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Genotype by environment interaction and adaptation in barley breeding: basicconcepts and methods of analysis

Jordi Voltas1, Fred van Eeuwijk

2, Ernesto Igartua

3, Luis Garca del Moral

4, Jos Luis Molina-Cano

5& Ignacio Romagosa

5

1Dpt. Producci Vegetal i Cincia Forestal, Universitat de Lleida, Alcalde Rovira Roure 177, Lleida 25198,Spain2 Dpt of Plant Sciences, Wageningen University, Laboratory of Plant Breeding, P.O. Box 386, 6700 AJWageningen, The Netherlands3 Estacin Experimental de Aula Dei CSIC, Apdo. 202, Zaragoza 50080, Spain4 Departamento de Biologa Vegetal, Facultad de Ciencias, Universidad de Granada, Granada 18001, Spain5Area de Cultius Extensius, Centre UdL-IRTA, Alcalde Rovira Roure 177, Lleida 25198, Spain

Abstract

Genotype by environment interaction (GE) has important consequences in barley breeding. It oftencomplicates testing and selection of superior genotypes, reducing genetic progress in breeding

programs. This drawback may be overcome by a better understanding of the genetic andenvironmental factors that determine GE and adaptation of genotypes. An important array of statisticaltechniques is nowadays available to breeders and researchers to cope with the presence of relevant GEin multi-environment trials. This paper begins with a review of recent literature on the latest barleystudies on GE and adaptation, including potential biotic and abiotic causes underlying GE. Moststudies reported are empirical, describing postdictively genotypic performance across environments.As an alternative, methods allowing a more analytical approach are proposed, in which genotypes andenvironments are characterized in terms of external variables that affect genotypic performance. Thesemethods are applied to a real barley data set. After data description, a number of selectedmultiplicative models are developed, namely the additive main effects and multiplicative interaction

(AMMI) model, and the factorial regression model. Finally, the implications of GE in barley breedingare discussed. As an appendix, the SAS programs are given for the models described.

Key-words: genotype by environment interaction, adaptation, AMMI, factorial regression, breedingprograms

Introduction

Barley breeding is largely empirical. In the first segregating generations, breeders focus on highlyheritable traits, such as height, spike morphology, phenology, to concentrate later on grain yield and

end-use quality. Extensive multilocation trials carried out during a series of years are used in the finalselection cycles to identify superior genotypes. This task is not generally easy due to the frequentpresence of genotype by environment interaction (GE). GE is differential genotypic expression acrossenvironments. It attenuates association between phenotype and genotype, reducing genetic progress in

breeding programs.

Means across environments are adequate indicators of genotypic performance only in the absence ofGE. If GE is present, use of means across environments ignores that genotypes differ in relative

performance over environments. In plant breeding, the most important type of GE is crossover orqualitative, which implies changes in the rankings of genotypes across environments (Baker, 1988).With non-crossover interactions, genotypes with superior means can be recommended for allenvironments. Crossover GE complicates breeding, testing and selection of superior genotypes.

Identification of specifically adapted genotypes then becomes a way for increasing genetic gains.

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For trials in which locations and genotypes are repeated across years, the sum of squares of GE can bepartitioned into genotype by locations (GL), genotype by years (GY) and genotype by locations byyears (GLY) interactions. This partitioning must be based on series of trials carried out over sets ofsufficient locations and years that are representative of the target area for the program. If so, it allowsfor an assessment of the spatial and temporal components of genotypic adaptation. If GL is thedominant portion of GE, then specific adaptation is exploitable by identifying homogeneous regionsthat minimize GE within regions and form uniform domains for release and recommendation ofgenotypes. Where GY and GLY terms dominate, as too often happens, no simplification involvingspatial subdivision of growing regions is possible.

The statistical analysis of GE and its breeding implications are among the most recurrently addressedtopics in breeding literature and have been reviewed throughout the years (most recently by vanEeuwijk (1996), Kang and Gauch Jr. (1996), Cooper and Hammer (1996), and Kempton and Fox(1997)). Most studies are purely empirical describing postdictively fixed genotypic performancesacross a fixed sample of environments. A preferred analytical approach should characterize bothgenotypes and environments in terms of a number of biotic and abiotic variables, which directly affect

performance. The objective of this work is not to present a historical review of the subject, nor to

discuss in a statistical sense a subset of methods from the array of available techniques. Our approachinvolves the analysis of a specific barley data set to describe and illustrate current statistical modelsfocussing on interpretable GE variation. The methodology proposed is based on the selection ofindependent genetic, physiological and biophysical variables, and aims at being a predictive breedingstrategy.

The structure of this chapter is as follows. First, a review of the latest barley studies on GE isprovided, briefly describing both the biotic and abiotic causes underlying GE. Next, a worked exampleof a barley trial is given. After description of the data, a series of alternative multiplicative models aredeveloped. Finally, the implications of GE in barley breeding are discussed. As an appendix, the SAS

programs (SAS Inst. 1989a, 1989b, 1997) are given for the models described.

Genotype by environment interaction in barley

Genotype by environment interaction (GE) for grain yield in barley has been reported in numerousstudies under several designations (e.g. different response patterns, adaptation, or stability ofgenotypes). Although it is always difficult to identify a causal relationship between genetic orenvironmental factors and the phenotypic expression of GE, knowledge of the crop physiology andagronomy, together with a rational use of statistical techniques, are likely to shed light on the probablecauses of this phenomenon. Most often, however, no clear cause of GE has been reported in theliterature due to lack of information about the environments (weather, soil) or about the genotypesthemselves. In a recent paper about GE and its implications for wheat breeding in Australia, Basfordand Cooper (1998), following Baker (1990), recognized two major categories of studies on GEdepending upon the level of understanding of the genotypes and/or the environments. The firstcategory listed defined causes, such as the presence of diseases, soil borne constraints, drought, etc.The second category was reserved for those studies that showed GE without an apparent biotic and/orabiotic explanation. The approach proposed by Basford and Cooper (1998) has also been followed inthis study. A total of 215 hits were returned from the Commonwealth Agricultural Bureaux (FarnhamRoyal, UK) databases for the period 1973 1999 (September), when searching for barley andgenotype-by-environment. Out of them, 77 specifically dealt with grain yield (sometimes amongother traits). The majority (52) followed in the second category, whereas 25 attempted to give someinsight on the causes of GE.

Most studies in which the magnitude of GE for grain yield was measured detected a statistically

significant interaction. Generally, only studies with limited genotypic and/or environmental diversitypresented negligible interaction. Some of the most interesting studies in this area have been carried outby Ceccarelli and co-workers under Mediterranean conditions (1991, 1994, 1996a, 1998, among

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others). This series of experiments consistently reported a crossover-type GE, that is, the bestperforming varieties in low- and high-yielding environments differed. Other studies, however,identified a few barley varieties presenting good yield and stability across large target areas eventhough GE was present, as Berbigier and Denis (1981) for Europe, or Atlin, McRae and Lu (1999) andKong et al. (1994) for Canada. This apparent discrepancy might be explained by differences in the

productivity ranges among studies, and in the nature of germplasm evaluated.

The climatic variables that most affect barley yields are temperature and rainfall. These two factorsalso play a primary role in the occurrence of GE. One of the two main distinguishing characteristics inthe barley germplasm pool is the suitability of cultivars for autumn or spring sowing (the other would

be spike row number). This suitability is governed by an overall response to temperature (earlinessperse), the ability to hasten growth after exposure to cold temperatures (vernalization), the cold tolerance,and the photoperiod response (Borthwick, Parker and Heinze, 1941; Jones and Allen, 1986; Ellis et al.,1989). All but the last of these phenomena are driven by temperature. Overall, they govern thedevelopment of the plant by triggering its growth phases and modulating their duration. The mostnoticeable outcome of this environmental control is the variation in heading date of the genotypeswhen exposed to contrasting environments. There are many reports showing GE for heading date and

also for cold tolerance in barley collections, but few of them establish the association between GE forthese traits and yield response patterns. Talamucci (1975) and Bouzerzour and Refoufi (1992) found astrong sowing date x variety interaction for yield when comparing autumn and spring sowings, beingmost likely caused by differential genotypic sensitivities to temperature or photoperiod.

Drought is one of the most limiting factors encountered by barley. It is a function of rainfall,temperature and soil water holding capacity. Differential responses of genotypes in low- and high-yielding environments often reflect the consequences of differences in rainfall regimes (e.g. Solimanand Allard, 1991; van Oosterom et al., 1993; Voltas et al., 1999c). In Mediterranean climates, terminalwater stress is a common event as grain filling usually develops under an increasingly higherevapotranspirative demand. In this situation, variation in heading date is usually an important cause ofGE for yield: earlier cultivars generally perform better than later ones in low-yielding environments

because of higher water availability at the end of the crop season (van Oosterom et al., 1993; Jacksonet al., 1994; Abay and Cahalan, 1995). This advantage disappears under high-yielding rainfed orirrigated conditions (Jackson et al., 1994). In a few occasions, true drought tolerance mechanisms have

been related to yield GE in barley. For instance, Muoz et al. (1998) found that GE between old andmodern cultivars was correlated with differences in transpiration efficiency indirectly estimated by 13Cdiscrimination.

