E L S E V I E R Field Crops Research 47 (1996) 117-127
F i e l d Crops R e s e a r c h
Genotype-environment interaction in faba bean: comparison of AMMI and principal coordinate models
F. Flores a,*, M.T. M o r e n o a A. Mart inez a J.I. Cubero b 9
" Dpto. de Mejora y Agronomia, Apartado 4240, Centro de Investigacidn y Desarrollo Agrdrio (CIDA), 14080 Cdrdoba, Spain l b Opto. de Gendtica, Apartado 3048, Universidad de Crrdoba, 14080 Crrdoba, Spain 2
Received 19 February 1995; revised 13 July 1995; accepted 4 March 1996
Abstract
This study analyses the genotype-by-environment (G × E) interaction of 11 genotypes of Vicia faba L., grown in 17 environments in Andalucla (Southern Spain) by two multivariate methods (AMMI and Principal Coordinate Analysis). Results of the stability analyses indicated that the most stable genotypes for resistance were not the same as those for yield. However three, L1, L2 and VF107I, were by far the most Orobanche -resistant materials and were as productive as well-established cultivars, but their yields showed low stability among environments. Progress in selection for both Orobanche resistance and yield is hampered by large environmental variation between locations. More breeding effort is needed in these three experimental genotypes in order to improve the yield stability and therefore acceptability to farmers. Multivariate analysis has shown its advantage as a helpful tool in identifying the best genotypes for a new cycles of crossing and selection. For the cultivars and environments analyzed in this study, the two methods gave equally satisfactory results in detecting cultivars that perform well and remain stable under different environment conditions.
Broomrapes ( O r o b a n c h e sp., Orobanchaceae), well-known parasites of many legumes, were de- scribed by Teophrastus as early as 300 BC and have been included in old botanical and agricultural writ- ings. Agronomic practices and breeding for resis- tance have both been tried as control measures (Cubero and Moreno, 1979). Success by either
method depends on the particular host/parasi te sys- tem. A favorite host of O r o b a n c h e c rena ta is faba bean. When it is parasitized, yields are reduced and farmers abandon its cultivation.
The problem is particularly grave in most rainfed Mediterranean environments and also in irrigated areas such the Nile Valley (Saxena and Stewart, 1983). In semiarid conditions as those found in North Africa, the Near East, Southern Italy and Southern and Eastern Spain, the problem is aggra- vated because few crops are available for cultivation and because of the extended viability of O r o b a n c h e
118 F. Flores et a l . / Field Crops Research 47 (1996) 117-127
other susceptible hosts ( Vicia sativa, Lens culinaris) should be components of a sustainable agriculture in these regions, but broomrape limits their cultivation. Therefore, a major objective of any breeding pro- gramme in the Mediterranean region is to develop broomrape-resistant varieties of faba bean that are well adapted to a wide range of environments.
Resistance produced by major genes has been found in very few host/parasite systems. But even in these cases, in which clear, necrotic lesions in the roots can easily be used for screening, the mecha- nism of the resistance is not known (Lane and Bailey, 1991; Pustovoit and Shkuropat, 1978). Much less is known of quantitative systems. Despite exten- sive research on biochemical and physiological as- pects of faba bean/O, crenata (among others: Anonymous, 1973; Pieterse et al., 1994; Wegmann and Musselman, 1991; Cubero et al., 1994). Toler- ance (i.e., the host can produce a significant yield in the presence of the parasite) is also known, but not the mechanism, although it may be related to the ability of the crop to compete with the parasite for assimilates and water. Tolerant cultivars cannot be recommended as they sustain or even increase the seedbank in the soil (a single plant of Orobanche crenata can yield up to half a million seeds (for a review see Cubero, 1984).
