Assessment of different genetic distances in constructing cotton core subset by genotypic values

Assessment of different genetic distances in constructing cotton core subset by genotypic values 1 2 first-author 1 corresp ‡Corresponding Author ‡Corresponding Author †E-mail:jhu@dial.zju.edu.cn †E-mail:jhu@dial.zju.edu.cn jhu@dial.zju.edu.cn 1 1 Seed Science Center, College of Agriculture and Biotechnology, Zhejiang University, Hangzhou 310029, China Seed Science Center, College of Agriculture and Biotechnology, Zhejiang University, Hangzhou 310029, China Crop Research Institute, Shandong Academy of Agricultural Sciences, Jinan 250100, China Crop Research Institute, Shandong Academy of Agricultural Sciences, Jinan 250100, China One hundred and sixty-eight genotypes of cotton from the same growing region were used as a germplasm group to study the validity of different genetic distances in constructing cotton core subset. Mixed linear model approach was employed to unbiasedly predict genotypic values of 20 traits for eliminating the environmental effect. Six commonly used genetic distances (Euclidean, standardized Euclidean, Mahalanobis, city block, cosine and correlation distances) combining four commonly used hierarchical cluster methods (single distance, complete distance, unweighted pair-group average and Ward’s methods) were used in the least distance stepwise sampling (LDSS) method for constructing different core subsets. The analyses of variance (ANOVA) of different evaluating parameters showed that the validities of cosine and correlation distances were inferior to those of Euclidean, standardized Euclidean, Mahalanobis and city block distances. Standardized Euclidean distance was slightly more effective than Euclidean, Mahalanobis and city block distances. The principal analysis validated standardized Euclidean distance in the course of constructing practical core subsets. The covariance matrix of accessions might be ill-conditioned when Mahalanobis distance was used to calculate genetic distance at low sampling percentages, which led to bias in small-sized core subset construction. The standardized Euclidean distance is recommended in core subset construction with LDSS method. Core subset Mixed linear model Least distance stepwise sampling (LDSS) method Standardized Euclidean distance Mahalanobis distance INTRODUCTION 1 The concept of core collection was proposed by Frankel ( 1984 1984 ) and developed by Brown ( 1989 1989 ). A core collection is defined as a representative sample of the entire collection with minimum repetitiveness and maximum genetic diversity of a plant species and its relatives, and the other part of the initial collection is defined as reserve collection (Frankel, 1984 1984 ). The core collection serves as a working collection that can be evaluated and utilized preferentially, which provides a convenient way to study and utilize germplasm resources and has received extensive attention all over the world. One common approach for constructing a core collection is stratifying the whole collection by growing regions or ecotype and then selecting representative core accessions from each of the classified groups to form core subsets, and the whole core collection is constructed by combining all core subsets (Brown, 1995 1995 ; Qiu et al., 2003 2003 ). For a core collection, representativeness is the most important property. The main way to improve the representativeness of a core collection is to select more representative core subsets from the whole collection (Wang et al., 2007a 2007a ). Cluster analysis has been widely used as an important tool to reduce redundancy and select core accessions within groups in germplasm research (van Hintum, 1995 1995 ; Zewdie et al., 2004 2004 ; Upadhyaya et al., 2006 2006 ; Mosjidis and Klingler, 2006 2006 ). Genetic distance and cluster method are main impact factors in core subset construction. Different genetic distance or cluster method leads to different core subset. In core subset construction, the least distance stepwise sampling (LDSS) has been proved to be a valid method for eliminating the influence of different cluster methods (Wang et al., 2007b 2007b ). However, genetic distance calculation is premise for cluster analysis. The validities of different genetic distances in constructing core subsets by LDSS method have not been deeply investigated. The objective of present research was to use different common genetic distances and different common cluster methods to construct core subsets to evaluate the validities of different genetic distances. MATERIALS AND METHODS 1 Materials 2 One hundred