Soil characteristics have been seldom identified as responsible factors for GE in barley (Tewari, 1975;Talbot, 1984). It has to be acknowledged, however, that this is an area often overlooked by breeders,as soil data are sometimes difficult to obtain. Of the many studies focusing on the optimization of thelevels of fertilizer, only few found differences between cultivars. Interestingly, one of the few GEevents reported for nitrogen fertilization (Lekes and Zinisceva, 1990) actually found that modern

spring barley varieties had a better response to increased levels of nitrogen (up to 80 kg ha-1) ascompared to old spring ones. Soil acidity (Barszczak and Barszczak, 1990) and salinity (Isla, Royoand Arags, 1997) have also been reported as factors responsible of producing crossover-type GE foryield of barley varieties.

Studies addressing GE for disease reactions rarely extend to the effects on yield. Abo-Elenin, Morsiand Gomaa (1977), and Soliman and Allard (1991), reported that GE for yield could be partiallyexplained by contrasting disease tolerance to net blotch and leaf rust, and net blotch and scald,respectively, in the varieties studied. Wright and Gaunt (1992) also reported that several diseasesinfluenced yield differentially in two barley cultivars.

Other genotypic features that are major cause of GE for yield have been revealed by the allocation ofcultivars to different germplasm groups. For example, some studies reported contrasting yieldresponses across environments between 2-row and 6-row types (Talamucci, 1975; Nurminiemi,

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Bjornstad and Rognli, 1996), North American arctic vs. temperate varieties (Dofing et al., 1992), locallandraces vs.improved material (Ceccarelli and Grando, 1991), or old vs.modern cultivars (Muoz etal., 1998). In addition, the genetic structure of the varieties may also be important, as pointed out bySoliman and Allard (1991): composite crosses (a population constituted by intercrossing severalcultivars) proved to be less interactive than inbred cultivars.

There have been attempts to break down GE for yield in terms of yield components in the belief thatyield components may be less interactive and easier to deal with in breeding programs. Some authorshave reported that high-yielding ability under favorable conditions is mostly associated to kernelnumber per unit area (Dofing et al., 1992; Jackson et al., 1994). Conversely, more components appearto be related to higher yields in harsher environments: kernel number, kernel weight and also drymatter accumulation prior to or after anthesis (Jackson et al., 1994); or spikes per unit area, kernels perspike and kernel weight (Dofing et al., 1992).

A helpful tool to describe GE for grain yield has been the use of barley mutants (Arain, 1975;Gustafsson, Ekman and Dormling, 1977; Molina-Cano et al., 1990; Romagosa et al., 1993). Usually,the mutant strains and their wild parents diverge for just a few traits (such as height, spike density,

heading date, erectoides trait). The comparison of mutant strains to their parents provides a simple testfor association of various agronomic traits and yield. This approach will be developed extensively inthe following section.

In the last decade, efforts to elucidate the genetic factors causing GE have veered towards the use ofmolecular markers. Quantitative trait loci (QTLs) responsible for adaptation have been reported inseveral populations: Steptoe/Morex (Hayes et al., 1993; Romagosa et al., 1996; Zhu et al., 1999),Harrington/TR306 (Tinker et al., 1996), and Blenheim/Kym (Bezant et al., 1997). The magnitude ofindividual QTL effects (measured as the amount of GE variance explained by a particular QTL) variedamong populations, being much larger in Steptoe/Morex than in the other two populations. SomeQTLsfor GE were coincident with those for the genotype main effect within a given population, butthe agreement for loci among populations was low. Its implementation in breeding programs remains a

challenge.

An example data set: yield of a series of barley isogenic lines in Spain

We want to use real barley data to illustrate how available empirical (genotypic yields), genetic andecophysiological information can be integrated into a single model for adaptation. To that end, we

propose the use of true near-isogenic lines, which share a common genetic background, as aframework to aid to understand the magnitude and nature of GE. The available plant material consistsof three mutants (M01, M02 and M03) induced in the two-rowed variety Beka and their three binaryrecombinants (M12, M13 and M23). These lines were grown in a multi-environment trial conducted insome of the most important Spanish barley-producing regions from 1985 to 1989: Granada (G),Sevilla (S), and Central Plateau of Spain (C) (Table 1) (the latter includes the provinces of Badajoz,Palencia, Soria and Toledo). The experimental layout at each environment was a randomized complete

block design with four replicates. Climatic records included the variables average mean temperature(T), rainfall (R), and ratio of rainfall to total evapotranspirative demand (R/ETP) for three consecutivegrowth periods: tillering, jointing, and grain filling. The lines were characterized by means of ninemorphophysiological measurements taken for two years in two contrasting locations (Table 2): no. ofleaves per plant and leaf area at both anthesis and physiological maturity, leaf angle, length of themain shoot, days from emergence to anthesis, days from anthesis to maturity, and spike density.Although the genetic basis of the mutations is not exactly known, most of the phenotypic variationrecorded, including grain yield, is probably the effect of only three recessive Mendelian genessegregating 3:1 in F2 (Molina-Cano, 1982). Accordingly, the terms gene/mutation will be used

interchangeably throughout the text. A detailed description of the seven near-isogenic barley lines,including the original variety Beka, their underlying genetic constitution, and the overall experimentalconditions can be found in Molina-Cano et al. (1990) and Romagosa et al. (1993).

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Table 1. Description of the 13 trials used.

Location Coordinates Altitude Year Environmentcode

Mean grainyield (t/ha)

Climatic characterization

Province City Tillering (t) Jointi

Tmean (C) R (mm) R/ETP Tmean

BADAJOZ Mrida 3854'N 620'W 270 1989 BA9 3.96 8.9 28 0.30 13

GRANADA Colomera 3723'N 342'W 706 1988 G18 4.11 7.2 123 1.73 10

Cotilfar 3730'N 330'W 912 1987 G27 4.44 10.5 391 2.85 16

1988 G28 7.27 8.2 157 1.28 12

1989 G29 3.41 8.0 162 0.98 8

PALENCIA Villarramiel 4202'N 450'W 900 1988 PA8 3.14 8.9 121 0.75 13

SEVILLA Alcal del Ro 3732'N 558'W 10 1985 S15 5.89 8.7 135 3.12 13

1986 S16 6.04 9.9 162 1.98 10

Brenes 3729'N 549'W 20 1988 S28 5.74 11.2 126 1.42 15

1989 S29 5.51 9.9 41 0.89 12Ecija 3732'N 505'W 112 1989 S39 5.15 9.5 22 0.47 11

SORIA Almazn 4129'N 232'W 938 1989 SO9 3.17 6.7 98 0.53 12

TOLEDO Tembleque 3941'N 330'W 725 1989 TO9 1.56 5.0 18 0.15 10

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Table 2. Morphophysiological characterization of the genotypes studied for two years in twocontrasting locations.

a List of characters: LPLA: No. of leaves/plant at anthesis; LPLM: No. of leaves/plant at maturity; LAA: Leaf area at anthesis(cm2); LAM: Leaf area at maturity (cm2); LANGLE: Leaf angle (degrees); SHOOT: Length of the main shoot (cm);DEMAN: Days emergence-anthesis; DANM: Days anthesis-maturity; SPIKE: Spike density (no. kernels/cm of rachis).

Line Code Morphophysiological traitsa

LPLA LPLM LAA LAM LANGLE SHOOT DEMAN DANM SPIKEBeka BEKA 15.2 5.8 9.7 4.9 70.4 76.9 131 31 2.8

Mutant-1 M01 13.4 4.6 6.2 2.7 71.3 60.4 124 31 2.9

Mutant-2 M02 13.7 6.2 8.7 5.5 68.5 63.7 134 30 4.4

Mutant-3 M03 14.4 5.6 10.3 5.4 70.3 70.9 135 29 3.6

Mutant-12 M12 12.5 6 6.2 3.2 72.1 53.1 125 31 4.4

Mutant-13 M13 13.5 4.6 6.5 3.7 72.3 59.7 128 29 3.5

Mutant-23 M23 13.7 6.3 10.4 5.3 68.2 63.1 136 29 4.3

A previous GE analysis of a related data set (Romagosa et al., 1993) showed that the genotypicinteractive pattern over environments could be explained by the morphophysiological constitution ofthe mutants. However, the statistical analysis in that study did not integrate in a single model externalgenetic and physiological data of the different lines, and physical data of the environments used. Theexample developed hereafter aims at re-examining the usefulness of integrating ecophysiological andstatistical tools in the interpretation of GE based on the joint application of two multiplicative modelsfor interaction: the additive main effects and multiplicative interaction (AMMI) model (Gauch, 1988),and the factorial regression model (Denis, 1988). Both provide information and insight beyond theclassical analysis of variance of two-way genotype by environment tables. AMMI represents anempirical approach (based on yield itself) to analyze GE. Factorial regression attempts to describeinteraction by including external genetic, phenotypic and environmental information (e.g.morphophysiological traits, climatic data, etc) on the levels of the genotypic and environmentalfactors. It implies a more analytical approach to the study of GE.

The following strategy of analysis will be followed in this example: AMMI will be used to get firstinsight into the data. External information will be superimposed on the AMMI description of the datawith the aid of a graphical representation of the AMMI-fit to the GE: the biplot. Subsequently, variousfactorial regression models will be fitted, based upon the results of the AMMI analysis and thesubsequent biplot interpretation.

