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Published online 24 June 2005
Published in Crop Sci 45:1603-1609 (2005)
© 2005 Crop Science Society of America
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PLANT GENETIC RESOURCES

Simultaneous Agronomic and Molecular Characterization of Genotypes via the Generalised Procrustes Analysis

An Application to Cucumber

S. J. Bramardia, G. P. Bernetb, M. J. Asínsb and E. A. Carbonellb,*

a Facultad de Ciencias Agrarias, Universidad Nacional del Comahue, 8303 Cinco Saltos, Río Negro, Argentina
b Instituto Valenciano de Investigaciones Agrarias (IVIA), Apartado Oficial, E-46113 Moncada (Valencia), Spain

* Corresponding author (ecarbo{at}ivia.es)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Characterizing entries in a germplasm bank by molecular markers and/or agronomic attributes is a common practice, but studies that simultaneously use molecular and agronomic traits are less frequent. Generalised Procrustes Analysis (GPA) was used to determine the relationships among 41 entries of cucumber (Cucumis sativus L.) via the simultaneous use of 16 agronomic traits (nine qualitative variables and seven quantitative variables) and 33 random amplified polymorphic DNA (RAPD) markers using a set of 11 primers. Other techniques like generalization of the simple matching coefficient, Gower's general similarity coefficient, and discretizing the quantitative variables were compared with GPA. The ordinations of cultivars using each trait individually did not fully characterize the cultivars. In fact, on the basis of the qualitative traits, only two groups were formed, with cultivars belonging to Beth-{alpha} and Dutch constituting a single group and the slice and gherkin types another group. The quantitative traits and also the molecular traits further separated the cultivars belonging Beth-{alpha} and Dutch types. The utilization of all variables together showed a greater discrimination power of genotypes. Four groups were defined which were consistent with Dutch, gherkin, slice, and Beth-{alpha} types. GPA was the most precise technique to cluster the entries. The final configuration was an average of the individual configurations. For other methods, those traits with more variants (but not necessarily more genetic information) had more influence on the final results. Besides, GPA allowed a deeper study of the relationships among relative ordinations of a same genotype under different types of descriptors to establish concordance between characterizations.

Abbreviations: GPA, Generalised Procrustes Analysis • MST, Minimum Spanning Tree • PcoA, Principal Coordinate Analysis • QTL, quantitative trait loci • UPGMA, unweighed pair-group method based on arithmetic averages algorithm


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
THE LIMITED GENETIC DIVERSITY of crops renders them vulnerable to disease and insect epidemics and jeopardizes the potential for sustained genetic improvement in the long run. Because new cultivars are usually derived from crosses among genetically related modern cultivars, and in the future more cultivars may arise by genetic transformation of a very few elite cultivars, it is ironic that the plant-breeding process itself threatens the genetic base on which breeding depends.

Worldwide, there are more than 700 documented seed collections that contain an estimated 2.5 million entries, including many exotics. The USA alone spends about $20 million per year on germplasm acquisition and preservation (Tanksley and McCouch, 1997). The establishment and maintenance of such germplasm banks must be coupled with the ability to actively utilize the materials in storage.

An important discovery from quantitative trait loci (QTL) analysis is that favorable alleles that increase the trait value are present not only in the high parent but also in the low parent. Therefore, the use of phenotypic evaluation to determine the breeding value of an accession is likely to be misleading with respect to quantitative traits. To date, numerous QTL analyses have been performed in the main crop species and provide a source of molecular markers (sometimes very informative and polymorphic, e.g., microsatellites) that are closely linked to QTL or genes of large effect. Moreover, the rapid advance of plant genomics is expected to facilitate the identification and cloning of genes responsible for those traits. Entire collections of these crop species should be genotyped for such genes, or closely linked highly polymorphic markers, as a searching strategy to unveil new alleles that could be used in prebreeding programs after further investigation. Therefore, in addition to the descriptors recommended by the International Plant Genetic Resources Institute (IPGRI) for each crop species, the molecular characterization of its accessions is expected to become the norm in the future. Then, statistical tools to manage such a mix of agronomic and molecular characterizations are urgently needed to obtain a more complete description of the genetic resources, which should facilitate their efficient utilization.

