**3.7. Population expansions**

The sample size for most of the populations was more than 30, so the detection of population expansion was performed at the individual population level (data not shown) and in all haplotype sequences. Liu et al. showed the mismatch distribution analysis of the complete dataset (lineages A, B, C, D and 15 Tibetan sheep populations of mtDNA D-loop) [29]. Neutrality tests (Ewens-Watterson test, Chakraborty's test, Tajima's D test, Fu's FS test) were used to detect population expansion [29]. The charts of the mismatch distribution for the samples of the 15 Tibetan sheep populations and the total samples were multimodal. However, the mismatch distribution for LZ was a unimodal function. The mismatch distribution of the complete dataset showed that there were two major peaks, with maximum values at 4 and 27 pairwise differences and two smaller peaks at 45 and 51 pairwise differences [29]. These results suggest that at least two expansion events occurred during the population demographic history of the Tibetan sheep population. The mismatch distribution analysis revealed a unimodal bell-shaped distribution of pairwise sequence differences in lineages A, B and C, but that of the lineage D was a sampling function duo to small sample effects. The complete dataset of 15 Tibetan sheep populations did not produce a significantly negative Ewens-Watterson test, whereas Chakraborty's neutrality test of JZ was significant (12.63, *p* = 0.03), and Tajima's D neutrality of TJ test was also significant (−0.47, *p* = 0.02). Fu's *FS* value was −7.48 for the 15 Tibetan sheep populations, of which GN, QK, HB, GB, GJ, QH, QL and TJ were highly significant (*p* < 0.01 or *p* < 0.001). This finding suggests the occurrence of two expansion events in the demographic history of the 15 Tibetan sheep populations. This result is consistent with a demographic model showing two large and sudden expansions, as inferred from the mismatch distribution.