Weak resistance is present in a few genotypes (especially those belonging to the paucijuga group) and is thought to be the result of a poor root-branch- ing habit. Until now, the only source of agronomi- cally useful resistance was found by Egyptian scien- tists in experimental genotypes derived from sponta- neous crosses between Egyptian and Mediterranean sources (Nassib et al., 1982). This resistance was demonstrated to be polygenic (Hernfindez, 1987) and was transferred to Spanish cultivars by recurrent selection (Cubero et al., 1992). The cultivar 'Baraca' was derived from some Spanish resistant genotypes and shows greater resistance than the original F402 (Zaitoun and ter Borg, 1994). This resistance is not surprising as the recurrent scheme has been able to incorporate minor genes responsible for weak resis- tance (from paucijuga) or even of tolerance (from the cv. 'Alameda'). A susceptible genotype that sur- vives parasitism can have up to 10 Orobanche shoots per plant. While a resistant plant from our best experimental genotypes shows an average of 0-0.2
shoots per host plant. In farmer's fields 'Baraca' shows an average of 0.4. Two broomrapes per host plant are enough to halve yield in a moderately susceptible cultivar (Mesa-Garc~a et al., 1986), but a tolerant one, as 'Alameda', can have up to four without a significant loss of yield.
This resistance has proved to be stable and effec- tive in the Nile Valley, Southern Spain, Morocco and Syria (Hanounik and Bisri, 1991). It is a horizontal type of resistance, sensu Van der Plank. However, genotypes resistant to O. crenata can be attacked by other broomrape species, as with the rare O. foetida, where its range overlaps with that of the host, as occurs in Tunis.
Resistance to O. crenata has only been detected under field or greenhouse conditions. In vitro, filter paper and agar germination tests are not correlated with field or greenhouse results (Aalders and Pieters, 1987; Van Woerden, 1993). The lack of a suitable in vitro screening method remains a major difficulty in looking for other sources of resistance. Thus, the most reliable index for screening remains the number of Orobanche plants per host or any equivalent value. The expression of resistance to broomrape is known to show large G X E interaction (Cubero et al., 1992). Further, a resistant cultivar also has to show high and stable yield.
The G × E interaction structure is an important aspect of the plant breeding programs and of the introduction of new crops and cultivars. A significant G X E interaction for a quantitative trait such as seed yield or resistance to a pest can seriously limit gains in selecting superior genotypes for both new crop introductions and improved cultivar development (Kang, 1990). In this case, the large G X E variation usually impairs the accuracy of both yield and the number of Orobanche/plot, and reduces the heri- tability of yield. Environmental variation causes dif- ferential genotypic responses that result in rank changes of genotypes.
The response of a genotype in E different envi- ronments may be conceptualized as a pattern in E dimensional space, with the coordinate of an individ- ual spatial axis being the grain yield or number of Orobanche/plot of the genotype in one environ- ment. Since genotype responses are multivariate rather than univariate (Lin et al., 1986; Van Oost- erom et al., 1993), multivariate techniques are
F. Flores et al./Field Crops Research 47 (1996) 117-127
Table 1 Genotypes included in trials (1990-1992)
119
Code number N a m e Characteristics Mean yield (kg ha- ~ ) Mean number of Orobanche/plot
1 RUMBO b Commercial cultivar 2031 206 2 VF 1071 Resistant genotype 2113 25 3 BROCAL b Commercial cultivar 2238 179 4 NV3 b Experimental genotype 2163 125 5 NV2 b Experimental genotype 2183 150 6 PROTHABON Comercial, susceptible cultivar 1761 276 7 AMCOR b Commercial cultivar 2190 193 8 L2 a Experimental resistant genotype 2185 27 9 NV5 b Experimental genotype 2228 103
a L1 and L2 are foundation genotypes of the recently released resistant cultivar 'Baraca'. b Level of resistance unknown before the trials.
preferable as they are usually more effective in explaining G × E interactions than linear regression models (Zobel et al., 1988; Gauch and Zobel, 1988;
Nachit et al., 1992). The Additive Main effects and Multiplicatit~e In-
teraction (AMMI) model with prediction assessment was proposed for analysis of two-way tables. In this model, main effects are first accounted for by an analysis of variance, whereafter the interaction is analyzed by a principal component analysis (Gauch, 1988; Gauch and Zobel, 1988). The optimum num- ber of interaction principal component axes (IPCA) to be retained in the model, in order to obtain the most accurate estimation for both grain yield and number of Orobanche/p lo t , can be determined by two different assessments referred to in the literature as 'predictive' and 'postdictive' . The predictive as- sessment splits the data set into a part for model validation and uses the cross validation technique
(Wold, 1978; Krzanowski, 1983; Gauch, 1988; Gauch and Zobel, 1988). The neologism 'postdictive' refers to a different method of validation which uses an F-test to identify the significance of each IPCA.
