A New Fluctuating Asymmetry Index, or the Solution for the Scaling Effect?

Two principal methods are commonly employed for the estimation of developmental instability at the population level. Some studies use variances of morphological traits (σ2p), while others use fluctuating asymmetry (FA). In both cases, differences in the degree of developmental instability can be tested with an F-test, which is the most common way to compare variances. However, the variance is expected to scale proportionally to the square of the mean as there is a tendency in biological data for σ2p to scale proportionally to the square of the mean ( ): σ2p = Z ξ, where ξ is the scaling exponent, which is expected to be two for pure statistical reasons, is the mean of the trait and Z is a measure of individual-level variability. Because of this scaling effect, the fluctuating asymmetry will be affected, FA is estimated as the variance between the right and the left sides of a trait (σ2r − l = σ2r + σ2l − 2rσrσl), where σ2r and σ2l are the variances of the right and the left trait values, respectively. In this paper, we propose a novel method that allows an exact correction of the scaling effect, which will enable a proper comparison of the degree of fluctuating asymmetry for a trait. The problem of the scaling of the FA with the trait size is quite crucial if FA is to be considered an indicator of fitness or an indicator of environmental or genetic stress, as different stresses or fitness levels are typically accompanied by a change of the traits’ .

[1]  S. Kark,et al.  Fluctuating asymmetry as an indicator of fitness: can we bridge the gap between studies? , 2002, Biological reviews of the Cambridge Philosophical Society.

[2]  A. Møller,et al.  Asymmetry, Developmental Stability, and Evolution , 1998 .

[3]  V. Loeschcke,et al.  On the brink between extinction and persistence , 2008, Biology Direct.

[4]  V. Loeschcke,et al.  The increase of fluctuating asymmetry in a monoclonal strain of collembolans after chemical exposure - discussing a new method for estimating the environmental variance , 2004 .

[5]  L. R. Taylor,et al.  Aggregation, Variance and the Mean , 1961, Nature.

[6]  Anders Pape Møller,et al.  A meta-analysis of fluctuating asymmetry in relation to heterozygosity , 1999, Heredity.

[7]  L. Zhivotovsky,et al.  Effects of extreme temperatures on phenotypic variation and developmental stability in Drosophila melanogaster and Drosophila buzzatii , 1997 .

[8]  V. Loeschcke,et al.  Implementation of mixture analysis on quantitative traits in studies of neutral versus selective divergence , 2012 .

[9]  V. Loeschcke,et al.  Variation of skull morphometry of Eurasian otters (Lutra lutra) in Denmark and Germany , 1998 .

[10]  V. Loeschcke,et al.  Morphological variability and developmental instability in subpopulations of the Eurasian badger (Meles meles) in Denmark , 2003 .

[11]  V. Loeschcke,et al.  Variation in body size and life history traits in Drosophila aldrichi and D. buzzatii from a latitudinal cline in eastern Australia , 2000, Heredity.

[12]  V. Loeschcke,et al.  Maternal and grandmaternal age effects on developmental instability and wing size in parthenogenetic Drosophila mercatorum , 2004, Biogerontology.

[13]  Orkun S. Soyer,et al.  The Details in the Distributions: Why and How to Study Phenotypic Variability This Review Comes from a Themed Issue on Systems Biology Experimental Methods for Studying Phenotypic Variability within Genotype Variability between Genotype Variation between Plate Technical Variation between Environment , 2022 .

[14]  V. Loeschcke,et al.  Intraspecific hybridization, developmental stability and fitness in Drosophila mercatorum , 2002 .

[15]  W. Valdar,et al.  Detecting Major Genetic Loci Controlling Phenotypic Variability in Experimental Crosses , 2011, Genetics.

[16]  R. Fisher.  The relation between variability and abundance shown by the measurements of the eggs of British nesting birds , 1937 .

[17]  T. Markow,et al.  Developmental Instability: Its Origins and Evolutionary Implications , 1994, Contemporary Issues in Genetics and Evolution.

[18]  Windig,et al.  How to compare fluctuating asymmetry of different traits , 1999 .

[19]  D. Falconer,et al.  Introduction to Quantitative Genetics. , 1961 .

[20]  V. Loeschcke,et al.  Developmental stability in the Eurasian Otter (Lutra lutra) in Denmark , 1997 .

[21]  V. Loeschcke,et al.  Developmental instability, hybridization and heterozygosity in stick insects of the genus Bacillus (Insecta; Phasmatodea) with different modes of reproduction , 2006 .

[22]  L. Lens,et al.  Developmental instability and inbreeding in natural bird populations exposed to different levels of habitat disturbance , 2000 .

