitat structure: surface convolution and living space for species in complex environments , 2008 .

[8]  Charles Chubb,et al.  Cuttlefish camouflage: The effects of substrate contrast and size in evoking uniform, mottle or disruptive body patterns , 2008, Vision Research.

[9]  R. Jovani,et al.  Fractal bird nest distribution produces scale-free colony sizes , 2007, Proceedings of the Royal Society B: Biological Sciences.

[10]  I. Cuthill,et al.  Using digital photography to study animal coloration , 2007 .

[11]  G. Bortolotti.  1. Natural Selection and Coloration: Protection, Concealment, Advertisement, or Deception? , 2006, Bird Coloration, Volume 2.

[12]  J. Blas,et al.  Condition and androgen levels: are condition-dependent and testosterone-mediated traits two sides of the same coin? , 2006, Animal Behaviour.

[13]  Nathalie Jacobs.  Springer , 2006 .

[14]  J. Endler,et al.  Comparing entire colour patterns as birds see them , 2005 .

[15]  J. R. Castrejón-Pita,et al.  Fractal Dimension in Butterflies’ Wings: a novel approach to understanding wing patterns ? , 2005, Journal of mathematical biology.

[16]  S. Hartley,et al.  Uses and abuses of fractal methodology in ecology , 2004 .

[17]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[18]  E. García‐Berthou,et al.  On the misuse of residuals in ecology: testing regression residuals vs. the analysis of covariance , 2001 .

[19]  J. Stevenson,et al.  Asymmetry, developmental stability, and evolution , 2000 .

[20]  G. Bortolotti,et al.  Simplifying the phytohaemagglutinin skin‐testing technique in studies of avian immunocompetence , 1999 .

[21]  Bruce J. West,et al.  Multiplicative and Fractal Process in DNA Evolution , 1998 .

[22]  Deborah J. Aks,et al.  Quantifying Aesthetic Preference for Chaotic Patterns , 1996 .

[23]  P. Palmqvist,et al.  Fractal analysis of the Orce skull sutures , 1995 .

[24]  B Burlando,et al.  The fractal geometry of evolution. , 1993, Journal of theoretical biology.

[25]  Craig Loehle,et al.  Home range: A fractal approach , 1990, Landscape Ecology.

[26]  J. Endler.  On the measurement and classification of colour in studies of animal colour patterns , 1990 .

[27]  G Sugihara,et al.  Applications of fractals in ecology. , 1990, Trends in ecology & evolution.

[28]  Bruce T. Milne,et al.  Indices of landscape pattern , 1988, Landscape Ecology.

[29]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[30]  E. Barr.  A common mistake , 1976 .

[31]  H. Cott.  Adaptive Coloration in Animals , 1940 .

[32]  M. Rivera.  R and R , 2012 .

[33]  L. Pérez‐Rodríguez,et al.  Parasites, condition, immune responsiveness and carotenoid-based ornamentation in male red-legged partridge Alectoris rufa , 2009 .

[34]  G. Hill,et al.  Function and evolution , 2006 .

[35]  Ben R. Newell,et al.  Fractals: A Resonance between Art and Nature , 2005 .

[36]  Nikolaos Pandis,et al.  Analysis of Covariance , 2005 .

[37]  Departament de Ciències Ambientals.  On the misuse of residuals in ecology : testing regression residuals vs . the analysis of covariance , 2001 .

[38]  Bruce T. Milne,et al.  Applications of Fractal Geometry in Wildlife Biology , 1997 .

[39]  George Sugihara,et al.  Fractals: A User's Guide for the Natural Sciences , 1993 .

[40]  C. M. Lessells,et al.  Unrepeatable repeatabilities: a common mistake , 1987 .