Principal Coordinate Analysis is a multidimen- sional scaling or ordination technique used in this analysis to represent the structure or pattern that may be present in the observed original data matrix and provide a geometrical configuration of points in a low-dimensional space (Gordon, 1980). The distance between points in the low-dimensional diagram will reflect the relationship between items in the original observed matrix. Similar items are, therefore, repre- sented by points which are close together and dissim- ilar items are represented by points distant from each other.
The objectives of this study were: (1) to deter- mine the magnitude of G × E interaction effects on both yield and broomrape resistance for diverse envi-
Table 2 Description of the environments included in the trials
Location Year Site trial Coordinates
Province City Codes
Altitude (m) Climate type Soil type
C6rdoba C6rdoba 1990-91-92 1-7-13 37°5 I'N 4°51'W Sevilla Carmona 1990-91-92 2-8-14 37°28'N 5°38'W Cfidiz J e rez 1990-91-92 3-9-15 36°41'N 6°08'W J a e n M e n g i b a r 1990-91-92 4-10-16 37°46'N 3°47'W Granada Granada 1990-91 5-11 37°12'N 3°35'W Mfilaga Churriana 1990-91-92 6-12-17 36°50'N 4°26'W
alluvial vertisol calcareous with slope clay clay loam sandy loam
120 F. Flores et al . / Field Crops Research 47 (1996) 117-127
ronments in the Andalusian region; and (2) to exam- ine and compare the results obtained by AMMI and Principal Coordinate Analysis applied to faba bean cultivar trials conducted from 1990 to 1992.
2. Material and methods
2.1. Plant material and environments
Eleven genotypes of faba bean were grown in 17 environments (location-by-year combinations). De- tails of the genotypes and the environments are given in Tables 1 and 2, respectively. Fig. 1 shows the locations of the trials. The genotype VF 1071 was derived from Giza 402 which showed a good level of broomrape resistance in the Nile Valley (Nassib et al., 1982). L1 and L2 are two foundation compo- nents of the recently released broomrape resistant
Spanish cultivar 'Baraca' (Cubero et al., 1992). Three commercial cultivars ( 'Prothabon', 'Rumbo' and 'Amcor') , two checks ( 'Alameda' and 'Brocal ') and three experimental advanced genotypes (NV2, NV3 and NV5) were also included. 'Alameda' is a toler- ant cultivar. As indicated in Table 1, the level of resistance for some of these genotypes or cultivars was not known.
The trial was a randomized complete block design with four replications at each location. Plots were 4.2 m wide (6 rows, 70 cm apart) and 10 m long. Sites were selected after consulting with experimental farms and extension service agents about recent severely infested plots. Before performing the trials, the plots were sown with the tolerant cultivar 'Alameda' to ensure infestation. The most infested area at each site was chosen for the experiment. The plots were cross ploughed twice before sowing. The fertilizer applied was a 0 - 1 4 - 7 ( N - P - K ) complex
h
/ ) S P A I N
, oR.,,NAoA /
Y /
\
<.
Fig. 1. The locations of the trials in Andalucia, Spain.
F. Flores et al . /Field Crops Research 47 (1996) 117-127 121
type (450 kg/ha) . Grain yield and number of Orobanche /p lo t were obtained from a sample of 28 m 2 in the center of the plots.
2.2. Statistical methods
1. The AMMI model is
N
Yij ~- t -L + gi q- ej + Z h k ' g i k B j k Jr- gij 1
where Y~j is either the yield or the number of Orobanche/p lo t of the i-th genotype in the j-th environment; Ix is the grand mean; gi and ej are the genotype and environment deviations from the grand mean, respectively; )t k is the eigenvalue of the prin- cipal component analysis (PCA) axis k; "/ik and gjk are the genotype and environment principal compo- nent scores for axis k; N is the number of principal components retained in the model; and eij is the residual term. Environment and genotype PCA scores are expressed as unit vector times the square root of h k (i.e., environment PCA score = h°£58jk; genotype PCA score = h°/5 ~ik) (Zobel et al., 1988).
