Analyses of breeding traits in Maiwa yak

Zh. Jincheng, Ch. Zhihua, Z. Xiangdong and W. Yongli

Department of Animal Science, Southwest Nationalities College, Chengdu 610041, Sichuan, P.R. China

Summary

The paper presents results of analyses of nine breeding traits in Maiwa yak using principal component and cluster approaches. Results revealed that the nine traits could be divided into three groups: body size traits, milk traits and, hair and horn. The first two groups are the most important for yak production in terms of growth and development and should be considered as the basis for selection and breeding of the Maiwa yak.

Keywords: Cluster analysis, Maiwa yak, principal component analysis

Introduction

Maiwa yak, one of the fine breeds of yak in China, are mainly produced in Hongyuan and Ruoergai Counties of Sichuan Province. In order to improve productive performances (milk and meat), a series of selection and breeding trials and controlled mating have been conducted in recent years. However, the selected traits are mainly quantitative traits. These traits are highly correlated and some desirable ones are negatively correlated with undesirable ones. In this article, nine traits were analysed by two multivariate methods-principal component and cluster analyses so as to determine the relationship amongst the quantitative traits and to provide theoretical basis for breeding work of the Maiwa yak.

Materials and methods

The data analysed in this study were obtained at Longri Stud Farm in Sichuan Province. The nine traits were recorded on 353 healthy female yak. The traits were: body weight (x₁), body height (x₂), body length (x₃), heart girth (x₄), presence or absence of horns (x₅), hair colour (x₆), milk fat ratio (x₇), milk yield (x₈) and hair yield (x₉).

Cluster analysis: Euclidean distance between two traits was used (Tong 1986). The distance, Dij, was calculated as: D_ij = [Σ(X_ik –X_jk)²]^1/2. The shortest distance method was used for Cluster analysis.

Principal component analysis: After data standardisation, the relevant matrix among variables is [R], where R_ij, the elements of the matrix, was calculated as R_ij = ΣX_ki X_kj/n, thus forming the formula of characteristics: Rb = λb. The characteristic root and the corresponding characteristic vector were determined by adopting Jacobi method. With λ₁ > λ₂ > ... λ_m and the corresponding characteristic vector, the principal components were sequentially determined: Y_ij = b₁₁x_1i + b₁₂x_2i + ... + b_1mx_mi, as well as the contribution rate, cumulative contribution rate and factor load (Tong 1986).

Results and discussion

Correlation of the traits

From the correlations of the traits (Table 1), body weight was found to have significant positive correlation to heart girth, body length, body height and milk yield, and there was also very significant positive correlation among the three body size traits (height, length and heart girth). There were significant correlations between horn and heart girth, body length and body weight as well.

Table 1. Correlation matrix among the nine traits.

Traits	Body weight	Height	Length	Heart girth	Horn	Colour	Milk fat	Milk yield
Height	0.74**
Length	0.79**	0.68**
Heart girth	0.86**	0.77**	0.74**
Horn	–0.13*	–0.08	–0.12*	–0.15**
Colour	0.02	0.003	–0.05	–0.02	0.05
Milk fat	–0.09	0.02	–0.01	0.002	–0.05	0.004
Milk yield	0.39**	0.17*	0.11	0.25**	0.11	–0.03	–0.31**
Hair yield	–0.15	–0.08	–0.16*	–0.13	0.01	–0.08	–0.15	0.08
** = very significant; * = significant.

Classification of the traits

Results of clustering of traits based on Euclidean distance indicated that the three body size traits (body height, body length and heart girth) aggregated to a group first, then sequentially aggregated with the body weight, milk yield and milk fat, and finally aggregated with the hair colour and yield. This also reflected the correlations among the traits (Figure 1).

Figure 1. Cluster on nine traits of Maiwa yak.

Factor load and index combination

It can be seen from Table 2 that all characteristic roots with principal components analysis from correlation matrix of traits are not very good. Until the fifth principal component, its cumulative contribution rate is just up to over 85%. The factor load of the first five principal components and their index combinations of main traits were further analysed and the results are shown in Table 3.

Table 2. Characteristic root (λi), contribution rate (٨ ) and cumulative contribution rate (٨i).

Components	1	2	3	4	5	6	7	8	9
λi	3.43	1.42	1.09	0.93	0.84	0.66	0.32	0.21	0.10
٨(%)	38.09	15.78	12.07	10.33	9.34	7.36	3.51	2.37	1.15
٨i (%)	38.09	53.88	65.94	76.27	85.62	92.97	96.49	98.85	100.00

Table 3. The factor load of the first five principal components.

Traits	1	2	3	4	5
Body weight	0.949	0.074	0.043	–0.019	–0.019
Heart girth	0.927	–0.048	–0.026	0.001	0.076
Length	0.868	–0.131	–0.036	0.055	0.045
Height	0.860	–0.070	–0.006	0.031	0.199
Milk fat	–0.059	–0.740	–0.007	0.279	0.336
Milk yield	0.336	0.708	0.132	0.057	–0.191
Horn	–0.019	–0.099	0.736	–0.621	0.246
Colour	–0.162	0.316	0.569	0.651	0.295
Hair yield	–0.179	0.482	–0.447	–0.187	0.705

As is visible from the factor load, the 1st principal component mainly synthesises the body weight, body height, body length and hearth girth and their factor loads are greater: all are above 0.8. These traits mainly reflected size-type information. The second principal component mainly synthesises the milk fat and milk yield, and the factor load is over 0.7. The third and fourth principal components synthesise information about hair colour and horn, and the factor load is over 0.6. The fifth principal component synthesises information about hair yield. These results show that all nine traits can be summarised into body size, milk fat and yield, and hair colour and horn as well as hair yield.

Classification of principal components

Based on factor load (Table 3), taking the first principal component value as abscissa and the second as ordinate, one can draw a plane to co-ordinate point cluster (Figure 2). The result shows that the 1st group of traits included body weight, body height, body length and hearth girth, the 2nd group of traits covered milk fat percent and hair colour, and the 3rd group of traits involved milk yield, horns and hair yield, which confirmed to the abovementioned cluster resul

Figure 2. Two-dimensional distribution for the nine traits of Maiwa yak.

Both clustering and principal components classification for Maiwa yak breeding traits have basically the same results. However, from principal components classification it can be seen that:

1. the closer the distance in various factors, the stronger the positive correlative action. The positive correlative action is gradually reduced in magnitude.
2. the stronger the positive-going and negative-going action of the factor, the farther the factor is away from the second main axis (Y2). The factor without notable positive-going and negative-going action is located at left and right sides near Y2 axis, and the positive-going one is at right side of Y2 axis. All of these show that the information derived by principal components classification is substantial.

It can be seen from the results of principal components analysis that the 1st principal components mainly contain body-size traits, the 2nd principal components mainly milk traits, and their factor load is higher, which indicate that these traits have greater influences on yak growth and development as well as production. Therefore, special emphasis should be laid on selecting these traits in future Maiwa yak breeding programmes and, at the same time, it shall be further analysed in selection and considered in co-ordination, so as to ensure successful breeding work.

Reference

Tong Shouzheng. 1986. Multi-statistic analysis method. China Forestry Press, Beijing, P.R. China. pp. 20–30. [in Chinese].