maller 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 the population change. The method assumes an exponential model of population size change. In this model, prior distributions for N0, N1, T and μ are assumed to be log normal. The mean and the standard deviations of these prior log normal distributions are drawn from priors (or hyperpriors) distributions.
Wide “uninformative” priors were used to perform multiple runs for this approach (Table S6). For minimal effect towards the posterior distributions variances for the prior distributions were kept large. The total number of iterations was always 2 × 106.
The generation time for tigers is known to be about five years , and we used this information for all analyses.
Figure showing investigated mitochondrial regions and the variable positions (lines) and the associated heterozygosities of these positions for all tiger subspecies. The colored boxes highlight the regions amplified by our primers for this study.
(0.52 MB TIF)
(A) Population size change for the tigers in the Indian subcontinent, with black and green curves corresponding to the posterior distributions under models of exponential and linear population size change, respectively. The prior distribution is represented by flat dotted line. Irrespective of various models, there is no support for population increase. (B) The posterior distributions for ancestral (red curve) and present (green) population size are represented here. The priors are represented by the dotted line (present population) and dashed line (ancestral population). (C) The posterior distribution for the time since the population decline started for Indian tigers (black curve) is represented here. The priors are shown by the dashed lines. The distribution has a median value at around 270 years. (D) Joint posterior distribution of ancestral and current population size based on South and Central India tiger data. The 90%, 50%, and 10% highest probability density (HPD) limits are plotted for the joint distribution of ancestral and current population size on a logarithmic scale. The diagonal line c