Several authors (Faccioli et al., 1995; Tatineni et al., 1996; Hoey et al., 1996; Sneller et al., 1997; Franco et al., 2001; among others) have called attention to the need for a joint treatment of the information coming from different sources. In general, however, most of the published works do not include a representation of the relationships among taxa on the basis of several simultaneous characterizations. A common drawback of studies where different types of characters are simultaneously evaluated is the failure to establish an adequate definition of distance among taxa. In fact, to measure the degree of similarity on the basis of molecular-marker information, several measures are available (Nei, 1996), but they are not suitable for information based on agronomic traits. For qualitative, quantitative, or traits measured as frequencies, the definition of distances is generally different.

The GPA proposed by Gower (1975) harmonizes the individual configurations, or geometrical representations in a plane, through iterative algebraic steps that transform each individual configuration. These steps include translation, rotation, reflection, and scaling of their point's coordinates under two premises: to maintain the relative distance among elements of the individual configurations and to minimize the sums of squares between analogous points, i.e., points that correspond to the same element under different configurations. The consensus configuration is obtained as the average of all these transformed individual configurations.

In matrix notation, if each matrix (providing an individual configuration) is represented by Xi (i = 1, 2,..., m) with n rows and pi columns where the jth row provides the coordinates of a point (element) Pj referred to as pi axis, the scaling, rotation, and translation can be algebraically expressed by the transformation

where {rho}i is an scaling factor, Hi an orthogonal matrix that rotates Xi and Ti is a translation matrix. All of them are calculated to minimize the expression:

where {Delta} is the Euclidean distance between the point Pj (i = 1, 2, 3, ....m) and the centroid of the m analogous points Pj designated as Gj.

After the initial standardization or translation, once all configurations have been transformed, one iteration is completed. Then, a consensus configuration is calculated as the mean of all the transformed individual configurations and a new iteration is initialized; the process is repeated until the change between two consecutive steps in the residual sums of squares is less than a given value. A convergence tolerance of 0.0001 is considered satisfactory (Gower, 1975).

The most common usage of the GPA is to analyze data from sensory profiling where several evaluators or "judges" quantify different attributes and produce as many configurations as the number of evaluators (Dijksterhuis and Gower, 1992; Russell and Cox, 2004). The GPA also has been used in geometric morphometrics (Adams et al., 2004; Frost et al., 2003; Rohlf, 2003) and molecular alignment in structure-activity studies (Kroonenberg et al., 2003). However, in spite of being a powerful technique for producing a common configuration by consensus, its application in studies of genetic variability in germplasm collections has been limited (Faccioli et al., 1995; Bramardi, 2000).

In the present paper, we illustrate the use of GPA as a method to ordinate the entries of a well-known collection of cucumber cultivars on the basis of simultaneous usage of agronomic and molecular data. We evaluate, on the basis of the known type of these cucumber cultivars, the results obtained from GPA and compare them with those provided by ordinations given by alternative approaches of combining different types of data.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Plant Material
Seedlings from 41 Cucumis sativus L. (36 different cultivars) seed samples, coded V1 to V41, were obtained from Centro de Ensayos de Valencia (INIA-OEVV). Entries constituted a reference collection of cucumber involving Dutch, gherkin, slice, and Beth-{alpha} types. Every entry had been evaluated for agronomic traits as suggested by the International Union for the Protection of New Varieties of Plants (U.P.O.V.), (Table 1). The evaluation was mostly related to fruit shape and size. Four to six seedlings per entry were characterized for RAPD markers. A final set of 11 out of 121 primers was used according to the clarity and reproducibility of banding patterns. Thirty-three polymorphic bands were scored (for more details see Bernet et al., 2003). External controls were (i) V4 and V6 were the same cultivar, the same seed lot; (ii) V8 and V12 were the same cultivar, different seed lots; (iii) V13, V14, and V41 were considered to be the same cultivar for agronomic traits; (iv) V26 and V27 were also considered the same cultivar for agronomic traits; (v) V33 and V34 were the same cultivar, different seed lot; and (vi) V38 and V39 were the same cultivar and the same seed lot.


