Table 4. Expansion time estimates for geographic sub-populations of Lineages I, II and IV.

	tau	Mutation rate		k	generation time		expansion time estimate (ybp)
Lineage		u1	U2		GT1	GT2	u1+GT1	u1+GT2	u2+GT1	u2+GT2
Lineage I Indian	3.052	2.3	4	945	0.3	1	21063	70209	12111	40370
Lineage I ‘ship rat’	2.486	2.3	4	945	0.3	1	17157	57189	9865	32884
Lineage II Mainland	6.766	2.3	4	945	0.3	1	46694	155648	26849	89497
Sublineage IIA	1.956	2.3	4	945	0.3	1	13500	45000	7762	25900
Sublineage IIB	1.857	2.3	4	945	0.3	1	12800	42700	7369	24600
Lineage IV Indochina	6.49	2.3	4	945	0.3	1	44790	149298	25754	85847

Estimates of tau ( = expansion time in mutational units) were obtained from coalescent simulations as implemented in DnaSP version 5.10.1 [77]. These were converted into years before present (ybp) with the formula ybp = generation time (GT) multiplied by tau/2uk (where u = mutation rate per site per year and k = sequence length; [83]). We used four different estimates of u (all shown as 10×10⁻⁸), drawn from studies of murine rodents in general [98]–[99] or from analysis of the Rattus Division [100], and two values for generation length (0.3 and 1.0, the former being the shortest time to first breeding in Rattus rattus [101] and the latter representing a situation where breeding occurs on a seasonal basis and only once each year). The four values of u are derived as follows: u1 = 3^rd codon position substitutions only, estimate based on results from arvicoline and murine rodents [98]; u2 = lower estimate of substitution rate for all positions within the Rattus Division [100], based on origin of the genus Rattus at 3.0 mya (maximum age suggested by murid-wide analysis of two nuclear genes: IRBP and RAG1); u3 = upper estimate of substitution rate for all positions within the Rattus Division [100], based on origin of the genus Rattus at 2.0 mya (minimum age suggested by murid-wide analysis of IRBP and RAG1 genes and fossil record); u4 = estimate of silent divergence rate from comparative analysis of mammalian sequences [99]. The combination of values for each parameter produces eight expansion time estimates for each lineage. The expansion time model u4+GT1, using the most rapid mutation rate (10×10⁻⁸ per site per year) and the shortest generation time (0.3 yr), produced values closest to expectation based on archaeological and historical evidence for the time of major dispersal events. The very wide range in estimates of mutation rate reflect intense saturation of the cyt b gene at quite low levels of divergence, even when silent substitutions alone are considered.