Gauch and Zobel (1988) created the term 'post- dictive' symmetrical to 'predictive' in order to mea- sure the level of success of the prediction. Postdic- tive success was measured by approximate F-test by comparing each principal component's mean square with the pooled within-environment error mean square. Those PCA axes that were not significant were pooled into a residual term.
Predictive assessment was carried out by the cross-validation procedure described by Gauch and Zobel (1988). The data were split into two sub- groups, model data and validation data. For each treatment (i.e., genotype and environment combina- tion), two replicates were selected at random to be modelled by AMMI, and the other two were reserved as validation observations.
Six models were fitted to the data. The first was the AMMI0 model which estimated the additive main effects (i.e., genotypes and environments) with- out considering interaction. The second, AMMI1, combined the main effects from AMMI0 with inter- action effects estimated from the first interaction principal component axis (IPCA1). The third model, AMMI2, considered main effects plus two interac-
tion principal components. AMMI3-AMMI4 in- cluded cumulatively one more interaction principal component axes. The seventh model (DATA) with 10 PCA axes was the full model, which completely specified the data matrix and equalled the average of the two replicates selected at random for modelling.
Predicted values for each model were compared with the validation data by computing the sum of squared differences over all genotypes and environ- ments. This sum of squared differences was divided by the number of validation observations and the square root was taken to give the Root Mean Square Predictive Difference (RMS PD). A small value of RMS PD indicates good predictive success. The average RMS PD value of 25 validation runs was used. The best model was selected (on the basis of the average RMS PD (Crossa et al., 1991)) and re-applied to the data including all replicates.
2. The stability analysis method, based on Princi- pal Coordinate Analysis, proposed by Westcott (1987) and used by Crossa (1988) was also used. Westcott's (1987) measure of similarity between two genotypes X and Y, in a given environment i is:
S i ( X , Y ) = [ H i - ( X i + Y i ) / 2 ] / H i - L i
where H i = highest mean yield of a genotype in environment i; L i = lowest mean yield of a genotype in environment i; X i = mean yield of genotype X in environment i; and Yi = mean yield of genotype Y in environment i.
When more than one environment is considered, the similarity between genotypes X and Y is defined as the average of Si(X, Y ) across environments.
As detailed by Crossa (1988) the similarity mea- sured between any given pair of genotypes indicates the proximity of its average to Hi (it was used for yield), and the dissimilarity [1 - Si(X, Y)] indicates the proximity of its average to L i (it was used for number of Orobanche / plot). For example, for yield, smaller values for S indicate greater proximity to H (greater dissimilarity to L), and higher values for S indicate greater proximity to L (greater dissimilarity to H). Crossa (1988) stated that "the analysis deter- mines a point (genotype) from which all other geno- types radiate. This point, with maximum value for S, is the center of the scattergram (see Westcott, 1987, on minimum spanning tree). Therefore, genotypes with higher values for S are represented by points
122 F. Flores et al. / Field Crops Research 47 (1996) 117-127
clustered near the center of the scattergram and genotypes with smaller values for S are represented by points far from the center".
According to Westcott (1987), the environments are first ranked in descending order of mean yield and the low- and high-yielding environments are then analyzed in cycles. Genotype performance is first analyzed for the lowest yielding environment (called cycle L1), the second cycle (L2) involves analyzing the two lowest-yielding environments, and so on. The same procedure is followed for the high- est yielding environments (cycle H1, H2 . . . . etc). The high yielding genotypes are represented by points located further away from genotypes that yield be- low the average mean. The stable genotypes are the ones that are consistently good over cycles (West- cott, 1987). Rather than including a larger number of scattergrams, the stability patterns of the genotypes are described in the text and only two scattergram (Fig. 3a and b), corresponding to cycles H5 (a, for grain yield), and L4 (b, for number of Orobanche/ plot), are presented.
Table 5 shows the mean length of the minimum spanning tree including only the lowest environ- ments (MEDLI), including only the highest environ- ments (MEDHI) and including all environments (MEDTO) (Cubero and Flores, 1994).