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  		Table 1. Agronomic traits.

 
Data Analysis
Molecular Traits
For all entry samples the relative frequency of presence of a RAPD band was registered. The Prevosti distance (Prevosti, 1974, cited by Wright, 1978), also named Gregorious distance (Gregorious, 1974, 1984), between cultivars was calculated as

where dij is the distance between element i and j, p is the total number of bands and xik and xjk represent the relative frequency for presence of band k.

The matrix of genetic distances was subjected to Principal Coordinate Analysis (PcoA) (Gower, 1966).

Agronomic Traits
An extension of the simple matching coefficient of similarity between entries was calculated for qualitative variables (A, B, H, and J) and binary variables (C, D, E, O, and P) (Table 1). Level "unknown" was taken as missing. The definition of the similarity coefficient sij was the number of characters common to entries i and j divided by the total number of characters. Relationships among the 41 entries were investigated via PcoA and depicted in a two-dimensional scatter plot. For the quantitative traits (F, G, I, K, L, M, and N) a Principal Component Analysis on the standardized variables was performed by the PRINCOMP procedure in SAS version 8.2 (SAS Institute, 1990).

Joint Analysis
GPA was performed by Genstat 5 release 3.2 (Genstat 5 Committee, 1996). To illustrate the consensus configuration generated by the GPA, the Euclidean distance between cultivars in the consensus space was calculated. Cluster analysis was conducted on these Euclidean distance matrices with unweighed pair-group method based on arithmetic averages algorithm (UPGMA).

To compare the results from the GPA with alternative approaches, we used a cucumber data set in the following way.

  1. PcoA was used on similarity matrices obtained via (i) generalization of the simple matching similarity coefficient, defined as above, after discretizing all variables and (ii) Gower's general similarity coefficient (Gower, 1971).
  2. Correspondence Analysis by the Chi-square distance was determined by the Escofier (1979) method to discretize the quantitative variables.

Mantel test (Mantel, 1967) was used to establish the relationships between the molecular, agronomic, and joint distances–similarity matrices. In all ordinations, a Minimum Spanning Tree (MST) from the corresponding distance–similarity matrix was added. PcoA, scatter plot, Cluster Analysis, and Mantel test statistics were calculated by the NTSYS (Numerical Taxonomic System ver. 2.11) program (Rohlf, 2002).


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Ordinations of Cultivars According to the Type of Variable
Qualitative Agronomic Traits
The three main eigenvalues of the PcoA on the simple matching similarity matrix explained 51.29, 10.95, and 8.80% of the total variation, respectively. Figure 1a shows the configuration of the cultivars in the plane defined by the first two coordinates and a minimum-spanning tree. Two main groups are formed at the left and right sides of the plane. All individuals belonging to the Beth-{alpha} and Dutch fruit type constituted a group, whereas at the right of the plane, the individuals belonging to the slice and gherkin types formed another group. Regarding the external controls, this characterization does not distinguish among cases 1, 2, 5, and 6. For case 4, the result is ambiguous because V26 was resistant to Cucumber mosaic virus (CMV) (trait P), whereas this information was unknown for V27; therefore, there is not enough information to ensure the equality of both samples.



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  		Fig. 1. Two-dimensional agronomic ordination of the 41 entries of cucumber and Minimum Spanning Tree (MST): (a) Principal Coordinate (PcoA) for qualitative traits and (b) Principal Component Analysis (PCA) for quantitative traits.

 
Quantitative Agronomic Traits
Results from the Principal Component Analysis using standardized variables show that the first three components are responsible for 60.46, 15.91, and 9.82%, respectively, of the total variation. Figure 1b depicts the projection of the individuals on the main plane of the analysis. Entries tend to gather in three groups mainly following a gradient through the first axis. Two of these groups involve cultivars of the Dutch and Beth-{alpha} types, respectively, whereas, the third group contains all the cultivars belonging to the slice and gherkin types. Only four pairs of cultivars have identical quantitative characters: V4-V6, V26-V27, V33-V34, and V38-V39; hence, these facts along with those above, indicate that the discriminatory power of the quantitative variables is higher than that of the qualitative ones.

Molecular Traits
The first three factors of the PcoA from the Prevosti distance matrix accounted for 43.30, 12.53, and 10.30% of the total variation, respectively. Figure 2 shows the plane defined by the first two factors. Cultivars belonging to the Beth-{alpha} and Dutch types form two distinct groups, whereas slice and gherkin types once again are confounded. The MST shows that there is poor agreement between the relationships found in the bidimensional space and those in the original distance matrix. Except for the Dutch group where points that are close in the bidimensional representation and are also connected by the MST branches, the entries of the other types show peculiar situations. As far as the controls are concerned, they were verified for the cases 1, 2, and 6.



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  		Fig. 2. Two-dimensional ordination of the 41 entries of cucumber after a Principal Coordinates Analysis using RAPD markers data and Minimum Spanning Trees (MST).

 
The relationship between the distance matrices for the characterization according to the three types of variables is presented in Table 2. The correlations between the two types of agronomic variables, and more so with the molecular classification, are relatively low but highly significant on the basis of the Mantel test.


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  		Table 2. Correlations between matrices of distance—similarity according to the type of variable: agronomic qualitative using simple matching, agronomic quantitative using Euclidean distance and molecular using distance of Prevosti.

 
Joint Characterization Provided by the Generalised Procrustes Analysis
The consensus configuration based on both qualitative and quantitative agronomic traits is presented in Fig. 3a. The first three components are responsible for 61.05, 12.75, and 8.83% of the total variation, respectively. Although all agronomic traits are considered here, there is still not clear differentiation between cultivars belonging to slice and gherkin types although the latter are generally located to the left of the group. On the other hand, there is a well-defined configuration for the Beth-{alpha} and Dutch types as already shown determined on the basis of the quantitative variables.



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  		Fig. 3. Configuration of consensus matrix of Generalized Procrustes Analysis (GPA) in first two axes with Minimum Spanning Trees (MST): (a) consensus between qualitative and quantitative agronomic data, and (b) consensus between agronomic traits and molecular traits.

 
Finally, a consensus configuration between the previously found agronomic characterization and the molecular one was obtained and is represented in Fig. 3b. The GPA clearly identified four distinct groups, one in each quadrant, that correspond to the known classification of these cucumber cultivars, except for entries V21 and V29, which have interchanged their groups. Nevertheless, when the MST is added in the plane, entry V21 is connected to V22 and, through that entry, to the rest of the gherkin group. Similarly, V29 is connected to V31. When the third axis is considered (Fig. 4), the method allows a definite separation of the groups corresponding to entries belonging to the slice and gherkin types, including V21 and V29. Moreover, the use of GPA allows calculation of the degree of closeness between analogous points (corresponding to the same entry, but obtained from ordinations based on different types of traits). This measure will correspond to the concordance between the agronomic and molecular characterizations. For this purpose, the Euclidean distance between analogous points was calculated and the results are shown in Table 3.



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  		Fig. 4. Configuration of consensus matrix of Generalized Procrustes Analysis (GPA) in first and third axis.

 

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  		Table 3. Agreement between agronomic and molecular characterization from the GPA: Distribution of the Euclidean distance between analogous points for each entry, Q1: first quartile (0.0866), Med: median (0.1093), and Q3: third quartile (0.1497).

 
To study the behavior of the controls, an UPGMA dendrogram using the Euclidean distance between points of the three-dimensional space was determined (Fig. 5). Here, the grouping of the cultivars according to the type of cucumber is clear, in contrast to the other approaches. The two controls that were the same cultivar and seed lot (V4-V6 and V38-V39) verified their genetic uniformity, whereas those that belong to the same cultivar but different seed lots (V8-V12 and V33-V34) showed minimal differences. Similar results were obtained for those entries considered to be the same cultivars because of their agronomic characteristics; however, there were doubts as to their origin (V13-V14-V41 and V26-V27). Regarding the latter, it is important to note that these cultivars were identical for molecular markers and the nonuniformity found in the cluster was simply due to the unknown resistance to CMV of V27.



