Palmer, A.R. 1994. Fluctuating asymmetry analyses: A primer. p. 335-364. In: Developmental Instability: Its Origins and Evolutionary Implications. (T. Markow, Ed.). Kluwer, Dordrecht.
(download a portable-document-file (pdf) version of the original MS with figures; size of download is 201K= 35 pages).
1.0 Fluctuating asymmetry and developmental stability: A cursory overview
2.1 Asymmetry in an individual vs pattern of asymmetry variation in a sample
2.2 Patterns vs. processes
3.0 Indices for describing the level of FA in a sample
3.1 FA indices
3.2 Pros & cons of different FA indices
3.3 Relationships among FA indices
3.4 General recommendations regarding FA indices
4.0 Choice of traits
4.1 Pros & cons of meristic vs metrical traits
4.2 Two idiosyncrasies of meristic traits
4.3 Single vs multiple traits
4.4 Choose traits that are developmentally independent
4.5 Choose traits that exhibit 'ideal' FA
5.0 Sample sizes
6.0 Measurement error
6.1 Why is measurement error a particular concern in studies of FA?
6.2 Error in meristic traits
6.3 Error in metrical traits
6.4 Quantizing error in image analysis systems
6.5 Recommended procedure for conducting repeated measurements
6.6 Tests for the significance of FA relative to measurement error in metrical traits
6.7 Tests for the significance of FA relative to counting error in meristic traits
7.0 Directional Asymmetry
7.1 Why test for DA in studies of FA?
7.2 Tests for DA
8.0 Departures from normality (e.g. antisymmetry and skew)
8.1 Why test for departures from normality in studies of FA?
8.2 Tests for departures from normality: general comments
8.3 Tests for departures from normality in either meristic or metrical traits
8.4 Tests for departures from normality in small samples of metrical traits
9.0 What to do when traits depart from ideal FA
10.0 Size dependence of FA
10.1 Why is size-dependence a concern in studies of FA?
10.2 Tests for size dependence of FA within samples
10.3 Tests for size dependence of FA among samples
11.0 Care when conducting multiple tests
12.0 Adequate presentation of descriptive data
13.0 Significance tests for differences in FA
13.1 Between two samples
13.2 Among three or more samples
13.3 Among samples using multiple traits simultaneously
14.0 Correlations of subtle asymmetries among traits
14.1 Between parents and offspring (heritability)
14.2 Among individuals: Are some individuals more stable developmentally than others?
14.3 Among samples
15.0 Correlations between asymmetry & fitness: Can asymmetry predict mate choice?
16.0 Checklist for studies of FA
16.0 Checklist for studies of FA
- ____ Has FA variation been examined in several developmentally independent traits? Because the 'signal' of FA variation is often very weak, and can sometimes be biased in unexpected ways, correlated patterns of FA variation among several traits can greatly strengthen inferences about levels of developmental stability (Sect. 4.0).
- ____ If meristic traits have been used, have concerns about the dependence of FA on the proximity of mean (R - L) to whole integer values been adequately addressed? (Sect. 4.2)
- ____ Are sample sizes large enough to be able to detect differences in FA among samples? (Sect. 5.0)
- ____ Has the measurement protocol been described in sufficient detail? What landmarks were used to measure particular features? Were repeat measurements conducted totally blind (Sect. 6.5)? Did more than one observerč take measurements, and if so did the estimate of measurement error include differences among observers? Did any dimensions share a common landmark?
- ____ Was measurement error estimated accurately? In other words, did it include all possible sources of variation: temporal variation in observer accuracy, among-observer variation if more than one observer took measurements, variation in ease of measurement for live and dead specimens, digitizing or quantizing error (Sect. 6.5)?
- ____ Is FA significantly larger than measurement error in all traits? Because measurement error yields the same pattern of between-sides variation as FA, such a test is essential to all studies of FA (Sect. 6.0). This is perhaps the most common (and important!) oversight in studies of FA.
- ____ Do all traits exhibit ideal FA of R - L (i.e. mean zero, normal variation)? If not, have those traits departing from ideal FA in due to DA, antisymmetry or skew been eliminated from the analyses (Sects. 7.0, 8.0)? If they must be included, have tests been conducted to verify they they have not biased FA indices or biased the conclusions about differences among samples (Sect. 9.0)?
- ____ Does asymmetry correlate with trait size? If so, have the appropriate corrections for such dependence been applied (Sect. 10.0) and has the size correction been confirmed to eliminate any dependence of asymmetry on size? If not, have the proper FA indices been used (i.e. those that do not correct for trait size; Sect. 3.0)?
- ____ Where multiple related statistical tests have been conducted, have the P-values been corrected to reflect this fact? (Sect. 11.0)
- ____ Have the data describing bilateral variation among traits and among samples been presented in sufficient detail? Has more than one index of FA been included with these descriptive data (Sects. 3.4, 12.0)?
- ____ Have the proper statistical tests been used to test for differences in FA among samples? (Sect. 13.0)
- ____ If heritability estimates for asymmetries are presented have the analyses distinguished between heritability of developmental stability vs. heritability of subtle asymmetries? (Sect. 14.1)
- ____ If deviations from symmetry have been used as an index for fitness, have a sufficiently large number of traits been used to obtain valid differences among individuals? (Sects. 14.2, 15.0)
- ____ In the final paper, have terms referring to patterns (which are observed) been kept distinct from those referring to processes (which are inferred)? (Sect. 2.2)
- ____ Have the indices used to estimate FA been identified unambiguously in ALL table and figure legends? (Sect. 3.0)
Original material on this page copyright © A. Richard Palmer. All rights reserved.
(revised Nov. 4, 2002)