Analysis of variance of multi-environment trials

The classical fixed two-way analysis of variance (ANOVA) model with interaction for multi-environment trials includes additive terms for the maineffects of genotypes and environments togetherwith an extra additive term to account for the interaction effect. In this situation the expectation ofgenotype i in environmentjis

E(Yij) = + gi+ ej+ geij (1)

where is the grand mean, giand ejare genotypic and environmental main effects, and geijaccountsfor the specific response of genotype i in environment j. This model was applied to our barley data(Table 3). The magnitude of the sum of squares (SS) for GE was large, i.e. about three times thegenotype main effect SS, and highly significant when tested against the pooled intra-block error. The

information provided by this ANOVA model is restricted, we merely know that some form of GEmust be present. Further approaches to examine GE should dissect the information included in the

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term geij. The exploration of GE starts by fitting a multiplicative model for interaction, the additivemain effects and multiplicative interaction (AMMI) model.

Table 3. Analysis of variance for grain yield (t/ha) of the seven barley genotypes grown at 13environments.

aEnvironmental main effect tested against Reps(E); **, significant at 1% level;

Source of variation df Sum ofsquares

Meansquare

Variance

ratioaR (%)b

Total 363 920.7

Environment (E) 12 806.1 67.18 131.73**

87.6

Reps(E) 39 19.9 0.51 2.2

Genotype (G) 6 15.8 2.63 21.64**

1.7

GxE 72 50.3 0.70 5.74**

5.5

Error 234 28.5 0.12 3.0 ns, not significant.

b Fraction of sum of squares associated to each term or interaction

AMMI model

In AMMI, the interaction geij is partitioned into successive multiplicative terms or products of theform cidj, where ci can be interpreted as the genotypic sensitivity of genotype i to a hypotheticalenvironmental variable d, which has value djin environmentj. Alternatively, djcan be interpreted asthe environmental potentiality of environment j to an hypothetical genotypic variable c, which takes

value cifor genotype i. AMMI generates a family of models as follows:

=

+++=K

k

jkikjijidcegYE

1

)( (2)

where K is the number of multiplicative terms needed to provide an adequate description of theANOVA interaction. The K hypothetical environmental/genotypic variables have the property ofdiscriminating maximally between genotypes/environments and can be obtained by applying either asingular value decomposition or a principal components analysis to the interaction. The AMMI modelis a very powerful tool to get insight into GE (Gauch, 1988, 1992; van Eeuwijk, 1995, van Eeuwijkand van Tienderen, 2000). It is recognized to provide parsimony, i.e. it captures real structure or

pattern with fewer degrees of freedom (df) than the standard ANOVA interaction term.

The application of AMMI to the barley data set is shown in Table 4. The first four terms of AMMIwere significant using an approximate F-statistic (Gollob, 1968). It is important to keep in mind thatGollobs test most often retains axes of little practical relevance (with a low proportion of explainedGE variation). In fact, most of the interaction (77.8%) was accounted for by the first and secondmultiplicative terms. Such a result may suggest that AMMI4 is actually over-fitting the data, whichmeans that a portion of the total noise included in the interaction term is also retained by the AMMImodel. An easy inspection of this phenomenon can be done by estimating the amount of noise presentin the interaction from the pooled intra-block error. This value is then compared with the SS retainedin consecutive AMMInmodels (Gauch, 1992). Such a procedure may help to fix an adequate numberof multiplicative terms containing real structure. For our data set, the intra-block error was 0.12 and

the interaction had 72 df; accordingly, the interaction contained about 0.12x72=8.65 noise SS (17.2%),and 50.3-8.65=41.65 pattern SS (82.8%). This last percentage, which is slightly larger than that

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retained by the first two multiplicative terms, shows that AMMI2 is more parsimonious and effectivethan the original ANOVA model, i.e. it requires fewer dffor an adequate description of the interactionand excludes most of its actual noise. We would tend to exclude the 3 rdand 4th(and later) axes fromthe AMMI model. The ANOVA interaction is then replaced by the first two multiplicative terms,which can easily be visualized with the aid of a biplot (Figure 1).

Table 4. Summary of the AMMI analysis for grain yield.

a **, significant at 1% level; ns, not significant.

Source of variation df Sum ofsquares

Meansquare

Variance

ratioaR (%)b

GxE 72 50.3 0.70 5.74**

AMMI1 17 26.4 1.55 12.91**

52.5

AMMI2 15 12.7 0.85 7.08** 25.3

AMMI3 13 5.6 0.43 3.58

**

11.2AMMI4 11 4.0 0.36 3.03

**7.9

Residual 16 1.6 0.10 0.83ns

3.1

Error 234 28.5 0.12

bFraction of sum of squares associated to each interaction term

Biplot representation

In Figure 1 genotypes and environments are depicted as points on a plane. The position of the point for

genotype iis given by the estimates for the genotypic scores, (ci1, ci2); similarly, the point coordinatesfor environment joriginate from the estimates for the environmental scores (d i1, di2). Distances fromthe origin (0,0) are indicative of the amount of interaction that was exhibited by either genotypes overenvironments or environments over genotypes. For example, the genotype M01 showed a highlyinteractive behavior, whereas the environment PA8 exhibited low interaction. The nearly additive

behavior of PA8 indicates that genotypic yields in that environment were highly correlated with theoverall genotypic means across environments. In a vector representation, the genotype andenvironment points determine lines starting at the origin (0,0). The interaction effect of genotype iinenvironmentjis approximated by projecting the genotype point (c i1, ci2) onto the line determined bythe environmental vector, which has a slope di2/di1, where distance from the origin providesinformation about the magnitude of the interaction. Theangle between the vectors of genotype iandenvironmentjtells us something about its nature: the interaction is positive for acute angles, negligible

for right angles, and negative for obtuse angles.

Lets now examine the distribution of genotypes in Figure 1. The original variety, Beka, lay on thelower left-hand side, not very far from the origin when compared with the three original mutants(M01, M02 and M03) that exhibited larger interactions. These mutants were further away from eachother, drawing a nearly perfect equilateral triangle in the biplot. Their position relative to their binaryrecombinants informs us about the non-allelic combinations and/or interactions that are controllingadaptation to specific environments. For instance, M12 was intermediate in position to M01 and M02,from which an additive behavior of the non-allelic genes 1 and 2 can be inferred with respect toadaptation. An identical situation arises for M23, which can be found approximately in between M02and M03. M13 was considerably closer to M01, suggesting that both genotypes exhibited similaradaptive patterns. In a genetic context, this means that dominance is somehow exerted by gene 1 ongene 3, i.e. gene 1 is epistatic to gene 3. The genetic information included in the biplot is notexhausted yet. A further examination reveals that the first multiplicative term separates those

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genotypes containing gene 1, at the right-hand side, from the rest, at the left-hand side. Similarly, thesecond term distinguishes between genotypes incorporating gene 2, at the upper side of the biplot,from the rest, at its lower side.

-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2

Axis-2

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

+

S16

S15

G28

G18

G27

S39

G29

S29

S28

BA9TO9

SO9

M02

M12

M01

M03

BEKA

M23

PA8

M13

Figure 1. Biplot of the AMMI analysis for grain yield. Genotypes are represented in italic letters,environments in capitals. The lines connect contrasting environments (in bold) from the Sevilla region(solid lines) and the Granada region (dashed lines).

A better understanding of the interaction patterns described so far is possible if we succeed to 1)identify the physiological systems affected by the mutations playing a role in the phenotypic responseto the environment; and 2) identify the environmental factors interacting with the genetic make-upunderlying the adaptive physiology .

Assessment of the genetic and physiological basis of adaptation based on the AMMI analysis

This step may be addressed by relating the genotypic scores of AMMI2 to additional information suchas the genetic constitution of the mutants and/or their phenotypic characterization. Directions ofgreatest change for genotypic variables can be included in the biplot. These directions can be obtainedfrom a regression of the external variables on the genotypic scores for axes 1 and 2. The regressioncoefficients in relation to the origin (0,0) define a line that, after projection of the genotypes on it,gives an ordering of these genotypes with respect to that variable. The half line from the originthrough the point defined by the regression coefficients represents the above average value for thatgenotypic variable, the opposite half line represents the below average value for the same variable.

The technique of including external genotypic information is applicable to both quantitative andqualitative variables. For example, three new variables can be defined for each of the three mutant

genes characterizing the genetic constitution of Beka, its mutants and their recombinants (Table 5).These variables were included in the biplot according to the methodology described above (Figure 2).The enriched biplot corroborates that gene 1 resembles the first multiplicative term and gene 2 the

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second one. Indeed, correlations between the genotypic scores of Axis-1/Axis-2 and gene 1/gene 2were 0.96 and 0.93, respectively. Both mutations arise as the main genetic factors underlying GE andadaptation in this example. Gene 3 was poorly related to either Axis-1 or Axis-2, being better reflectedin the third multiplicative term of AMMI (r=0.69). In a hypothetical 3-D representation of theinteraction, each of the three mutant genes would nearly represent a particular dimension in theAMMI3-derived figure.

Table 5. Coefficients for the identification of single mutant genes. The presence/absence of a gene isindicated by a value of 1/0.

Genotype

Gene 1 Gene 2 Gene 3

BEKA 0 0 0

M01 1 0 0

M02 0 1 0M03 0 0 1

M12 1 1 0

M13 1 0 1

M23 0 1 1

Genetic codification

-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2

Axis-2

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

BEKA

M01

M02

M03

M12

M13

M23

+

++

+

+

+ +

+

+

+

+

+

+

+gene 1

gene 2

gene 3LPLA

LAA

LPLM

LAM

LANGLESHOOT

DEMAN

SPIKE

Figure 2. Biplot of the AMMI analysis including genetic and morphophysiological information. The

arrows indicate directions of greatest change for genetic (solid lines) and morphophysiological (dashedlines) variables. Environments are represented by crosses.