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  		Fig. 5. Cluster analysis for 41 entries of cucumber for agronomic traits and random amplified polymorphic DNA (RAPDs) using Euclidean distance for consensus configuration obtained of Generalized Procrustes Analysis (GPA) and unweighed pair-group method using arithmetic averages (UPGMA) groping method. Encircled entry labels correspond to external controls.

 
Joint Characterization Based on Alternative Approaches
On the basis of the extension of the simple matching coefficient and PcoA, the first three axes were responsible for 31.41, 10.57, and 7.27% of the total variation, respectively. In addition to what has been observed with the individual characterizations, there seems to be a differentiation between the cultivars belonging to the slice and gherkin types (data not shown) with a transition area constituted by cultivars V21, V29, and V31. For Gower's general similarity coefficient, results were almost identical to the approach above; in fact, the correlation between both similarity matrices was 0.9950.

The first three eigenvalues for the correspondence analysis were 29.90, 10.52, and 9.62, respectively. With this approach cultivars tend to cluster in the first factorial plane according to their fruit type, each one in a different quadrant (data not shown). The exceptions to this pattern were entries V29 (slice type) that is located in the gherkin group and V10 and V11 (Beth-{alpha}) that are away from their group (these cultivars have in fact the worst quality of representation). The Dutch group was the most homogeneous.

The correlation between the different approaches of simultaneous characterization with each of the individual characterizations is presented in Table 4. The three types of characters (qualitative, quantitative, and molecular) had similar contribution to the consensus characterization provided by the GPA (mainly for GPA2), whereas the influence of the molecular data was much higher in the final results obtained by either the generalization of the simple matching coefficient or the correspondence analysis.


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  		Table 4. Correlation coefficient between the joint distance–similarity matrices and each individual characterization distance–similarity matrix. SM: extension of the simple matching coefficient. CA: Correspondence analysis using Escofier's approach. GPA1: Consensus agronomic characterization using Generalised Procrustes Analysis. GPA2: Overall consensus characterization using Generalised Procrustes Analysis.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
The present results allow the evaluation of GPA as a means for the simultaneous characterization of entries on the basis of agronomic and molecular traits. A collection of Cucumis has been used as example. Entries tend to be associated according to the type of fruit. However, results of the individual characterizations produced different configurations and did not properly classify the cultivars. This fact is very noticeable in the case of the slice and gherkin types. Moreover, the characterization using qualitative agronomic traits did not distinguished cultivars belonging to the Dutch and Beth-{alpha} types that were separated on the basis of either the quantitative or the molecular traits. On the other hand, the correlation between the three characterizations is fairly low, even in the case of both types of agronomic variables (see Table 2). The different configurations obtained indicate that the individual characterizations offer information that can be considered complementary. A unique pattern of association between the samples does not exist, and this fact emphasizes the importance of studying the different descriptors jointly so that the best description and interpretation of the genetic diversity can be obtained (Hillis and Moritz, 1990; Franco et al., 2001).

For a simultaneous characterization, the use of an extension of the simple matching coefficient is a logical alternative to deal with variables of different nature; its application is simple and interpretation easy. However, it has some problems stemming from the fact that there is a loss of information. First, to consider the different values of a quantitative variable or an ordinal variable as levels of a multistage qualitative variable omits the sense of ordering that they imply. Second, in the molecular characterization, we need to code data as presence or absence; then, when there is nonuniformity within the cultivar (neither 0 nor 1), the allelic frequency is in the range between 0 and 1, which should be recoded as a single value (either 0 or 1). In our case, all values different from 0 were recoded as 1. This characterization improved the results found for each individual type independently; however, the final outcome is much closer to the molecular characterization than that based on agronomic traits. This is an indication that the weight of the molecular data in the joint characterization is higher than that of the rest of the traits and is due to the fact that there are many more molecular markers than agronomic traits. Gower's general coefficient of similarity is designed to deal with mixed type of variables as in our case and is calculated as a weighed sum of similarities. Results for our data were very similar to the approach of the extension of the simple matching coefficient because the quantitative agronomic traits have a low range (Table 1) and is due to the low nonuniformity of the entries for the molecular data. Then, the same problems described above also apply for this approach.

