Figure 10.—
The coalescent in a bounded habitat. Values derived from simulations for the cumulative density function of the coalescence time for a pair of sequences are compared to values given by Equations A23 and A28. Three sampling locations from a rectangular habitat of dimension 10 × 5 were considered: (1, 1), (8, 2), and (6, 3). For each of the six pairs of locations (a–f), 100,000 coalescence times were simulated with N = 10,000 (ρ = 200). Analytic results derived from equations in the text are indicated by solid lines, and simulation results by crosses or solid and open circles. The three dispersal rate values were used, and the corresponding long-term effective population sizes were determined using Equation 6: σ = 0.15 (Nb = 56.5, Ne = 11,454, solid circles); σ = 0.25 (Nb = 157.1, Ne = 10,483, crosses); and σ = 0.4 (Nb = 402.1, Ne = 10,235, open circles). The transition times were determined from Equation 7 (a–c and f) or Equation 8 (d and e). The numbers of images used in a–f were 27, 30, 20, 18, 23, and 18, respectively.