Table 3
Additive main effects and multiplicative interaction analysis of
variance for grain yield (kg ha - I ) and the number of
Orobanche/plot including the first three and two interaction
principal component analysis (IPCA) axes, respectively
a Hypothesis constructed based on a mixed model, the signifi-
cance of the A M M I models based on postdiction. NS, *, * *,
• * * : P > 0.05; 0.05 > P > 0.01; 0.01 > P > 0.001; 0.001 > P >
0.000. Mean Square x 105
b Fraction of sum of squares associated to each term or interac-
tion. c Mean Square x 104.
a df = 112.
3. Results
3.1. AMMI for grain yield
Additive main effects and multiplicative interac- tion analysis showed that environments, genotypes, and G X E interaction were highly significant (P < 0.01) and accounted for 56.4, 2.3, and 13.6% of the total sum of squares (SS), respectively (Table 3). The criterion of postdictive success for AMMI using all the data (all four replications) and F-tests at the 0.05 probability level recommended the inclusion of the first two interaction PCA axes in the model (Table 3). The model captured 94.6% of the treat- ments SS (environment + genotype + G × E interac- tion SS), using 74 degrees of freedom (df): 10 for genotypes, 16 for environments and 48 for IPCA1 and IPCA2.
The first PCA axis accounted for 57.6% of the
interaction sum of squares, the second axis explained 13.6% and the third 9% of the G X E sum of squares (Table 3).
In the predictive assessment, AMMI1, the model including only the first IPCA, had the lowest value for RMS PD and was hence most predictive (Table 4). This model accounted for 92.0% of the treat- ments SS using 51 df; the remaining 8.0% of the treatments SS was non-interpretable random varia- tion.
AMMI analysis provides a graphical representa- tion (or biplot, Fig. 2a), it shows main effect means on the abscissa and IPCA1 values of both genotypes and environments simultaneously. Displacement along the abscissa reflects differences in main ef- fects, whereas displacement along the ordinate illus- trates differences in interaction effects. Genotypes with IPCA1 values close to zero show wider adapta- tion to the tested environments. A large genotypic
F. Flores et al. / Field Crops Research 47 (1996) 117 -127 123
IPCA1 value reflects more specific adaptation to environments with IPCA1 values of the same sign.
Three groupings of genotypes are evident from Fig. 2a:
Group 1 includes genotypes 2, 8, and 11, that is, broomrape-resistant genotypes. They show a homo- geneous mean yield response close to the grand mean and a similar large negative interaction. For
• G E N O T Y P E S ,& E N V I R O N M E N T S - - G R A N D MEAN
Fig. 2. Biplots of principal component analysis ( IPCA 1) axis 1 against (a) mean yield (kg ha -1 ) and (b) the number of Orobanche/plot for 11 genotypes grown at 17 environments. The vertical line represents the grand mean of the experiment. The numbers on the biplot refer to environments ( • E 1) l - 17 or genotypes ( O G 1 ) l - 11.
124 F. Flores et al. / Field Crops Research 47 (1996) 117-127
these genotypes, the AMMI1 model predicts geno- type yields that are close to those of the AMMI0 model in environments with IPCA1 values near zero, larger yields than the AMMI0 model in environ- ments with negative environment IPCA1 values, and smaller yields than the AMMI0 model in environ- ments with positive environment IPCA1 values.
Group 2 consists of genotypes 1 and 6, two commercial genotypes, susceptible to broomrape. Their IPCA1 scores are positive and large while their mean yields differ from each other.
Group 3 consists of genotypes 3, 4, 5, 7, 9, and 10. It is a very heterogeneous group, consisting of experimental and commercial genotypes. They show a similar mean response above the grand mean. They show the smallest interactions, and are therefore the most stable genotypes.
The environments show much variability in both main effects and interactions, IPCA1 for environ- ments showing no clear patterns (Fig. 2a).
3.2. Principal coordinate analysis
Table 5 Lengths of the minimum spanning tree (m.s.t.) for grain yield and the number of Orobanche/plot a
a Data are based on 11 faba bean genotypes grown in 17 environ- ments in Spain. MEDLI: Length mean of the m.s.t, including only the lowest environments. MEDHI: Length mean of the m.s.t. including only the highest environments. MEDTO: Length mean of the m.s.t, including all environments. The bolded values are the genotypes represented by points the most far from the center of the scattergram in each cycle (LI, HI and LI + HI).