[23]  V. Loeschcke,et al.  Effect of the 1990 die‐off in the northern Italian seas on the developmental stability of the striped dolphin Stenella coeruleoalba (Meyen, 1833) , 2000 .

[24]  V. Loeschcke,et al.  Consequences of reduced genetic variance on developmental instability estimators , 2003 .

[25]  M. Tokeshi.  On the mathematical basis of the variance-mean power relationship , 1995, Researches on Population Ecology.

[26]  D. Falconer.  Introduction to quantitative genetics. 1. ed. , 1984 .

[27]  V. Loeschcke,et al.  Effects of temperature and maternal and grandmaternal age on wing shape in parthenogenetic Drosophila mercatorum , 2007 .

[28]  F. Allendorf,et al.  Fluctuating asymmetry as an indicator of stress: Implications for conservation biology. , 1989, Trends in ecology & evolution.

[29]  V. Loeschcke,et al.  Developmental instability as an estimator of genetic stress , 2006, Heredity.

[30]  Mats Björklund,et al.  Scaling of the mean and variance of population dynamics under fluctuating regimes , 2014, Theory in Biosciences.

[31]  The effect of maternal and grandmaternal age in benign and high temperature environments , 2005, Experimental Gerontology.

[32]  M. Delibes,et al.  Morphological consequences of range fragmentation and population decline on the endangered Iberian lynx (Lynx pardinus) , 2005 .

[33]  C. Strobeck,et al.  Fluctuating Asymmetry: Measurement, Analysis, Patterns , 1986 .

[34]  V. Loeschcke,et al.  Lerner’s theory on the genetic relationship between heterozygosity, genomic co-adaptation, and developmental instability revisited , 2006 .

[35]  V. Loeschcke,et al.  The consequences of the variance-mean rescaling effect on effective population size , 2007 .

[36]  V. Loeschcke,et al.  Heat-induced maternal effects in Drosophila mercatorum and its evolutionary consequences , 2005 .

[37]  V. Loeschcke,et al.  Developmental instability in sexually reproducing and parthenogenetic populations of Bacillus rossius rossius and Bacillus rossius redtenbacheri , 2001 .

[38]  C. Pertoldi,et al.  Consequences of Environmental Fluctuations on Taylor’s Power Law and Implications for the Dynamics and Persistence of Populations , 2012, Acta Biotheoretica.

[39]  V. Debat,et al.  Phenotypic and genetic variability of sternopleural bristle number in Drosophila melanogaster under daily thermal stress: developmental instability and anti-asymmetry , 2006 .

[40]  R. Frankham,et al.  Can fluctuating asymmetry be used to detect inbreeding and loss of genetic diversity in endangered populations? , 2000 .

[41]  R. Carvalheiro,et al.  Genetic and environmental heterogeneity of residual variance of weight traits in Nellore beef cattle , 2012, Genetics Selection Evolution.

[42]  A. Hoffmann,et al.  THE ASSOCIATION BETWEEN FLUCTUATING ASYMMETRY, TRAIT VARIABILITY, TRAIT HERITABILITY, AND STRESS: A MULTIPLY REPLICATED EXPERIMENT ON COMBINED STRESSES IN DROSOPHILA MELANOGASTER , 1999, Evolution; international journal of organic evolution.

[43]  D. C. Freeman,et al.  Developmental stability: A sensitive indicator of populations under stress , 1993 .

[44]  Sasha F. Levy,et al.  Network Hubs Buffer Environmental Variation in Saccharomyces cerevisiae , 2008, PLoS biology.

[45]  V. Loeschcke,et al.  The use of fluctuating asymmetry and phenotypic variability as indicators of developmental instability: a test of a new method employing clonal organisms and high temperature stress , 2003 .

[46]  Shmuel Raz,et al.  Fluctuating Asymmetry: Methods, Theory, and Applications , 2010, Symmetry.

[47]  V. Loeschcke,et al.  A new method for estimating environmental variability for clonal organisms, and the use of fluctuating asymmetry as an indicator of developmental Instability. , 2001, Journal of theoretical biology.

[48]  Guk-Rwang Won.  American Society for Testing and Materials , 1987 .

[49]  V. Loeschcke,et al.  Heat stress and age induced maternal effects on wing size and shape in parthenogenetic Drosophila mercatorum , 2005, Journal of evolutionary biology.

[50]  V. Loeschcke,et al.  The phenotypic variance gradient – a novel concept , 2014, Ecology and evolution.

[51]  V. Loeschcke,et al.  Craniometrical variability and developmental stability. Two useful tools for assessing the population viability of Eurasian otter (Lutra lutra) populations in Europe. , 2000 .

[52]  M. Björklund,et al.  Why some measures of fluctuating asymmetry are so sensitive to measurement error , 1997 .