*3.3. Relationships among the Studied Breeds*

The first component of the PCA explained 5.178% of the genetic variability and split the Kazakh white-headed and Hereford breeds from the other studied breeds. The second component, responsible for 3.773%, divided the museum and modern Kyrgyz cattle. The Mongolian cattle were localized in the middle of the PCA plot, explaining their contribution to the development of the studied steppe breeds. The museum Kalmyk samples did not form a clear cluster. A possible explanation could be the different genetic backgrounds of the museum specimens of Kalmyk cattle (Figure 2a).

**Figure 2.** (**a**). Principal component analysis (PCA) of the museum and modern cattle populations. X-axis, principal component 1 (PC1); Y-axis, principal component 2 (PC2); (**b**). Genetic structure of museum and modern cattle populations revealed by STRUCTURE analysis for the number of clusters K = 2. Museum populations: KALM\_H—Kalmyk, KRGZ\_H— Kyrgyz, KZKH\_H—Kazakh, modern populations: KALM\_M—Kalmyk, KRGZ\_M—Kyrgyz, KZWH\_M—Kazakh White-Headed, HRFD\_M—Hereford, MONG\_M—Mongolian cattle.

Calculation of the Δ*K* values for the different number of clusters (K) from one to five showed that the most probable number of ancestral populations that participated in the development of studied breeds is two. STRUCTURE analysis at K = 2 showed differences in the genetic structure of the studied breeds by the rate of native and Hereford-specific genetic components. The museum samples of the Kyrgyz and Kazakh cattle had similar genetic structures with the greatest rate of native genetic components, while part of the museum Kalmyk cattle revealed an admixed genetic structure. The modern Kalmyk and Kyrgyz cattle kept most of the native genetic components, while in the Kazakh whiteheaded cattle, the Hereford-specific components dominated (Figure 2b).

Analysis of *F*ST and Jost's D genetic distances showed a lack of allelic differentiation between pairs of museum populations: Kalmyk–Kyrgyz (*F*ST and Jost's D = 0) and Kalmyk–Kazakh (*F*ST = −0.020, Jost's D = −0.013). The modern Kalmyk and Kyrgyz cattle were closest to the museum populations of their ancestral breeds (*F*ST = 0.018 and 0.025; Jost's D = 0.017 and 0.047, respectively), while the Kazakh white-headed breed was most distant from museum populations (*F*ST = 0.048, 0.082, and 0.096; Jost's D = 0.089, 0.175 and 0.079 for museum Kalmyk, Kyrgyz and Kazakh cattle, respectively). Museum cattle revealed a stronger Mongolian genetic background (*F*ST = 0–0.019; Jost's D = 0–0.015) compared to the modern cattle breeds (*F*ST = 0.026–0.052; Jost's D = 0.039–0.098) (Supplemental Materials, Table S5).

A similar allelic pattern of the museum populations was reflected in their neighbored localization on the edges of the Neighbor-Net tree constructed based on Jost's D values (Figure 3) and *F*ST values (Supplemental Materials, Figure S3). Modern populations of the Kalmyk and Kyrgyz breeds were localized in the same cluster, but formed their own branches. This suggests that the development of these breeds was based on the historical genetic background. The Kazakh white-headed cattle formed a separate cluster with the Hereford breed, reflecting the great contribution of the latter in the development of the allele pool of the Kazakh white-headed cattle (Figure 3).

**Figure 3.** Neighbor-Net graphs based on Jost's D genetic distances characterizing genetic relationships between studied museum and modern cattle populations. Museum populations: KALM\_H—Kalmyk, KRGZ\_H—Kyrgyz, KZKH\_H—Kazakh, modern populations: KALM\_M— Kalmyk, KRGZ\_M—Kyrgyz, KZWH\_M—Kazakh White-Headed, HRFD\_M—Hereford, MONG\_M— Mongolian cattle.

A single migration event was found to be the most optimal for describing the demographic history of the studied populations using TreeMix. The most stable TreeMix tree showed migration from the ancestors of the museum Kazakh cattle and Herefords to the Kazakh white-headed breed that agrees with the origin and development of the last (Figure 4).

**Figure 4.** (**a**) Maximum likelihood tree inferred from studied cattle populations with single migration edge. Scale bar shows 10 times the average standard error (SE) of the estimated entries in the sample covariance matrix. Putative gene flow is indicated by the arrow, pointing in the direction of flow from the donor to the recipient population, and coloured in orange, proportional to the gene flow intensity. (**b**) Residual matrix plotted from a TreeMix analysis under single migration event and expressed as the number of SE of the deviation. Positive SE values between pairs of populations indicate that populations are more closely related to each other than in the modeled tree, while negative SE values show that the observed covariance is overestimated. Museum populations: KALM\_H—Kalmyk, KRGZ\_H—Kyrgyz, KZKH\_H—Kazakh, modern populations: KALM\_M—Kalmyk, KRGZ\_M— Kyrgyz, KZWH\_M—Kazakh White-Headed, HRFD\_M—Hereford, MONG\_M—Mongolian cattle.