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The morphophysiological attributes of the mutants could also be incorporated in the biplot as truequantitative variables, but only those variables that explained enough variation by the regression onthe genotypic scores merited imposition. For this example, the arbitrary threshold used to pre-screenthe external data was fixed to about 60% variation (Figure 2). The joint inclusion of genetic and

phenotypic information makes the biplot extremely informative, e.g. the morphophysiological traitsresponsible for adaptation can be related rather straightforwardly with their genetic rationale. Thus,genotypes carrying gene 1 had smaller leaf area at anthesis and maturity, and were earlier in heading.This information is provided in the biplot by the opposite direction of gene 1 in comparison with thatfor the phenotypic variables LAA, LAM, and DEMAN. Such phenotypic traits proved to be highlyassociated: the very early genotypes are likely to possess limited photosynthetic machinery broughtabout by their inferior vegetative period. Genotypes carrying gene 2 were characterized by denserspikes (note the coincident directions of both vectors), and those carrying gene 3 by shorter grainfilling periods (this last information could be inferred by the inclusion of a third multiplicative term).Additionally, both gene 1 and gene 2 seemed to influence the expression of phenotypic features suchas the length of the main shoot, which was reduced in those genotypes bearing one or both genes. Insummary, all the above-mentioned morphophysiological traits are adaptively sound and have anexplicit genetic background that could be identified according to the information revealed by the

biplot.

Incorporation of genetic and ecophysiological information into factorial regression models

A second type of multiplicative models is the so-called factorial regression model. The maindifference with AMMI is that now the ANOVA-interaction, ge ij, is partitioned in one or moremultiplicative terms composed of explicit (rather than hypothetical) variables containing genetic,

phenotypic or environmental information. For example, suppose that we want to assess the extent towhich one or more genetic (specific genes, QTLs, etc) or phenotypic (morphophysiological) featuresare advantageous or detrimental for grain yield (or any other response variable) in each of Jenvironments. The factorial regression model then takes the general formulation:

=+++=

K

kjkikjiji xegYE 1)( (3)

where xik refers to the value of any type of genetic/phenotypic variable k, either qualitative orquantitative, for genotype i; and jkrepresents an environmental potentiality of environment j to theexplicit genetic/phenotypic variable k. The heterogeneity in the js for successive x1...xK variables

accounts for the interaction, while the sum of multiplicative terms approximates the

ANOVA term, geij. To facilitate interpretation, the external variables can be centered to mean zero andstandardized to unit standard deviation. The parameters jkcan easily be estimated by standard leastsquares techniques, as the model (3) is a linear model.

=

K

k

jkikx1

Alternatively, we may be interested in monitoring the response of several genotypes to a set ofclimatic and/or edaphic factors. The multiplicative portion of model (3) is then replaced by the

summation , wherezjhindicates the value of environmental variable hin environmentj, and

ihis the genotypic sensitivity of genotype ito the explicit environmental variable h. For further detailson theory and application of factorial regression models see Denis (1988), van Eeuwijk (1995), vanEeuwijk et al. (1995), and van Eeuwijk and van Tienderen, (2000).

=

H

h

jhihz1

Genetic information of different types can be incorporated in the factorial regression model (3). Thismethodology may aim at identifying the molecular genetic variation, in terms of either major genes or

polygenes through quantitative trait locus (QTL) mapping, involved in different adaptive responses. It

can readily be applied to our barley data using the genetic characterization of the mutants. The factthat most of the phenotypic variation recorded could be ascribed to the effect of only three apparently

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The genetic description of the genotype main effect is of little interest in the presence of substantialinteraction. A biological interpretation should concentrate on the examination of the GE term. Themodel shown in Table 6 suggests that the most important gene accounting for specific adaptation wasgene 1 followed by genes 2 and 3, while an epistatic effect of gene 1 to gene 3 seemed also present.The inclusion of all three mutant genes in the regression model could be anticipated from the AMMIanalysis. Together with the epistatic effect of gene 1 to gene 3, the gene x environment termsexplained about 93% of the GEI SS with 67% of its degrees of freedom. The amount of interactionretained by just gene 1 and gene 2 in the factorial regression model (71.7%) was comparable to that ofAMMI2. This observation corroborates that the two multiplicative terms of AMMI2 were closelylinked to those mutant genes. It was already postulated that AMMI2 seemed to retain mostly pattern,

but it was unclear whether further terms could account for something more than interaction noise. Thegenetic analysis suggests that AMMI2 was probably leaving out some structure hidden in the GEmatrix. In fact, the third multiplicative of AMMI term might deserve further attention given its relationwith gene 3. The factorial regression model presented so far reveals that gene 1, gene 3, and theepistatic effect of gene 1 to gene 3 seemed simultaneously responsible for the genotype main effectand the specific adaptation of genotypes to the environments. Gene 2 had importance only for theexplanation of the interaction effect.

The physiological mechanisms of adaptation underlying the three recessive mutant genes were roughlysketched after examination of the AMMI2 biplot (Figure 2). A more detailed interpretation could beobtained by correlating the indicator variables for the three genes (as described in Table 5) with themeasured morphophysiological traits (see Table 7). Hence, the ecophysiological basis foradaptation/misdaptation brought about by gene 1 can be summarized in extreme earliness, low leafarea index, and, to a lesser extent, erect leaves and short stems. Gene 2s influence on adaptive traitsresumes in dense spikes and, to a much lesser extent, in few leaves per plant, short stems andrelatively horizontal leaves. Finally, a short grain filling duration coupled, to some extent, with a longvegetative period is the only adaptive effect that can readily be ascribed to gene 3.

Table 7. Correlation matrix between morphophysiological traits and gene descriptors.

**, significant at 1% level;*, significant at 5% level; ns, not significant

Genes Morphophysiological traits

LPLA LPLM LAA LAM LANGLE SHOOT DEMAN DANM SPIKE

Gene 1 -0.707 -0.927** -0.959** -0.955** 0.841* -0.750* -0.917** 0.312 -0.136

Gene 2 -0.522 0.510 0.079 0.226 -0.487 -0.480 0.238 0.000 0.906**

Gene 3 0.106 0.075 0.371 0.334 -0.101 -0.071 0.495 -0.935** 0.136

Incorporation of environmental information into factorial regression models

Once the underlying physiology and genetics of adaptation have been established, the example mayproceed focusing on the determination of those environmental factors to which the genotypes areresponding differentially. To this end, a good starting point is the biplot of Figure 1. An initialinspection may consist in checking whether the distribution of environments throughout the biplotfollowed any apparent pattern. For example, is it feasible to group trials belonging to identicalagroecological regions? In our data set three different geographical regions are distinguished: Granada(G), Sevilla (S), and Central Plateau of Spain (C). Environments of either Granada or Sevilla could noteasily be clustered in the biplot. In contrast, trials of the Central Plateau grouped together around the

origin, showing little or no interaction. It could therefore be expected that GE concentrated onparticular environments from Sevilla and Granada. A further examination of the biplot reveals that two

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AMMI methodology was used for the pre-selection of climatic variables meriting further testing infactorial regression models. The procedure is analogous to that employed for the genetic andmorphophysiological data. First, the environmental factors are regressed on the environmental scoresof AMMI axes 1 and 2. The resulting regression coefficients thus determine the coordinates for theenvironmental variables in the biplot, provided that enough variation is explained by the regression onthe scores. The application of this methodology to our barley data proved unfruitful, since none of theavailable climatic variables was related highly enough to the first two multiplicative terms of AMMI.A possible explanation to this apparent inadequacy arises from the fact that, as suggested in model (4),the adaptive variation should also be searched for within particular regions. This is ignored whenAMMI is fitted to the complete GE table. The climatic variables must then be examined within each

particular region responsible for interaction, such as Sevilla or Granada. This was achieved by fittingseparate AMMI models for Sevilla and Granada, in order to relate later the environmental informationto the interaction. Two multiplicative terms provided a good description of interaction, capturing89.5% and 92.4% of GE for Sevilla and Granada, respectively.

Three climatic variables were closely associated to the environmental scores of the AMMI2 model for

Sevilla: the ratio of rainfall to total evapotranspirative demand during tillering (R/ETPt, R

2

=86%) andduring grain filling (R/ETPgf, R2=58%), and the mean temperature during grain filling (Tgf, R

2=61%).For Granada, the climatic variables that most precisely resembled the environmental scores were themean temperature during jointing (Tj, R

2= 85%), and the ratio of rainfall to total evapotranspirativedemand during grain filling (R/ETPgf, R

2= 95%). One must be cautious when establishing an arbitrarythreshold for the selection of external variables. The decision should be based upon the number ofenvironments to which to relate this additional information. For example, the threshold must be high ifrelatively few environments are involved in the analysis, as is the case for Sevilla and Granada.

Nonetheless, with such a limited number of environments a tacit uncertainty exists for any relationshipto be casual rather than causal. If more environments had been included in the analysis then thethreshold could have been relaxed, and the danger of erroneously selecting external variables wouldhave decreased.