Stability analysis performed for 8 low- and 9 high-yielding environments indicated that genotypes 3, 5, 7 and 10 were the most stable in the L cycles and genotypes 3, 5, 7, 9 and 11 were the most stable in the H cycles (Table 5).
The genotypes 3, 5 and 7 showed a clear pattern of stability in all cycles (in all environments). Fig. 3a shows the relationship among genotypes indicated by results of analysis for the five highest-yielding envi- ronments (H5). Genotype 11 performed well in H5
Table 4 Average RMS PD (kg ha-1 and number of Orobanche/plot) for seven models based on 25 randomizations a
a Data are based on 11 faba bean genotypes grown in 17 environ- ments in Spain.
and had a remarkable stability pattern throughout all H cycles (Table 5)
3.3. AMMl for number of Orobanche /plot
Genotype and environment main effects and their interaction were statistically significant (Table 3), suggesting a broad range of genotypic diversity and environmental variation.
Significant differences among genotypes ac- counted for less than 7% of the total variation. In contrast, the environment sum of squares exceeded 31% and G X E accounted for close to 19% of the total variation (Table 3). The first IPCA axis ac- counted for 85% of the interaction sum of squares and the second axis explained 8.7% of the G X E sum of squares (Table 3).
Postdictive assessment by F-tests at the 0.05 prob- ability level recommended IPCA1, that is, inclusion in the model of one interaction PCA axis (Table 3). The model captured 95.2% of the treatments SS, using 51 degrees of freedom: 10 for genotypes, 16 for environments and 25 for IPCA1.
Predictive success, as measured by the average RMS PD for 25 random partitions, recommended the
F. Flores et al./Field Crops Research 47 (1996) 117-127 125
Fig. 3. Plots of the first two principal axes from a principal coordinate analysis of a set of faba genotypes in 17 environments, (a) in cycle H5 for grain yield and (b) in cycle L4 for the number of Orobanche/plot. Part of the minimum spanning tree is super- imposed on the plot, the distances shown between genotypes (e.g., G6-G9 = 0.48) being the similarities.
first interaction PCA axis as the most predictively accurate. The AMMI1 model had the lowest average RMS PD (187.46) (Table 4).
Fig. 2b shows the biplot for the AMMI1 model, which explains almost 95% of the treatments varia- tion. Four groupings of the genotypes are suggested.
Group 1 includes the broomrape resistant geno- types 2, 8, and 11. They show a similar mean number of Orobanche/plot and a homogeneous, large positive interaction.
Group 2 includes genotypes 4,9, and 10. The first two are experimental genotypes and 10 is a commer- cial cultivar that is tolerant although not resistant to broomrape. They show a similar mean near the grand mean but their interactions with environment differ.
The interaction PCA1 score for genotypes 9 and 10 are positive and moderate; genotype 4 is close to zero and it is therefore the most stable.
Group 3 includes genotypes 1, 3, 7 (commercial cultivars), and genotype 5 (experimental genotype). They show high mean (above the grand mean for the number of Orobanche/plot) and a similar negative interaction PCA1 scores.
Group 4 includes genotype 6, a susceptible com- mercial variety. It shows the highest mean number of Orobanche/plot and its interaction score is the largest negative.
Most of the environment IPCA1 scores are near zero except environments 7, 9, and 16 which show positive environment IPCA1 scores (Fig. 2b).
3.4. Principal coordinate analysis
Principal coordinate analysis of 10 locations with a low number of Orobanche/plot showed a clear pattern of stability for genotypes 2, 8, 10 and 11 (Table 5). Of these, genotype 10 was closer to the center in L 3 - L 1 0 cycles, genotypes 2, 8 and 1l failed to show as isolated points in L2 but appeared very stable in the other L cycles.
Genotypes 2, 8, 9 and 11 were the remotest points (and therefore the most stable) in the four H cycles, except in H2-H4, where genotype 9 did not feature. Therefore genotypes 2, 8 and 11 have shown consis- tent patterns of stability in both L and H cycles (Table 5).
