The performance of 𝔼[Lτ(ρ, x)] as an approximation for the expected length of trans-specificity
| ρ = | |||
|---|---|---|---|
| 0.1 | 1 | 10 | |
| τ = 5 | |||
| Approximation | 0.099 | 0.633 | 1.178 |
| n = 4 | 0.096 (0.009) | 0.563 (0.219) | 0.983 (0.516) |
| n = 8 | 0.096 (0.010) | 0.595 (0.214) | 1.190 (0.603) |
| n = 12 | 0.096 (0.010) | 0.603 (0.211) | 1.276 (0.642) |
| n = 16 | 0.096 (0.010) | 0.610 (0.215) | 1.336 (0.668) |
| n = 20 | 0.096 (0.010) | 0.614 (0.215) | 1.361 (0.679) |
| τ = 10 | |||
| Approximation | 0.095 | 0.349 | 0.378 |
| n = 4 | 0.092 (0.014) | 0.306 (0.162) | 0.330 (0.188) |
| n = 8 | 0.091 (0.015) | 0.322 (0.170) | 0.358 (0.206) |
| n = 12 | 0.091 (0.014) | 0.321 (0.167) | 0.365 (0.204) |
| n = 16 | 0.091 (0.014) | 0.327 (0.165) | 0.373 (0.211) |
| n = 20 | 0.091 (0.015) | 0.331 (0.169) | 0.370 (0.205) |
| τ = 25 | |||
| Approximation | 0.079 | 0.129 | 0.129 |
| n = 4 | 0.075 (0.021) | 0.103 (0.070) | 0.106 (0.068) |
| n = 8 | 0.073 (0.021) | 0.102 (0.070) | 0.109 (0.070) |
| n = 12 | 0.073 (0.021) | 0.103 (0.069) | 0.108 (0.070) |
| n = 16 | 0.074 (0.021) | 0.104 (0.071) | 0.110 (0.071) |
| n = 20 | 0.073 (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.