The performance of this greatly reduced set of variables in a factorial regression model was tested. Asgrain yield is a complex process taking place over the entire crop lifecycle, it is logical that the orderof inclusion of variables followed a temporal scale, beginning with variables observed during tillering(t), continuing with those for jointing (j) to assess whether additional information was added aftercorrection for the tvariables, and finally including those variables related to the grain filling period(gf). This scheme was applied separately for Sevilla and Granada according to the GE partition ofmodel (4) and Table 8. The resulting factorial regression proposal is shown in Table 9. The climaticvariables already pre-selected for Granada (Tjand R/ETPgf) were incorporated in the model. Togetherthey retained about 88% of the within-region GE with 67% of its degrees of freedom. For Sevilla, twoexternal variables were included in the model (R/ETPtand R/ETPgf), which captured about 71% of thewithin-region GE with 50% of its degrees of freedom. The feasibility of including all four external

variables was supported by the improved parsimony of the resulting model, as it captured a highamount of GE variation with fewer dfthan the initial within-region terms for Granada or Sevilla. Anadditional check consisted in the computation of the F-ratio MSgenotypeenv covariable / MSresidual for eachexternal variable, which can be calculated from Table 9. A significant F-value would definitelyindicate an appropriate GE partitioning. For example, the F-ratio for Tj in Granada was 3.73(p=0.067), for R/ETPgf in Granada 3.86 (p=0.062), for R/ETPt in Sevilla 3.26 (p=0.039), and forR/ETPgf in Sevilla 1.64 (p=0.219). The latter was the only environmental descriptor far fromsignificance, but we decided to keep it in the model since 1) its F-ratio was still much larger than unityand 2) R/ETPgf, as indicator of terminal drought, plays an important adaptive role in Mediterraneanclimates. We will come back later to this specific point.

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Table 9. Factorial regression model for the partitioning of GE for grain yield

a **, significant at 1% level;*, significant at 5% level; ns, not significant

Source of variation df Sum ofsquares

Meansquare

Variance

ratioaR (%)b

GxE 72 50.3 0.70 5.74**

GxRegion 12 10.9 0.91 7.49 21.7

GxGranada 18 15.5 0.86 7.07 30.8 GxTj 6 6.7 1.12 9.33 43.2

DEMAN*Tj 1 2.8 2.84 23.67 41.7

Deviations 5 3.9 0.77 6.42 58.3 GxR/ETPgf 6 7.0 1.16 9.67 45.2

DEMAN*R/ETPgf 1 4.8 4.75 39.58 68.6

Deviations 5 2.2 0.44 3.67**

31.4

Deviations 6 1.8 0.30 2.50 11.6 GxSevilla 24 22.0 0.92 7.53 43.7 GxR/ETPt 6 10.4 1.73 14.41 47.3

SHOOT*R/ETPt 1 5.2 5.21 43.42 50.0

Deviations 5 5.2 1.04 8.67 50.0 GxR/ETPgf 6 5.2 0.87 7.25 23.6

SHOOT*R/ETPgf 1 1.8 1.82 15.17 34.6

Deviations 5 3.5 0.69 5.75 65.4

Deviations 12 6.4 0.53 4.42 29.1

GxCentral Plateau 18 1.9 0.11 0.87ns

3.8

Error 234 28.5 0.12

bFraction of sum of squares associated to each term or interaction

Genotypic sensitivities to environmental changes

The genotypic sensitivities, ih, of the factorial regression partition of GE for each region, ,

are shown in Table 10. These sensitivities are indicative of the nature of the interaction exhibited byeach mutant. For example, M01 was highly sensitive to environmental changes in Granada, being

negatively affected, in relative terms, by high temperatures during jointing and good water availabilityduring grain filling. The performance of M13 was similar to that of M01 but, in contrast, M02 behavedin a completely different manner. Remarkably, sensitivities for recombinants 12 and 23 wereintermediate to those of their parental mutants, suggesting again an additive behavior of genes 1/2 and2/3. M03 did not show any particular response to the climatic variables of Granada but it exhibited thelargest sensitivity to the climatic variables of Sevilla, being favored by a low water availability duringtillering and grain filling. Recombinant 12 displayed an opposite behavior to M03 in Sevilla, andsimilar to that of its parental lines M01 and M02.

=

H

h

jhihz1

Genotypes showing large sensitivities to environmental variables are also expected to exhibit a highoverall interaction. The amount of interaction displayed by each genotype (ecovalence) (Wricke,1962) is given in Table 10. The most interactive genotype was M01, carrying gene 1, the mostsensitive mutant gene to environmental changes (cf. Table 6). This behavior can be inferred eitherfrom the biplot (Figure 2), or by the fact that, as indicated above, M01 was largely sensitive to most

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environmental variables (Table 10). M03 and M02 then followed M01. M13 was the most interactiverecombinant, probably because the epistatic effect of gene 1 to gene 3 approximated M13 to the

performance of M01. In contrast, the additive behavior of recombinants 12 and 23 turned into a higherstability. Finally, the mother variety Beka was the less interactive genotype over environments.

Table 10. Genotype mean grain yield, ecovalence (Wi) values, contribution (%) of genotypes to GEsum of squares (SS), and estimates of the regression coefficients of relevant environmental variablesfor each genotype according to the factorial regression model of Table 9.

*, **: Regression coefficients with confidence intervals that do not include zero at 1% and 5% level, respectively

Genotype Mean yield

(t ha-1)

Wi %SS (GE)

Tj R/ETPgf R/ETPt R/ETPgf

BEKA 4.64 4.24 8.4 0.34**

0.11 -0.20* -0.20*

M01 4.16 12.37 24.6 -0.51**

-0.63**

0.39**

0.13M02 4.73 7.14 14.2 0.59

** 0.37** 0.20* 0.28**

M03 4.75 7.91 15.7 0.11 0.12 -0.62** -0.30**

M12 4.36 6.48 12.9 -0.17 -0.02 0.41** 0.23**

M13 4.62 6.69 13.3 -0.50** -0.23* 0.06 -0.25**

M23 4.73 5.51 10.9 0.13 0.28** -0.24** 0.11

Granada Sevilla

Regression coefficients

The genotypic sensitivities to selected environmental variables are possibly related to one or more of

the morphophysiological traits characterizing the genotypes. An easy way to verify such relationshipsis to calculate correlations between regression coefficients and morphophysiological traits.Alternatively, a factorial regression model can be fitted in which regression coefficients i to anenvironmental variablezjare replaced by a constant, c, times a morphophysiological variable, xi, (i=c xi), where the constant c is estimated from the data. A residual term i*zj can be added to checkwhether the morphophysiological trait leaves a significant residual sensitivity. The aim is to relate theenvironmental factors to which the individual is reacting with the physiological systems involved inthe phenotypical response. The formulation of an extended model with one environmental variable zjand one genotypic variablexiis:

jhjijijizzcxegYE

*)( ++++= (5)

The terms for the fully expanded factorial regression proposal for Granada and Sevilla according tomodel (5) are shown in Table 9.

Morphophysiological traits that were best related to the environmental factors included in the modelwere days from emergence to anthesis (DEMAN) for Granada, and length of the main shoot(SHOOT)for Sevilla. Other traits could have been incorporated in the model instead of DEMAN and/or SHOOTwith a similar overall fitting. This result is not contradictory since, as already indicated, a number ofdifferent traits share the same genetic background. Once the relevant phenotypic traits weredetermined, the genotypic sensitivities could be associated with the underlying physiology responsiblefor adaptation. For Granada, genotypes such as M02, which showed an extended vegetative period anda higher leaf area (see Table 2), benefited from good water availability and high temperatures in thelater part of the growing cycle. These genotypes could therefore express their higher potentiality foryield under favorable conditions. In contrast, those lines characterized by a more limited pre-anthesis

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period (e.g. M01) performed relatively better under low temperatures during jointing (Tj). This maysuggest that, when temperatures are sub-optimal for growth, such genotypes are not penalized inexcess in spite of their restricted photosynthetic machinery. Besides, the favorable response of earlygenotypes to low R/ETP ratios during grain filling suggests the existence of an escape strategy to theabrupt termination of the growing season caused by drought (Loss and Siddique, 1994). For Sevilla,length of the main shoot (SHOOT) was likely to be associated to differences in lodging susceptibilityand/or harvest index (HI) among cultivars. Lodging susceptibility is typical of tall cultivars and causes

poor grain set and deficient grain filling. In addition, a high HI, which is inversely related to shootlength, is important to maximize yield potential in barley (Riggs et al. 1981). In this example, lineswith reduced shoots (i.e. M12, Table 2) took advantage of good water status during vegetative growthand grain filling, whereas taller cultivars performed relatively better when growing conditions wereharsher. The extent to which such a behavior is dependent upon genotypic differences in HI or lodgingsusceptibility remains unclear due to the lack of precise field records.

An interesting point of discussion that arises from the examination of the proposed model is therationale behind the distinctive incorporation of morphophysiological traits for the Granada andSevilla regions. Different adaptation patterns at each region were already unmasked using an empirical

model such as AMMI. It is therefore reasonable to expect different physiological systems controllinggenotypic adaptive responses. However, which agroecological features distinguish Granada fromSevilla that may aid to explain such a distinct control? Essentially, the Sevilla region is characterized

by a relatively high rainfall during the growing cycle, mild temperatures and deep, fertile soils. Theseproperties led to a higher average yield in Sevilla (5.7 t/ha) compared to Granada (4.8 t/ha), the latterbeing characterized by lower temperatures and a shallower soil. Yield potential is therefore superior inthe Sevilla region. In this area, larger genotypic dependence for higher yields is to be expected ontraits such as HI, which confer a productive advantage under near-optimal conditions. On the otherhand, Granada often suffers from drought and, under these circumstances, an escape strategy isrecognized to be a beneficial genotypic trait for maximizing yield.

