Null distributions of all test statistics were generated using coalescent simulations conditioned on the number of haplotypes in the sample with the mutation rate set to the population parameter θ (4Ne μ) estimated from the data using Watterson's estimator (Watterson 1975), as described in Zeng et al. (2007b).
The less-than-30-day tMRCA estimates for both the V3 and the T-form epitope lineages (∼ 18 days; Fig. 1A, Table S4) could be explained either by a prolonged eclipse period before viral expansion began, purifying selection retarding the accumulation of mutations [16], or variation in viral population parameters (e.g. mutation rate or R0 [14]).
Mutation, population size, number of generation, crossover, and reproduction parameters affected the evolution process.
Kimura provided theoretical underpinnings to molecular evolution by relating rates of sequence substitution, population parameters and mutation rates [ 2, 3].
To simulate a sample, we assumed the values of two crucial population parameters, population mutation rate θ = 4 N μ and population recombination rate ρ = 4Nr, where N is the effective population size and μ and r are mutation rate and recombination rate per gene per generation, respectively.
The expected distribution for an expanding population was generated using the following population parameters justified by published studies on human autosomal neutral loci [ 56]: pre-expansion population mutation parameter (θ0) = 1, post-expansion population mutation parameter (θ1) = 10.
SAMOVA-group estimates of population mutation rate parameter were moderate, with θW ranging 0.0031-0.0053 (Additional file 1: Table S5).
Studies of population mutation rate parameter θ demonstrate that N ≈ 8 samples are typically sufficient for characterizing genetic diversity, though estimates are improved by recombination and more loci [ 48, 49].
The prior distributions were uniform for mutation-scaled population size parameters theta, that are four times the product of the effective population size and the mutation rate, and mutation-scaled migration rates M, that is, migration rate scaled by the mutation rate, over the range of θ = 0 100 and M = 0 100.
We further estimated the population mutation parameter, θ, which in conjunction with the average mtDNA mutation rate was used to infer the effective population sizes of the different Chad Basin populations assuming a neutral model of molecular evolution (Table 4).