and sixty-eight cotton genotypes came from the same growing region and were used as a germplasm group to construct core subsets. All the 168 genotypes were planted for 2 years with 2 replications per year. The observed data of 20 quantitative traits on those plants were recorded. There were 11 agronomy traits (height of plant, height of fruiting branch, length of fruiting node, length of boll stalk, number of fruiting branch per plant, number of bolls per plant, incidence of infected plant, index of wilt disease, growth period, boll weight, and lint percentage), 5 fiber traits (length, uniformity, strength, elongation and micronaire) and 4 seed traits (seed length, seed width, ratio of length to width and kernel weight) in this initial germplasm group. Core subset construction 2 Core subsets were constructed by LDSS method (Wang et al., 2007b 2007b ). First, a precise sampling percentage of the core subset was determined based on other researches. Next, the genetic distances between accessions were calculated and accessions were grouped by hierarchical cluster analysis based on the genetic distance. One accession from a subgroup with the least distance, which was unique in the whole dendrogram, was randomly removed, and another accession of the subgroup was sampled. Then, the genetic distances among the remained accessions were calculated again, and the sampling was performed by the same way. The stepwise samplings were performed until the percentage of the remained accessions reached the given sampling percentage. The sampling performed in this method was based on the subgroup with the least genetic distance, which could efficiently eliminate redundant accessions. Moreover, the constructing result of this method was not affected by cluster methods because subgroup with least distance was unique in each procedure of cluster (Wang et al., 2007b 2007b ). Coincidence rate of range ( CR ) and variable rate of coefficient of variation ( VR ) (Hu et al., 2000 2000 ; Upadhyaya and Ortiz, 2001 2001 ; Kang et al., 2006 2006 ) were adopted to evaluate the representativeness of core subsets. Genetic distances and cluster methods 2 Six commonly used genetic distances (Euclidean distance, Euclid; standardized Euclidean distance, Seuclid; Mahalanobis distance, Mahal; city block distance, Cityblock; cosine distance, Cosine; correlation distance, Correlation) (Chen et al., 2002 2002 ) were used to assess genetic distances among accessions. Four hierarchical cluster methods (nearest distance method, Single; furthest distance method, Complete; unweighted pair-group average method, Average; Ward’s method, Ward) (Chen et al., 2002 2002 ) were used to perform clustering to construct different core subsets by combining six genetic distances. In each combination (a genetic distance plus a cluster method), 84 core subsets were constructed based on 21 sampling percentages ranging from 10% to 30% with 4 replications per sampling percentage. Further, 2016 core subsets were achieved from the 24 combinations (6 genetic distances combining 4 cluster methods) for 84 core subsets. Core subsets constructed by Complete random method were treated as controls. Validation of core subsets 2 The initial germplasm group was treated by the principal components analysis to validate the core subsets. Distribution of the core accessions and the reserved accessions was plotted by the first two principal components at the sampling percentages of 20%, 25% and 30%. Core subsets constructed by Complete random method were treated as control (Xu et al., 2006 2006 ). Data management 2 Mixed linear model approach (Zhu and Weir, 1996 1996 ) was used to predict genotypic values of all cotton genotypes in each quantitative trait to eliminate environmental and GE (genotypical×environmental) effects. The model is: Y hk ( ij ) = μ + E h + R i ( h ) + C j ( h ) + G k ( ij ) + GE hk ( ij ) + ε hk ( ij ) , where Y hk ( ij ) is the observed value of the k th genotype in the h th environment within the i th row and the j th column; μ is the population mean; E h is the fixed effect of the h th environment; R i ( h ) is the fixed effect of the i th row within the h th environment; C j ( h ) is the fixed effect of the j th column within the h th environment; G k ( ij ) is the random effect of the k th genotype within the i th row and the j th column, G k ( ij ) ~(0, σ G 2 ); GE hk ( ij ) is the random effect of the interaction between the h th environment and the k th genotype, GE hk ( ij ) ~(0, σ GE 2 ); ε hk ( ij ) is the residual effect, ε hk ( ij ) ~(0, σ ε 2 ). All genotypic values of each trait were standardized ( μ =0, σ =1) and used to construct core subsets. All analyses were conducted in MATLAB software, version 6.5. RESULTS 1 Evaluation of different genetic distances 2 CR had been proved to be more robust than VR (Wang et al., 2007a 2007a ), and we, therefore, chose CR to investigate the representation of different cluster methods combining different genetic distances in constructing core subsets. With the sampling percentage increasing, CR increased in all combinations (Fig. 1 1 ). In all the five genetic distances (Euclid, Seuclid, Cityblock, Cosine and Correlation), core subsets constructed by the four cluster methods (Single, Complete, Average and Ward) showed completely the same changing curve in CR . By comparing the accessions in each core subset, all these four core subsets with the same sampling percentage and genetic distance were composed of the same accessions. However, Ward combining Mahal showed different CR changing curve compared to the other three cluster methods when the sampling percentage was less than 12%, while the four cluster methods combining Mahal showed exactly the same CR changing curve when the sampling percentage was over 12% (Fig. 1 1 ). In order to find out why Mahal showed larruping to the other genetic distances in CR , we checked the courses of calculation in all the 6 genetic distances. The sample covariance matrix of Mahal was found to be ill-conditioned when the sampling percentage was less than 12% (more than 400 elements in initial data sample matrix). Representativeness of core subsets constructed by different genetic distances 2 Since all cluster methods constructed the same core subsets in one genetic distance (except Ward in Mahal), core subsets constructed by the cluster method of Single were used to determine the representativeness of core subsets constructed by different genetic distances. At all the five sampling percentages (10%, 15%, 20%, 25% and 30%), core subsets constructed by Euclid, Seuclid, Mahal and Cityblock had significantly larger ( α =0.05) CR than those constructed by Cosine and Correlation, and there was no significant difference for CR in core subsets constructed by Euclid, Seuclid, Mahal and Cityblock (Table 1 1 ). Core subsets constructed by Cosine had significantly larger CR than those constructed by Correlation at 25% sampling percentage, and there was no significant difference for CR in core subsets constructed by Cosine and Correlation at other four sampling percentages (Table 1 1 ). Values with different letters in the same sampling percentage are significantly different ( α =0.05) by Tukey test; Sampling percentage 2 Genetic distance 5 CR (%) 5 VR (%) 10% * * 15% 20% 25% 30% 10% 15% 20% 25% 30% Euclid 90.30a 92.60a 94.60a 96.06a 96.79a 151.31a 137.80a 132.15a 127.43a 123.49a Seuclid 89.61a 93.29a 95.92a 96.78a 98.03a 150.06a 139.66a 132.33a 127.46a 123.41a Mahal 81.12a 91.69a 93.83a 96.10a 97.56a 132.39b 134.82a 130.44a 125.64a 122.37a Cityblock 88.74a 92.39a 94.39a 95.41a 96.01a 148.73a 138.55a 130.12a 126.03a 122.39a Cosine 58.03b 63.33b 69.65b 72.92b 74.10b 93.16c 93.34b 94.37b 92.87b 93.78b Correlation 58.24b 68.52b 64.61b 66.88c 71.04b 94.68c 99.46b 90.75b 89.25b 91.45b There was no significant difference for VR in core subsets constructed by Euclid, Seuclid, Mahal and Cityblock at the sampling percentages of 15%, 20%, 25% and 30% (Table 1 1 ). At sampling percentage of 10%, core subsets constructed by Euclid, Seuclid and Cityblock had significantly larger VR than those constructed by Mahal, while there was no significant difference for VR in core subsets constructed by Euclid, Seuclid and Cityblock (Table 1 1 ). At all the five sampling percentages, there was no significant difference for VR in core subsets constructed by Cosine and Correlation (Table 1 1 ). Changing trend of the representativeness of core subsets constructed by different genetic distances 2 Fig. 2 2 shows the pattern of the representativeness of core subsets constructed by different genetic distances. With the increase of the sampling percentage, CR increased in all the six genetic distances (Euclid, Seuclid, Mahal, Cityblock, Cosine and Correlation). However, CR of core subsets constructed by Cosine and Correlation increased unstably. Core subsets constructed by Cosine and Correlation had significantly lower CR than those constructed by the other four genetic distances at all sampling percentages. Compared to Euclid, Seuclid and Cityblock, Mahal constructed relatively lower CR when the sampling percentage was less than 12%. However, when the sampling percentage was over 12%, Euclid, Seuclid, Mahal and Cityblock showed similar CR . Synthesizing all sampling percentages, core subsets constructed by Seuclid had slightly larger CR than those constructed by Euclid, Mahal and Cityblock. With the increase of the sampling percentage, except for core subsets constructed by Mahal at low sampling percentages (less than 12%), all VR declined (closing to 100%) in all six genetic distances. However, VR of core subsets constructed by Cosine and Correlation decreased unstably (Fig. 3 3 ). Core subsets constructed by Cosine and Correlation had significantly lower VR than those constructed by the other four genetic distances at all sampling percentages (Fig. 3 3 ). Compared to Euclid, Seuclid and Cityblock, core subsets constructed by Mahal had larger VR when the sampling percentage was less than 12% (Fig. 3 3 ). When the sampling percentage was over 12%, Euclid, Seuclid, Mahal and Cityblock led to similar VR (Fig. 3 3 ). Validation of core subsets by the principal component analysis 2 The above results suggest that Seuclid distance might be more suitable for core subset construction than the other five genetic distances. The principal component analysis was conducted to further validate core subsets constructed by Seuclid. The principal component analysis showed that the distribution of core and reserve accessions could be approximately presented by the first two principal components, which could account for 76.43% of the total genetic variation in initial germplasm group (Fig. 4 4 ). Most extreme accessions were selected in core subsets by Seuclid distance and Single cluster method, while there were many extreme accessions not selected in core subsets by Complete random method (Fig. 4 4 ). This phenomenon was more significant in low sampling percentages (Fig. 4 4 ). DISCUSSION 1 Phenotypic values are mainly used in the research of constructing core subsets (Rodiño et al., 2003 2003 ; Okpul et al., 2004 2004 ; Volk et al., 2005 2005 ; Yan et al., 2007 2007 ). The phenotypic values of germplasm materials are easily affected by field conditions and experimental errors. Moreover, the effects of interaction between genotype and environment (GE effects) exist in phenotypic values (Hu et al., 2000 2000 ). Therefore, a core subset based on phenotypic values may not accurately represent genetic diversity of the initial germplasm group (Tanksley and McCouch, 1997 1997 ). Mixed linear model approach is an effective method to predict genotypic values from phenotypic values, and eliminate effects of experimental errors, environmental effects and GE effects (Hu et al., 2000 2000 ; Li et al., 2004 2004 ). In present research, core subsets were constructed based on genotypic values, which enabled more accurate evaluation of the methods for core subset construction. The calculation of Mahal involves calculating sample covariance matrix, which may better reflect the genetic relationship among initial accessions. Some researches suggested that core subsets constructed by Mahal were not affected by scalar differences between traits, and more representative than those constructed by Euclid (Hu et al., 2000 2000 ). However, the results of the present study show that the validity of Mahal may not be better than those of Euclid, Seuclid and Cityblock after genotypic values of each trait were standardized. The present research shows that the covariance matrix of accessions might be ill-conditioned when Mahal was used to calculate genetic distance at low sampling percentages, which led to bias in calculating the genetic distance. It suggests that Mahal might not be suitable for constructing small core subset. The calculations of Euclid, Seuclid and Cityblock do not need to calculate sample covariance matrix, which means that they are available in small core subset construction. Our results also suggest that Seuclid is slightly more available for core subset construction than Euclid, Mahal and Cityblock. The principal component analysis validated LDSS method and Seuclid distance combining Single cluster method in core subset construction. 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Diallel analysis for sex-linked and maternal effects 10.1631/jzus.B0710615 Project supported by the National Natural Science Foundation of China (No. 30270759), the Cooperation Project in Science and Technology between China and Poland Governments (No. 32-38), and the Scientific Research Foundation for Doctors in Shandong Academy of Agricultural Sciences (No. [2007]20), China 2007-12-06 2008-02-27 2022-01-05 Copyright © 2008, Journal of Zhejiang University Science 2008 Journal of Zhejiang University-SCIENCE B (Biomedicine and Biotechnology) 05 09