am ARLEQUIN . The likelihood-based method used was the population growth rate estimation with program LAMARC . The likelihood-based Bayesian methods used were implemented in the MSVAR programs ,.
The Ewens, Watterson, Cornuet and Luikart approach .
This method uses two summary statistics of the allele frequency spectrum, number of alleles (nA) and expected heterozygosity (He) to achieve the patterns expected for a demographically stable population. Simulations were performed under three mutation models: infinite allele model (IAM), single stepwise model (SMM) and two-phase model (TPM) to obtain the distribution of He and the values are then compared to the real data values. For TPM model, 30% multi-step mutation events were allowed during the simulations. This method can detect departures from mutation-drift equilibrium and neutrality, which can be explained by any departure from the null model, including selection, population growth or decline. More importantly, consistent results from independent loci could be attributed to demographic events over selection. Thus, this approach allows the detection of population size changes across different mutational models.
The Garza-Williamson index/M ratio approach .
This method uses data on the frequency and the total number of alleles and the allelic size range to investigate population decline. In a reducing population, the expectation of the reduction of number of alleles is much higher than the reduction of allelic size range. Thus the ratio between the number of alleles and the allelic size range is expected to be smaller in recently reduced populations than in equilibrium populations.
Likelihood approach (LAMARC) .
This method provides maximum likelihood estimates of growth (or decline) rates using a Metropolis-Hastings Monte Carlo Markov Chain algorithm. As it is a time backward approach, a negative value of g indicates that the population has been shrinking (it was bigger in the past than it is now) and a positive value indicates that it has been growing (it was smaller in the past than it is now). Genetic data from ten microsatellite loci was used for these analyses.
The Beaumont approach .
This approach assumes that a stable population of size N1 started to change (either decrease or increase) ta generations ago to the current population size N0. This change in the population size is assumed to be either linear or exponential under stepwise mutation model (SMM). This bayesian approach uses the information from the full allelic distribution in a coalescent framework to estimate the posterior probability distribution of (i) r = N0/N1 (rate of population size change), (ii) tf = ta/N0 (time since the population size change started, scaled by N0), and (iii) θ = 2N0μ. A Markov Chain Monte Carlo (MCMC) algorithm is used to generate samples from the posterior distribution of these parameters. Although this method allows the quantification of a population increase or decrease, N0 and N1 cannot be estimated independently. Similarly, it can only approximate ta as a time scaled by N0, with N0 being unknown. Thus, the population size change can be quantified, but it cannot be dated. This model was employed to test for a genetic bottleneck under different model of population size change (linear or exponential).
For each analysis, at least three independent runs were performed using different parameter configurations and starting values. Most importantly, all the runs were carried out with positive starting values of log(r) (see Table S4 and 5), corresponding to a population expansion of various levels. This avoids favouring regions of the parameter space corresponding to a population decline.
Rectangular prior distributions were assumed for log(r), log(θ) and log(tf). Wide bounds were chosen (between 10−3 and 103 on a natural log scale) for minimum effects on posterior distributions.
The Storz and Beaumont approach .
This approach is an extension of Beaumont's method and allows quantification of effective population sizes N0 and N1, rather than their ratio along with T, time since th