Table 1 Simulation and theoretical values of parameters under stabilizing selection with state-dependent mutations
Nδγ (× 102)Vg (× 102)
Sim.Mat.App. 1App. 2Sim.Mat.App. 1App. 2Sim.Mat.App. 1App. 2Stab. sel.
MeanS.D.MeanS.D.MeanS.D.
κ = 25014.9 (0.3)6.7616.616.516.50.602 (0.012)0.2700.6720.6600.6602.89 (0.04)0.9762.832.882.872.97
z0 = 01007.54 (0.21)4.778.578.458.400.610 (0.017)0.3810.6910.6760.6856.14 (0.06)1.425.645.775.735.88
2004.37 (0.16)3.624.414.284.220.718 (0.026)0.5800.7150.6850.70212.7 (0.1)2.0410.111.811.411.5
4002.11 (0.11)2.422.242.152.100.711 (0.035)0.7740.7360.6880.72425.4 (0.1)2.9121.523.122.522.2
z0 = 205026.2 (0.3)6.7926.526.026.01.06 (0.01)0.2731.061.041.052.94 (0.04)0.9582.862.912.903.17
10013.3 (0.2)4.9013.613.313.31.08 (0.02)0.3931.091.071.086.05 (0.06)1.415.705.835.796.27
2007.13 (0.15)3.416.956.756.691.17 (0.02)0.5471.131.081.1112.5 (0.1)2.0411.211.711.512.3
4004.02 (0.11)2.423.583.393.321.34 (0.04)0.7801.171.091.1423.8 (0.1)2.7421.723.322.723.7
κ = 45031.9 (0.3)6.9133.633.033.31.29 (0.01)0.2771.351.321.324.40 (0.06)1.424.204.294.194.95
z0 = 010016.6 (0.2)5.1117.316.916.81.34 (0.02)0.4111.391.351.379.00 (0.08)1.758.388.628.759.80
2008.54 (0.16)3.628.978.568.451.39 (0.03)0.5801.441.371.4018.6 (0.1)2.5416.417.317.119.2
4004.70 (0.11)2.494.634.314.201.57 (0.36)0.7931.511.391.4435.0 (0.1)3.2631.434.633.737.0
z0 = 205042.0 (0.3)7.1843.542.542.51.68 (0.01)0.2871.741.701.714.42 (0.05)1.214.354.444.435.54
10021.6 (0.2)5.0222.421.821.81.75 (0.02)0.4021.801.741.769.31 (0.07)1.628.658.918.8610.1
20011.8 (0.2)3.6111.511.010.91.94 (0.03)0.5751.851.761.8018.7 (0.1)2.5316.917.817.621.5
4004.90 (0.11)2.485.985.555.431.63 (0.04)0.8011.961.781.8533.0 (0.1)3.3032.435.734.941.5
  • N is the population size; δ is the difference between the optimal and mean values of the trait, divided by a; γ is the scaled selection coefficient 4Ns for an A2 variant; Vg is the trait variance; κ is the mutational bias parameter; b is the ratio of the optimal value of the trait to ma. The mutation rate is u = 1 × 10−5; the selection parameters are S = 0.01, m = 1000, a = 0.1 (Sa2 = 0.0001). The columns headed by Sim. are values obtained from 500 stochastic simulations of each parameter set, with the mean in the top part of each cell, and the standard error (in parentheses); the standard deviations are given to the right of the mean. The value of γ is obtained by averaging 4NSa2(2δ + 2qi – 1) over all segregating sites. The columns headed by Mat. give the expected values for the relevant parameters obtained from iterations of the matrix equation for the probability distribution vector, f, to near to its equilibrium. The columns headed by App. 1 show the approximations for δ*, γ, and Vg* given by Equations A.3a, A.1, and A.4b, respectively. The columns headed by App. 2 show the values of these parameters using Newton–Raphson iteration of Equation A.2, as described in the Appendix, where γ is estimated as (1 – q*)γ2q*γ1 . The column headed by Stab. sel. are the approximate equilibrium genetic variances under pure stabilizing selection (δ* = 0), given by Barton (1989, Equation 8).