For all the genotypes three environments showed no Orobanche/plot. Fig. 3b shows the relationship among genotypes indicated by results of analysis for the four environments with the lowest number of Orobanche / plot (L4).
4. Discussion
According to Principal Coordinate Analysis the genotypes ' B R O C A L ' (3), NV2 (5) and 'AMCOR' (7) had relatively good yields, maintaining stability in unfavorable environments, and responding well to favorable environments.
Results obtained with the AMMI analysis indicate that genotypes ' B R O C A L ' (3), NV3 (4), NV2 (5), ' A M C O R ' (7), NV5 (9) and ' A L A M E D A ' (10) are
126 F. Flores e t al. / Field Crops Research 47 (1996) 117-127
the most stable because their IPCA1 scores are near zero. However, genotypes 4 and 10 performed well and maintained high yield levels only in low-yield- ing environments. Genotype 9 showed good stability only in high-yielding environments, according to Principal Coordinate Analysis.
Genotypes L2 (8) and L1 (11) also consistently maintained stable yield in high-yielding environ- ments. This result agrees with that from AMMI. Thus genotypes VF 1071 (2), L2 (8) and L1 (11) showed the largest negative IPCA1 scores. Most of high-yielding environments also showed either nega- tive or near zero IPCA1 scores.
Concerning the number of Orobanche/plot , the spatial method (or Westcott method) indicated that genotypes VF 1071 (2), L2 (8) and L1 (11) showed good stability across both low- and high-yielding environments. Two other genotypes also showed sta- bility: genotype NV2 (9) performed well only at environments with a high number of Orobanche/p lo t and genotype ALAMEDA (10) maintained its stabil- ity in environments with high number of Orobanche/p lo t , while responding well to environ- ments with a low number of Orobanche/plot .
These results agree with those obtained with the AMMI analysis (see biplot, Fig. 2b), except for genotype NV2 (9) which showed a similar IPCA1 to genotype ALAMEDA (10). Genotypes VF 1071 (2), L2 (8), NV2 (9), L1 (11) and ALAMEDA (10) showed adaptation to most environments, seem in the negative IPCA1 scores, while these genotypes had the largest positive IPCA1 scores. In this case a large genotypic IPCA1 score reflects more specific adaptation to environments with IPCA1 scores of the opposite sign.
Genotypes L1 (11), L2 (8) and VF1071 (2) were by far the most broomrape-resistant genotypes and were as productive as well-established genotypes, but their yields showed poor stability among envi- ronments. More breeding effort is needed in these three experimental genotypes to improve yield stabil- ity.
Two genotypes, 'BROCAL' and 'AMCOR', and one experimental genotype, NV2, proved to be the most widely adapted for yield in all environments despite the high number of Orobanche /p lo t recorded in their plots. High density of Orobanche is not favorable as it would increase the broomrape seed
reserve in the soil. Genotypes from these two groups are valuable for breeding faba beans combining high yield and broomrape resistance.
The results obtained with the spatial method are useful for comparing the merits of different geno- types, and indicate clearly which ones are capable of both stable yield and resistance across environments. For the genotypes and environments analyzed in this study, the spatial method gives results as satisfactory as the AMMI analysis in detecting genotypes that perform well and remain stable under different envi- ronmental conditions.
Our results show that the resistant genotypes be- have better than susceptible ones in conditions of heavy infestation but these resistant genotypes are not yet as stable as the best yielders even if the latter are susceptible. Thus, it seems necessary to perform one or two more cycles of recurrent selection after crossing the best and most stable yielders with the most resistant ones. At present, the use of a resistant genotype has to be recommended to farmers for infested fields. Otherwise, the use of good and sta- ble, although susceptible yielders (such as 'BRO- CAL'), is the best strategy. If the infestation level is unknown, farmers can sow 'Alameda', or any other highly tolerant and productive genotype. In this way, the crop can be assured and the level of infestation can be observed.
Acknowledgements
Authors are grateful to Prof. L. Musselman (Old Dominion University, NC, USA) and to two Field Crops Research anonymous referees whose com- ments and suggestions have greatly improved the manuscript.
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