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Measurement bias and fluctuating asymmetry estimates

Fluctuating asymmetry (FA), that is, small, random deviation from symmetry in bilateral characters (Van Valen 1962; Palmer & Strobeck 1986), is an increasingly popular measure of developmental instability. As such, it is used for many purposes in relation to the evaluation of environmental or genetic variation in population or individual quality (Markow 1995; Møller & Swaddle 1998). It may also be involved in mate choice, as an honest signal of individual quality (Watson & Thornhill 1994). A number of theoretical studies has shown that measurement error (i.e. random variation arising from inaccuracy of measurement devices) can lead to overestimation of FA (Palmer & Strobeck 1986; Palmer 1994; Swaddle et al. 1994; Merilä & Björklund 1995; Björklund & Merilä 1997). Standard methods based on replicate measures are now available to avoid this pitfall and produce FA estimates as free from measurement error as possible (Palmer & Strobeck 1986). These methods usually assume that the right and left sides of an individual are measured independently and are therefore subject to uncorrelated measurement errors (Merilä & Björklund 1995; Björklund & Merilä 1997; and implicit in Palmer & Strobeck 1986). However, in many cases, practical constraints may lead researchers to measure the left and right sides of a given individual successively or during the same session (when sample size is too big to measure all individuals at once). Therefore, the data are in the form of pairs of left and right values that share potential session bias, such as the calibration of an optical system, the light and position in which objects are observed and the state of mind of the experimenter. The influence of such biases has never been modelled, although they have been mentioned by Møller & Swaddle (1998, page 29). Here we describe the statistical consequences of such biases and show: (1) that they are not fatal to the estimation of FA; (2) that there are some simple ways to account for them when estimating either individual asymmetry or population FA; and (3) that the best strategy is always to take left and right values of an individual during the same session rather than in different sessions. We assume that several replicate measures of the same individual are taken on different sessions, although left and right values for that individual are measured during the same session. Replicate k of the trait value for side i of individual j is determined as follows