TABLE 2

The performance of 𝔼[Lτ(ρ, x)] as an approximation for the expected length of trans-specificity

ρ =
0.1110
τ = 5
Approximation0.099 0.633 1.178
n = 40.096 (0.009)0.563 (0.219)0.983 (0.516)
n = 80.096 (0.010)0.595 (0.214)1.190 (0.603)
n = 120.096 (0.010)0.603 (0.211)1.276 (0.642)
n = 160.096 (0.010)0.610 (0.215)1.336 (0.668)
n = 200.096 (0.010)0.614 (0.215)1.361 (0.679)
τ = 10
Approximation0.095 0.349 0.378
n = 40.092 (0.014)0.306 (0.162)0.330 (0.188)
n = 80.091 (0.015)0.322 (0.170)0.358 (0.206)
n = 120.091 (0.014)0.321 (0.167)0.365 (0.204)
n = 160.091 (0.014)0.327 (0.165)0.373 (0.211)
n = 200.091 (0.015)0.331 (0.169)0.370 (0.205)
τ = 25
Approximation0.079 0.129 0.129
n = 40.075 (0.021)0.103 (0.070)0.106 (0.068)
n = 80.073 (0.021)0.102 (0.070)0.109 (0.070)
n = 120.073 (0.021)0.103 (0.069)0.108 (0.070)
n = 160.074 (0.021)0.104 (0.071)0.110 (0.071)
n = 200.073 (0.021)0.104 (0.071)0.110 (0.071)
  • All calculations were made at x = 1/2, where approximation (9) can be calculated numerically. Mutation between the two allelic classes was symmetric at rate 0.01 (except for ρ = 0.1, when a rate of 0.001 was used). Samples were evenly distributed among species and allelic classes; i.e., n = 16 means four in each allelic class in each of two species. Estimates are based on 5000 simulations; numbers in parentheses are standard deviations.