It is always crucial to raise a word of caution on the use and misuse of analytical models for the

assessment of adaptation. Factorial regression models are little more than just plain regressions and,accordingly, it is important to be cautious about the inferences to be made from a regression analysis.Any strong association detected between a particular genetic, morphophysiological or environmentalvariable and grain yield by no means implies that such an external variable is unequivocally a cause ofyield variation. Previous knowledge on the subject is basic to choose an adequate array of factors forincorporation into factorial regression models. Even so, different combinations of variables may yieldsimilar results in terms of model fitting (Voltas et al., 1999b), because many variables are usuallyhighly correlated and many sets of variables will perform equally well in different models. Therefore,the choice of proper models should be based not only on statistical considerations, but also on a properecophysiological understanding of the phenomenon under study.

Breeding implications

The analytical models presented so far are prone to produce the erroneous impression that a singlemorphophysiological trait may systematically provide an adequate description of plant adaptiveresponses to environmental factors. Most often, yield increases associated with a particular trait have

been found to be small (Loss and Siddique, 1994), and breeders are reluctant to base a selectionstrategy upon the incorporation of a single, specific trait (Ceccarelli et al, 1991). The use of true near-isogenic lines in adaptation studies aims at avoiding the misleading results derived from the effect ofdifferent genetic backgrounds on yield (Rasmusson and Gengenbach, 1983; Molina-Cano et al., 1990).In our example, only three apparently recessive Mendelian genes were responsible for a broad range ofassociated physiological processes (Molina-Cano, 1982). The monitored responses to environmentalfactors are the effect of these genes and their non-allelic combinations, which demonstrates the role ofmajor genes in adaptation (Orr and Coyne, 1992). However, what we usually observe in anysegregation following a cross between two contrasting lines is the effect of many quantitative genes

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plus their interactions (Prez de la Vega, 1997). The framework provided by the use of near-isogeniclines may often be of limited practical importance to breeders whose objective may be precisely toincorporate a target trait into genotypes of wide genetic origin (Acevedo and Ceccarelli, 1989). Thevalue of this approach for understanding the mechanisms underlying GE and adaptation and theirimplications in plant breeding must also be recognized, as it has been illustrated previously.

Genotype by environment interaction has important implications in breeding programs (Fox, Crossaand Romagosa, 1997), including: (1) aim for wide or specific adaptation and choice of locations forselection; (2) resource allocation in advanced line testing across sites and/or years; and (3) trade-off

between empirical multi-environment testing of large numbers of genotypes and evaluation of alimited set of lines in detailed physiological studies.

Related to wide/specific adaptation is the question of breeding location(s): can selection underoptimum high-input environments identify genotypes adapted to more stressed environments? Asignificant body of the literature on the issue of wide versusspecific adaptation has been contributed

by Salvatore Ceccarelli and coworkers of the ICARDA barley breeding program (1989, 1994, 1996b).They have strongly advocated the exploitation of specific adaptation for optimum use of resources,

particularly in marginal environments, arguing that selection for high yield potential has not increasedyield under low-input conditions. Ceccarelli (1994) favored and demonstrated the benefits of selectionunder conditions similar to the target environment, concluding that barley genotypes bred for poorrainfed areas should be selected under these unfavorable conditions. On the contrary, CIMMYT wheatgenotypes bred under high input environments have shown to be superior in yield and havedemonstrated better adaptation across large ecological areas than genotypes developed locally, perhapswith the exception of very marginal sites (Braun, Rajaram and van Ginkel, 1997). Poor adaptation ofCIMMYT genotypes to specific environments often reflected susceptibility to specific plant diseases.

Success of CIMMYT in releasing wheat genotypes, which combine high yield potential and wideadaptation, involves a completely different approach from that followed at ICARDA. Continuousselection cycles, referred to as shuttle breeding, are carried out in alternative high yield potential

environments differing in altitude, latitude, photoperiod, temperature, rainfall, soil-type and diseasespectrum. Experiments where selection has taken place in alternate locations are scarce in barley. Forexample, Patel et al. (1987) found that when barley populations were alternated between diverse sites,representing different zones of adaptation, natural selection improved yields but less than whenselection was carried out in single locations. This dispute about breeding philosophies will continueuntil molecular studies shed light over the nature of genetic changes imposed by selection. So far, justa few studies of this kind have been published for barley. Allard (1999) found that natural selection ina composite cross II of barley (CCII) favored different allelic combinations of four esterase genes fordry andwet conditions in Davis, California. When natural selection in CCII was continued for another20 generations in Bozeman, Montana (with a harsh continental climate), the two winning alleliccombinations in California rapidly declined, and other combinations became dominant. Thus, differentalleles were favored in areas with rather different climates. Pomortsev et al. (1996) also studied the

fate of a barley population (cross of two cultivars) in the very distinct areas of Moscow and thePamirs, by analyzing several morphological and protein markers. Natural selection acted againstalleles at different loci in both locations, but they identified an association of Hordein A and B allelesthat provided adaptation for both conditions. This evidence is anecdotical, but in the years to come wewill undoubtedly witness an enormous expansion of our knowledge in this area.

An appropriate allocation of available resources is inherent to the success of any breeding program.Breeders aim to cover a representative sample of spatial and temporal environmental variation.Limited resources and increasing pressure to develop new cultivars can reduce the number of years oftesting below the minimum number required for representativeness. Significant GY suggests testingfor many crop cycles. However, breeders often substitute year with location variation, assuming thatGL interaction is of the same nature as GY (GLY). Resource allocation for multi-location-multi-yeartrials is discussed in extent by Talbot (1997). Decisions are based on the relative magnitude of the GL,GY, GLY and error variance components. In this context, the issue of repeatability of GE is also

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important (Basford and Cooper 1998): the lack of repeatability may be an inherent feature of thecomplex systems with which we deal with, or a result of the way in which we sample the system.However, little information is available about repeatability of GE. There is a need to assess the

proportion of GE associated to predictable and, thus, repeatable pattern and to noise. In the absence ofa sizeableproportion of repeatability, exploitation of GE is not possible. A series of papers (Fox andRosielle 1982, Romagosa and Fox 1993, Cooper and Fox 1996, Fox et al. 1997) have suggested theuse of reference and probe genotypes for the characterization of environmental variation and to assessrepeatability. A breeder could define a long-term target environment using relative ranks from acommon reference set of genotypes grown over locations and years. Results from each location in agiven year should be considered in accordance with its across-year representativeness. Probegenotypes with differential response to known biotic and abiotic conditions could also be used tocharacterize environments. However, the practical use of these two concepts is still limited.

In most breeding programs based on extensive multilocation trials, empirical selection of segregatingpopulations still enables genetic gains for unrecognized stresses. The alternative approach for theempirical testing of a large number of advanced lines is the exposure to a few key locations withdefined stresses. Once major stresses are identified, manipulation of the selection environment and

selection of specific parental crosses should result in an increase of the heritability of those traitsinvolved. Balance between both approaches should depend upon how well major stresses are defined.

Few barley breeders assess routinely genotypic adaptability and stability. Nonetheless, most of themdevelop a deep knowledge of their environments and of the adaptation of their genetic materials. Thisappreciation may arise from detailed field observations, often by visual comparison of newer lines tocheck varieties in many locations, in what frequently appears to be an intuitive process. However, we

believe that statistical assessment of genotypic adaptability (and stability) is needed, aiming not toreplace breeders' impressions, but to complement them (Fox et al.1997). We want to emphasize that itis essential that statistical assessment runs in parallel with agroecological understanding of thegenotypes and the environments. GE techniques will gain acceptance among breeders through better-documented, user-friendlier software that handles large unbalanced data, missing values and, for

certain species, multiple traits. Production of such mature software, which produces real-timeanalyses, is still a bottleneck (Fox et al. 1997, Basford and Cooper 1998).

APPENDIX

All models presented in the barley example may be fitted using SAS software. The most relevantstatements are presented below, with classification variables for genotypes, environments and blockslabeled as gen, loc, and block, respectively. In most cases other alternatives to the proposed SAS codesexist that yield identical results.

AMMI model

AMMI analysis can easily be performed using SAS/IML (Interactive Matrix Language) (SAS Inst.,1989b) software. PROC IML requests the two-way residuals from additivity of n genotypes in menvironments previously included in the SAS data set residual. These interaction effects are thentransferred to a column vector x that must be reshaped to originate a new matrix (resid) with

dimensions mn, prior to the singular value decomposition done by the SVD subroutine. The programoutput gives the squares of the singular values (the sum of squares corresponding to each axis) and theenvironmental and genotypic scores after being multiplied (scaled) by the square root of theircorresponding singular values. This program must be adjusted for the specific number of environmentsand genotypes, as shown in the text.

