Analysis of the diversity of STR-loci in the samples of bulls of Red Scandinavian and Holstein breeds

Standardized indicators of α- and β-diversity (𝒚′_𝒌𝒎) calculated by DNA microsatellites (STR) in samples of bulls of Red Scandinavian (RED, n = 29) and Holstein (HOL, n = 45) breeds (each with three sub-samples) were analyzed using one-two- and multivariate statistics methods. The data represented two 11×7 matrices: objects – 11 STR loci (Eth3, Inra23, Tgla227, Tgla126, Tgla122, Sps115, Eth225, Tgla53, Bm2113, Bm1824, Eth10; No.1-11), variables – three indicators of α-diversity (number of alleles and effective alleles per locus, heterozygosity) and four – β-diversity (indices: fixation by Nei, differentiation by Meirmans-Hedrick, Jost and Shannon-Sherwin). ANOVA, using a fixed-type model, revealed a statistically significant (p_value< 0.02) effect on the variability of 𝒚′_𝒌𝒎 factors «breed» (2 %), «locus» (36.7 %) and their interaction (15.6 %). According to the mixed-type model (the «locus» factor as random), only the interaction effect was statistically significant (25.8 %, p_value< 0.0001). The probability of a noncoincidence between the numbers of a randomly selected pair of loci from the RED and HOL samples was 31 %. The average Euclidean distance between the two samples, calculated by analogical loci, was 37.8±5.35 %. The Mantel correlation between the matrices of paired interlocus distances in RED and in HOL samples was 0.257±0.130 (p_value = 0.056). The ordinations of loci and their grouping (structuring) in the space of the two main components of the REL sample and the HOL sample differed (Procrust test: m² = 0.994, m₁₂ = 0.747, p_perm = 0.164, 𝒓^𝟐_{𝑷𝒓𝒐𝒄} = 0.253). Estimates of the distance between samples based on the profiles of the α- and β-diversity of loci did not contradict, in general, the genetic distances calculated by allelic frequencies (29–37 %). To analyze the covariance (commonality) of multivariate RED and HOL sample data, a two-block partial least squares (2B-PLS) method was used. The integrated latent variables (LV) maximized the total square of covariance («squared covar» = 14.3 %), in which 83 % accounted for the first LV with max «weights» in terms of α-diversity (aLV). The second LV accounted for 16.7 % with max «weights» in terms of β-diversity (βLV). The linear relationship between RED and HOL samples for aLV was 0.717 (p_value = 0.013), for βLV – 0.395 (p_value = 0.229), averaged – 0.56 (p_value = 0.025). The commonality (co-dispersion) of the two samples for aLV and βLV was estimated at 25,0–32.5 %. 2B-PLS analysis based on reduced data (only for α-diversity) showed a max «squared covar» of 0.393, in which 99.9 % accounted for the first LV (LV1). According to LV1, the linear relationship between RED and HOL samples was estimated at 0.659 (p_value = 0.0253), the co-dispersion was 43.4 % (according to aLV it was 51.4 %). The ordinations of loci in the coordinate space of the RED and HOL samples for the complete (αLV) and reduced (LV1) datasets had a good match (Procrust test: m² = 0.0742, m₁₂ = 0.0728, p_perm = 0.001, 𝒓^𝟐_{𝑷𝒓𝒐𝒄} = 0.927). In the structure of the inter-sample covariance, «clumps» of loci with a bootstrap probability of [grouping] 50, 75 and 100 % were distinguished. It can be assumed that the RED and HOL samples had some consistency (congruence) in terms of the α-diversity of the loci of the same name. The extension of the «multivariate» approach to descriptive statistics of α-diversity of 7 breeds of dairy cattle and 11 breeds of pigs showed a fairly good correspondence of the results (differentiation index, PCA-ordination) with those obtained using «traditional» methods (p_perm of matching ordinations 0.054 and 0.004). The approaches and methods considered expand the possibilities of population-genetic [and breeding-zootechnical] studies in which multidimensional data sets are the norm, not the exception.

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