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Results of numerical simulations Hypothetical repeatability of single trait unsigned asymmetry (R) and the coefficient of variation of DS (CV-DS) and instability (CV-DI) for simulated datasets were the distribution of DS followed a beta-distribution with different shapes (Fig.1). Results are means (SD) of 1000 samples of 10000 observations. |
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| β1 |
β2 |
shape of β-distribution |
CV-DS |
CV-DI |
R |
|
|
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| Symmetrical distributions |
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|
|
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| 1 |
1 |
Uniform |
0.58 (0.004) |
0.58 (0.004) |
0.16 (0.008) |
| 2 |
2 |
Symmetric around 0.5 |
0.45 (0.003) |
0.45 (0.003) |
0.10 (0.007) |
| 5 |
5 |
Symmetric around 0.5 |
0.30 (0.002) |
0.30 (0.002) |
0.04 (0.008) |
| 10 |
10 |
Symmetric around 0.5 |
0.14 (0.001) |
0.14 (0.001) |
0.01 (0.010) |
| 0.75 |
0.75 |
Bimodal |
0.63 (0.004) |
0.63 (0.004) |
0.20 (0.006) |
| 0.5 |
0.5 |
Bimodal |
0.71 (0.005) |
0.71 (0.005) |
0.25 (0.006) |
| 0.1 |
0.1 |
Bimodal |
0.90 (0.008) |
0.90 (0.008) |
0.40 (0.004) |
| 0.05 |
0.05 |
Bimodal |
1.03 (0.01) |
1.03 (0.008) |
0.41 (0.004) |
|
|
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| Skewed unimodal distributions |
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|
|
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| 3 |
5 |
Right skewed |
0.43 (0.003) |
0.26 (0.002) |
0.04 (0.010) |
| 2 |
5 |
Right skewed |
0.56 (0.004) |
0.21 (0.002) |
0.02 (0.009) |
| 1 |
5 |
Right skewed |
0.81 (0.005) |
0.17 (0.002) |
0.01 (0.009) |
| 1 |
10 |
Right skewed |
0.93 (0.007) |
0.09 (0.007) |
0.00 (0.009) |
| 0.75 |
1 |
Right skewed |
0.69 (0.005) |
0.52 (0.004) |
0.14 (0.007) |
| 0.5 |
1 |
Right skewed |
0.89 (0.006) |
0.45 (0.004) |
0.12 (0.007) |
| 0.1 |
1 |
Right skewed |
2.16 (0.02) |
0.22 (0.004) |
0.03 (0.008) |
| 0.05 |
1 |
Right skewed |
3.13 (0.04) |
0.16 (0.003) |
0.02 (0.009) |
| 5 |
3 |
Left skewed |
0.26 (0.002) |
0.43 (0.004) |
0.08 (0.009) |
| 5 |
2 |
Left skewed |
0.22 (0.002) |
0.56 (0.004) |
0.13 (0.008) |
| 5 |
1 |
Left skewed |
0.18 (0002) |
0.80 (0.005) |
0.22 (0.007) |
| 10 |
1 |
Left skewed |
0.09 (0.001) |
0.91 (0.007) |
0.26 (0.007) |
| 1 |
0.75 |
Left skewed |
0.52 (0.004) |
0.70 (0.005) |
0.22 (0.007) |
| 1 |
0.5 |
Left skewed |
0.45 (0.004) |
0.90 (0.006) |
0.30 (0.006) |
| 1 |
0.1 |
Left skewed |
0.22 (0.004) |
2.15 (0.02) |
0.55 (0.002) |
| 1 |
0.05 |
Left skewed |
0.17 (0.004) |
2.85 (0.04) |
0.58 (0.002) |
|
|
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| Asymmetric bimodal distributions |
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|
|
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| 0.5 |
0.75 |
Right asymmetric |
0.82 (0.006) |
0.54 (0.005) |
0.17 (0.007) |
| 0.1 |
0.75 |
Right asymmetric |
2.01 (0.021) |
0.27 (0.004) |
0.06 (0.008) |
| 0.05 |
0.75 |
Right asymmetric |
2.89 (0.037) |
0.19 (0.004) |
0.03 (0.009) |
| 0.1 |
0.5 |
Right asymmetric |
1.77 (0.017) |
0.35 (0.005) |
0.10 (0.008) |
| 0.75 |
0.5 |
Left asymmetric |
0.55 (0.005) |
0.82 (0.006) |
0.28 (0.006) |
| 0.75 |
0.1 |
Left asymmetric |
0.28 (0.004) |
2.00 (0.019) |
0.54 (0.002) |
| 0.75 |
0.05 |
Left asymmetric |
0.19 (0.004) |
2.86 (0.041) |
0.58 (0.001) |
| 0.5 |
0.1 |
Left asymmetric |
0.35 (0.005) |
1.75 (0.018) |
0.51 (0.001) |
Van Dongen and Lens BMC Evolutionary Biology 2002 2:11 doi:10.1186/1471-2148-2-11 |
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