PROC IML;USE residual;

READ ALL VAR{env gen r_yield};

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READ ALL VAR _NUM_ INTO x;

r_yield= x[,4]; /* column vector x */

m= 13; /* m is the number of environments */

n= 7; /* n is the number of genotypes */

resid=shape(r_yield,m,n); /* mn matrix containing residuals from additivity */

CALL SVD(u,q,v,resid); /* singular value decomposition of the resid matrix */

axes= 'Axis-1':'Axis-7'; /*7 is the lowest value of m and n */

b=q#q; /* eigen values, or squares of singular values q */

SUMb= SUM(b);

e=(b/SUMb)*100; /* percentage of SS corresponding to the axes */

sqq=SQRT(q); /* square root of singular values for scaling of the

scores */

d= DIAG(sqq); /* diagonal matrix containing the square root of singular

values */

uq=u*d; /* scaling of the genotypic scores */

vq=v*d; /* scaling of the environmental scores */

score='SCORE1':'SCORE7'; /*7 is the lowest value of n and m*/

PRINT 'Eigen Values', b[ROWNAME=axes COLNAME=SS FORMAT=12.4];

PRINT '%SS Explained by Each Axis', e[ROWNAME=axes COLNAME=%SS FORMAT=12.2];

PRINT 'Genotypic Scores', vq[ROWNAME=gen COLNAME=score FORMAT=12.4];

PRINT 'Environmental Scores', uq[ROWNAME=env COLNAME=score FORMAT=12.4];

QUIT;

Analysis of variance based on regional division of environments

The additive model (4) can be fitted using PROC GLM of SAS with fixed genotypes andenvironments and random blocks. The environmental main effect and its partitioning are then testedover the term region*env*block (blocks within environments within regions). The following code first

creates three different variables within a SAS data set in which to allocate environments according tothe previous assortment in three regions: Granada, Sevilla and Spanish Central Plateau. Environmentsnot belonging to a particular region are given a homogeneous value (e.g. zero). By using thismethodology, the within regions term of model (4), ge(r)ij(r), can immediately be split into three termsaccounting for the between environments variation at each of Granada, Sevilla and Central Spainregions. This is true after correction for the between regionsterm of the model, grir. Accordingly, typeI sum of squares should be used. The same procedure applies to the partition of the environmentalmain effect.

DATA ....;

...

IF region=granada THEN env_gr=env;

ELSE env_gr=0;IF region=sevilla THEN env_se=env;

ELSE env_se=0;

IF region=central THEN env_ce=env;

ELSE env_ce=0;

...

RUN;

PROC GLM;

CLASS region env env_gr env_se env_ce gen block;

MODEL yield = region env_gr env_se env_ce

region*env*block

gen

gen*region gen*env_gr gen*env_se gen*env_ce/SS1 E1;RANDOM region*env*block/TEST;

RUN;

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PROC MIXED;

CLASS gen env region block;

MODEL yield = region env*region env*region*blq

gen

gen*region

genot*cov_env1 genot*cov_env2

genot*cov_env3 genot*cov_env4/DDF=234;

PARMS 0.12/NOITER EQCONS=1;

ESTIMATE 'BEKA*Tj' GENOT*cov_env1 6 -1 -1 -1 -1 -1 -1/ DIVISOR=7;

ESTIMATE 'M01*Tj' GENOT*cov_env1 -1 6 -1 -1 -1 -1 -1/ DIVISOR=7;

...

ESTIMATE 'M23*Tj' GENOT*cov_env1 -1 -1 -1 -1 -1 -1 6/ DIVISOR=7;

RUN;

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REFERENCES

Abay, F. and C. Cahalan. (1995). Evaluation of response of some barley landraces in drought prone sites ofTigray (Northern Ethiopia). Crop Improvement22: 125-132.

Abo-Elenin, R.A., Morsi, L.R. and A.A. Gomaa. (1977). Yield stability parameters for barley cultivars in Egypt.Agricultural Research Review55: 189-206.

Acevedo, E. and S. Ceccarelli. (1989). Role of the physiologist breeder in a breeding program for droughtresistance conditions. In Drought Resistance in Cereals, ed. F.W.G. Baker, Wallinford (UK): CABInternational, pp 117-139.

Allard, R.W. (1999). Principles of Plant Breeding, New York: J. Wiley.

Arain, A.G. (1975). Adaptation studies of radiation-induced barley mutants.Experientia31: 526-528.

Atlin, G.N., McRae, K.B. and X. Lu. (1999). Genotype x region interaction for two-row barley yield in Canada.Crop Science(in press).

Baker, R.J. (1988). Tests for crossover genotype-environmental interactions. Canadian Journal of PlantSciences68: 405-410.

Baker, R.J. (1990). Crossover genotype-environmental interaction in spring wheat. In Genotype-by-EnvironmentInteraction and Plant Breeding, ed. M.S. Kang, Baton Rouge, LA: Lousiana State University, pp 42-51.

Barszczak, Z. and T. Barszczak. (1980). Tolerance of wheat and barley varieties to soil acidity.Wissenschaftliche Beitrage der Martin-Luther-Universitat Halle-Wittenberg20: 678-690.

Basford, K.E. and M. Cooper. (1998). Genotype x environment interactions and some considerations of theirimplications for wheat breeding in Australia.Australian Journal of Agricultural Research 49: 153-174.

Braun, H.J., Rajaram, S. and M. van Ginkel. (1997). CIMMYTs approach to breeding for wide adaptation. InAdaptation in Plant Breeding, ed. P.M.A. Tigerstedt, Dordrecht (The Netherlands): Kluwer Academic Publ.,pp 197-205.

Berbigier, A. and J.B. Denis. (1981). Variety x locality interaction. Analysis of spring barley yields in 1978.Comparison of 1977 with 1978.Agronomie 1:641-650.

Bezant, J., Laurie, D., Pratchett, N., Chojecki, J. and M. Kearsey. (1997). Mapping QTL controlling yield andyield components in a spring barley (Hordeum vulgare L.) cross using marker regression. Molecular

Breeding3: 29-38.

Borthwick, H.A., Parker, M.W. and P.H. Heinze. (1941). Effect of photoperiod and temperature on developmentof barley.Botanical Gazette103: 326-341.

Bouzerzour, H. and B. Refoufi. (1992). Effect of sowing date and rate, and site environment on the performanceof barley cultivars grown in the Algerian high plateaux.Rachis11: 19-24.

Ceccarelli, S. (1989). Wide adaptation: How wide.Euphytica40: 197-205.

Ceccarelli, S. and S. Grando. (1991). Environment of selection and type of germplasm in barley breeding forlow-yielding conditions.Euphytica57: 207-219.

Ceccarelli, S. (1994). Specific adaptation and breeding for marginal conditions.Euphytica77: 205-219.

Ceccarelli, S. (1996a). Positive interpretation of genotype by environment interactions in relation tosustainability and biodiversity. In Plant Adaptation and Crop Improvement, ed. M. Cooper and G.L.Hammer, Wallingford (UK): CAB International, pp 467-486.

7/27/2019 GE Chapter(1)

25/28

Ceccarelli, S. and S. Grando. (1996b). Drought as a challenge for the plant breeder. Plant Growth Regulation20:149-155.

Ceccarelli, S., Grando, S. and A. Impiglia. (1998). Choice of selection strategy in breeding barley for stressenvironments.Euphytica103: 397-318.

Cooper, M. and P.N. Fox. (1996) Environmental characterization based on probe and reference genotypes. InPlant adaptation and crop improvement, ed. M. Cooper and G.L. Hammer, Wallingford (UK): CABInternational, pp 529-547.

Cooper, M. and G.L. Hammer. (1996). Plant adaptation and crop improvement. Wallingford (UK): CABInternational.

Denis, J.B. (1988). Two-way analysis using covariates. Statistics19: 123-132.

Dofing, S., Berge, T.G., Baenziger, P.S. and C.W. Knight. (1992). Yield and yield component response of barleyin sub arctic and temperate environments. Canadian Journal of Plant Science72: 663-669.

Ellis, R.H., Summerfield, R.J., Roberts, E.H. and J.P. Cooper. (1989). Environmental control of flowering in

barley (Hordeum vulgare). III. Analysis of potential vernalization responses, and methods of screeninggermplasm for sensitivity to photoperiod and temperature.Annals of Botany63: 687-704.

Fox, P.N., Crossa, J. and I. Romagosa. (1997). Multi-environment testing and genotypeenvironmentinteraction. In Statistical Methods for Plant Variety Evaluation, ed. R.A. Kempton and P.N. Fox, London:Chapman and Hall, pp 117-137.

Fox, P.N. and A.A. Rosielle. (1982). Reducing the influence of environmental main effects in pattern analysis ofplant breeding environments.Euphytica31: 645-656.

Gauch, H.G. (1988). Model selection and validation for yield trials with interaction.Biometrics44:705-715.

Gauch, H.G. (1992). Statistical Analysis of Regional Yield Trials. Amsterdam: Elsevier.

Gollob, H.F. (1968). A statistical model that combines features of factor analysis and analysis of variancetechniques. Psycrometrika33:73-115.

Gustafsson, A., Ekman, G. and Dormling I. (1977). Effects of the Pallas gene in barley: phene analysis,overdominance, variability.Hereditas86: 251-266.

Hayes, P.M., Liu, B.H., Knapp, S.J., Chen, F., Jones, B., Blake, T., Franckowiak, J., Rasmusson, D., Sorrells,M., Ullrich, S.E., Wesenberg, D. and A. Kleinhofs. (1993). Quantitative trait locus effects and environmentalinteraction in a sample of North American barley germplasm. Theoretical and Applied Genetics87:392-401.