The main disadvantage of the correspondence analysis approach is that the chi-square distance on which it is based is insufficient to quantify the phylogenetical relationships from band patterns of molecular markers, mainly when they are dominant (Bramardi, 2000). There is a closer relationship between this characterization and that based on molecular traits than that based on agronomic traits (see Table 4). So, similarly to the previous approaches, it is very sensitive to the total number of columns of each trait in the data matrix, where those traits with more variants (but not necessarily more genetic information content) have more influence on the final results. And this is not always desirable.

The GPA allows use of the most suitable distance for each type of variable and the appropriate ordination method. When applying GPA to the agronomic data (both quantitative and qualitative traits), the correlations with the original distances were very similar in absolute values (0.8781 and 0.8892 in Table 4), which indicates that in fact the consensus configuration averaged both individual configurations. Moreover, the correlation of this agronomic consensus configuration with the molecular characterization was much higher than those presented in Table 2, which uses individual characterizations. Therefore, the joint agronomic configuration is compiling more information common to the molecular characterization than each of the individual ones.

The final configuration using all data is an average of the transformed configurations. The correlation with the individual variables shows very similar values with no individual type of trait having a predominant influence, in contrast to what happened with the alternative approaches used in this study (see Table 4). The method clearly distinguished four groups, one in each quadrant; these groups are in agreement with the grouping of cucumbers by their known varietal type. Moreover, the GPA method also allows a deeper study of the relationships between the analogs to establish the concordance between characterizations. Gower (1975) recommended calculating an ANOVA to comparatively break down the total sums of squares into between and within configurations. The latter is broken down further into the consensus and the residual sum of squares. This residual sum of squares measures the divergence between the two points corresponding to the agronomic and molecular characterization to the consensus one, respectively. We have used a simpler method to obtain the divergence between two points: to calculate the Euclidean distance between the pairs of points obtained from different ordinations. Denoting A1 and M1 the points for entry 1 for the agronomic and molecular characterizations, respectively, and C1 its centroid; Gower's approach calculates [d2(A1 – C1) + d2(G1 – C1)], whereas, in our case, we simply calculate d(A1 – G1), where d indicates distance. Given that in our case only two configurations are involved, the approach is equivalent to the contribution of each individual to the residual sum of squares of the ANOVA described by Gower (1975). According to Table 3, cultivars belonging to the Dutch group have similar ordination on the basis of molecular or agronomic variables, whereas those cultivars from the gherkin type show a high discrepancy between the two ordinations. Therefore, they should be responsible for the low correlation found between the individual configurations. The Beth-{alpha} and slice varietal types are in an intermediate position.

The comparison of results from different approaches suggests that the GPA was the alternative that better fit the known grouping of these cultivars and should be recommended as an approach to ordinate entries on the basis of different types of traits, since it is possible to use different distance measures for each type of trait previously representing the entries in an individual configurations. It also "averages" the configurations found for each type of trait in such a way that there is no overweight of those variables that have more classes than others. Furthermore, it allows a deeper study of the nature of the difference or similarities of individual entries comparing different configurations obtained when studying each type of trait separately.

We have used a collection of cucumber cultivars just to illustrate the merits of the GPA approach to characterize simultaneously a set of entries on the basis of a group of traits of heterogeneous nature, and GPA has been shown to be superior to the other approaches under study. However, we believe that the conclusions are of general applicability in plant evaluation, as it has already been shown in other areas. To our knowledge, this is the first report to show the merits of GPA in plant germplasm characterization.

Received for publication October 29, 2004.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 


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