Ann. Zool. Fennici 34: 133–137 ISSN 0003-455X Helsinki 27 May 1997 © Finnish Zoological and Botanical Publishing Board 1997 Commentary Why some measures of fluctuating asymmetry are so sensitive to measurement error Mats Björklund & Juha Merilä Björklund, M. & Merilä, J., Department of Zoology, Uppsala University, Villavägen 9, S-752 36 Uppsala, Sweden; Present address: Merilä, J., Laboratory of Ecology and Animal Systematics, Department of Biology, Turku University, FIN-20014, Finland Received 26 March 1997, accepted 1 April 1997 Introduction Fluctuating asymmetry has recently become a sub- ject of much theoretical and empirical interest as well as causing considerable discussion (Houle 1997, Leamy 1997, Markow & Clarke 1997, Møll- er & Thornhill 1997ab, Palmer & Strobeck 1997, Pomiankowski 1997, Swaddle 1997, Whitlock & Fowler 1997). This interest has been nurtured by results indicating that fluctuating asymmetry is caused by stress factors operating on the devel- opmental system (Van Valen 1962, Palmer & Strobeck 1986, Parsons 1990, 1992), and thus may be a potential indicator of the amount of stress imposed upon a given population, or conversely, the ability of individuals to cope with stress dur- ing their ontogeny. As all other estimators, measurements of fluc- tuating asymmetry are affected by measurement error (e.g. Palmer & Strobeck 1986, Swaddle et al. 1994, Merilä & Björklund 1995). This is par- ticularly serious in the case of fluctuating asym- metry since, by definition, it is expected to take on very small values. It has previously been shown (Swaddle et al. 1994, Merilä & Björklund 1995) that the most commonly used measure of fluctu- ating asymmetry, i.e. the absolute difference be- tween the sides (|R–L|), is highly sensitive to meas- urement error. While the fact that this measure is prone to high measurement error has been known for some time, the reason and its possible impli- cations have not been examined. Furthermore, on the basis of our results we think that measure- ment error is a very important issue that has been largely overlooked in the discussion. Theory In this note, we will give an explanation based on basic statistical theory why both the signed and the unsigned difference measures are so sensitive to measurement error. By doing that, we will use the approach taken by Whitlock (1996) with a slight, but very important modification. Generally, fluc- tuating asymmetry (FA) is defined as random de- viations from perfect symmetry of bilateral traits among a set of individuals (Palmer & Strobeck 1986). Random in this case means random in re- lation to side, either the left or the right side being larger, while the mean on average is zero. Thus, it is clear that FA is a population measure of indi- vidual asymmetry. FA can be expressed as the signed difference of the sides (L–R) or the un- signed (absolute) difference among the sides (| L–R|). If we assume that the measurements of each of