Isla, R., Royo, A. and R. Arags. (1997). Field screening of barley cultivars to soil salinity using a sprinkler anddrip irrigation system. Plant and Soil197: 105-117.

Jackson, P.A., Byth, D.E., Fischer, K.S. and R.P. Johnston. (1994). Genotype x environment interactions inprogeny from a barley cross: II. Variation in grain yield, yield components and dry matter production amonglines with similar times to anthesis. Field Crops Research 37: 11-23.

Jones, J.L. and E.J. Allen. (1986). Development in barley (Hordeum sativum).Journal of Agricultural Science,Cambridge107: 187-213.

Kang, M.S. and H.G. Gauch. (1996). Genotype by Environment Interaction: New Perspectives. Boca Raton:CRC Press.

Kempton, R.A. and P.N. Fox. (1997). Statistical Methods for Plant Variety Evaluation. London: Chapman andHall.

7/27/2019 GE Chapter(1)

26/28

Kong, D., Choo, T., Jui, P., Ferguson, T., Therrien, M.C., Ho, K.M., May, K.W., and P. Narasimhalu. (1994).Genetic variation and adaptation of 76 Canadian barley cultivars. Canadian Journal of Plant Science 74:737-744.

Lekes, J., and L. Zinisceva. (1990). Selection in spring barley with a view of more efficient nitrogen utilization.Communication to the Vereinigung osterreichischer Pflanzenzuchter, Gumpenstein, Osterreich, 20-22

November 1990. Austria: Bundesanstalt fur Alpenlandische Landwirtschaft, Gumpenstein, pp 107-114.

Loss, S.P. and K.H.M. Siddique. (1994). Morphological and physiological traits associated with wheat yieldincreases in Mediterranean environments.Advances in Agronomy52:229-275.

Molina-Cano, J.L. (1982). Genetic, agronomic, and malting characteristics of a new erectoides mutant induced inbarley.Z Pflanzenzuecht88: 34-42.

Molina-Cano, J.L., Garca del Moral, L.F., Ramos, J.M., Garca del Moral, M.B., Jimnez-Tejada, P.,Romagosa, I., and F. Roca de Togores. (1990). Quantitative phenotypical expression of three mutant genes inbarley and the basis for defining an ideotype for Mediterranean environments. Theoretical and AppliedGenetics80:762-768.

Muoz, P., Voltas, J., Araus, J.L., Igartua, E. and I. Romagosa. (1998). Changes over time in the adaptation ofbarley releases in North-eastern Spain. Plant Breeding117: 531-535.

Nurminiemi, M., Bjornstad, A. and O.A. Rognli. (1996). Yield stability and adaptation of nordic barleys.Euphytica92: 191-202.

Orr, H.A. and J.A. Coyne. (1992). The genetics of adaptation: A reassessment. American Naturalist140:725-742.

Patel, J.D., Reinbergs, E., Mather, D.E., Choo, T.M. and J.D.E. Sterling. (1987). Natural selection in a doubled-haploid mixture and a composite cross of barley. Crop Science 27: 474-479

Prez de la Vega, M. (1997). Plant genetic adaptedness to climatic and edaphic environment. In Adaptation in

Plant Breeding, ed. P.M.A. Tigerstedt, Dordrecht (The Netherlands): Kluwer Academic Publ., pp 27-38.

Pomortsev, A.A., Kalabushkin, B.A., Blank, M.L. and A. Bakhronov. (1996). Investigation of natural selectionin artificial hybrid populations of spring barley. Genetika (Moskva)32: 1536-1544.

Rasmusson, D.C. and B.G. Gengenbach. (1983). Breeding for physiological traits. In Crop Breeding, ed D.R.Wood, Madison, WI: Am. Soc. Agron., pp 231-254.

Riggs, T.J., Hanson, P.R., Start, N.D., Miles, D.M., Morgan, C.L. and M.A. Ford. (1981). Comparison of springbarley varieties grown in England and Wales between 1880 and 1980. Journal of Agricultural Science,Cambridge97: 599-610.

Romagosa, I., Fox ,P.N., Garca del Moral, L.F., Ramos, J.M., Garca del Moral, M.B., Roca de Togores, F. and

J.L. Molina-Cano. (1993). Integration of statistical and physiological analysis of adaptation of near-isogenicbarley lines.Theoretical and Applied Genetics86: 822-826

Romagosa, I. and P.N. Fox. (1993). Genotype-environment interaction and adaptation. In Plant Breeding,Principles and Prospects, ed. M.D. Hayward, N.O. Bosemark and I. Romagosa, London: Chapman and Hall,pp 373-390.

Romagosa, I., Ullrich, S.E., Han, F., and P.M. Hayes. (1996). Use of the additive main effects and multiplicativeinteraction model in QTL mapping for adaptation in barley. Theoretical and Applied Genetics93: 30-37

SAS Institute Inc. (1989a). SAS/STAT users guide. Version 6, First Edition. Cary, NC: SAS Institute Inc.

SAS Institute Inc. (1989b). SAS/IML software: Usage and reference. Version 6, First Edition. Cary, NC: SAS

Institute Inc.

7/27/2019 GE Chapter(1)

27/28

SAS Institute Inc. (1997). SAS/STAT software: Changes and enhancements through release 6.12. Cary, NC:SAS Institute Inc.

Soliman, K.M. and R.W. Allard. (1991). Grain yield of composite cross populations of barley: effects of naturalselection. Crop Science31: 705-708.

Talamucci, P. (1975). Comportamento di 16 cultivar di orzo in semina autunnale e primaverale nella montagnapistoiese. Sementi Elette21: 33-42.

Talbot, M. (1984). The identification of specific variety x environment interactions in spring barley. In CerealProduction. Proc. of the 2ndInt. Summer School in Agriculture, Royal Dublin Soc. & WK Kellog Foundation,Butterworth & Co Ltd, UK, p 110.

Talbot, M. (1997). Resource allocation for selection systems. In Statistical Methods for Plant VarietyEvaluation, ed. R.A. Kempton and P.N. Fox, London: Chapman and Hall, pp162-174.

Tewari, S.N. (1975). Path coefficient analysis for grain yield and its components in a collection of barley(Hordeum vulgare) germplasm. Third International Barley Genetics Symposium, authors T-Z, p 118.

Tinker, N.A. and D.E. Mather. (1995). Methods for QTL analysis with progeny replicated in multipleenvironments. Journal of Quantitative Trait Loci (on line). Avail. WWW:http://probe.nalusda.gov:8000/otherdocs/jqtl/jqtl1995-01/jqtl15.html

Tinker, N.A., Mather, D.E., Rossnagel, B.G., Kasha, K.J., Kleinhofs, A., Hayes, P.M., Falk, D.E., Ferguson, T.,Shugar, L.P., Legge, W.G., Irvine, R.B., Choo, T.M., Briggs, K.G., Ullrich, S.E., Franckowiak, J.D., Blake,T.K., Graf, R.J., Dofing, S.M., Saghai Maroof, M.A., Scoles, G.J., Hoffman, D., Dahleen, L.S., Kilian, A.,Chen, F., Biyashev, R.M., Kudrna, D.A., and B.J. Steffenson. (1996). Regions of the genome that affectagronomic performance in two-row barley.Crop Science36:1053-1062.

van Eeuwijk, F.A. (1995). Linear and bilinear models for the analysis of multi-environment trials. I. Aninventory of models.Euphytica84: 1-7.

van Eeuwijk, F.A., Keizer, L.C.P. and J.J. Bakker. (1995) Linear and bilinear models for the analysis of multi-environment trials. II. An application to data from the Dutch Maize Variety Trials.Euphytica84: 9-22.

van Eeuwijk, F.A. (1996). Between and Beyond Additivity and Non-Additivity: the Statistical Modelling ofGenotype by Environment Interaction in Plant Breeding. PhD Thesis. Wageningen, The Netherlands.

van Eeuwijk, F.A and P.H. van Tienderen. (2000). Analysis of genotype by environment interaction: ANOVAand beyond. In The Evolution of Phenotypic Plasticity, ed. P.H. van Tienderen and P.M. Brakefield, Oxford:Oxford University Press. (in press)

van Oosterom, E.J., Kleijn, D., Ceccarelli, S. and M.M. Nachit. (1993). Genotype-by-environment interactionsof barley in the Mediterrranean region. Crop Science33: 669-674.

Voltas, J., van Eeuwijk, F.A., Sombrero, A., Lafarga, A., Igartua, E. and I. Romagosa. (1999a). Integratingstatistical and ecophysiological analyses of genotype by environment interaction for grain filling of barley. I.Individual grain weight. Field Crops Research62: 63-74.

Voltas, J., van Eeuwijk, F.A., Araus, J.L. and I. Romagosa. (1999b). Integrating statistical and ecophysiologicalanalyses of genotype by environment interaction for grain filling of barley. II. Grain growth. Field Crops

Research62: 75-84.

Voltas, J., Romagosa, I., Lafarga, A., Armesto, A.P., Sombrero, A. and J.L. Araus. (1999c). Genotype byenvironment interaction for grain yield and carbon isotope discrimination of barley in Mediterranean Spain.

Australian Journal of Agricultural Research50: 1263-1271.

Wricke, G. (1962). ber eine Methode zur Erfassung der kologischen Streubreite in Feldversuchen. Z.

Pflanzenzchtg47: 92-93.

7/27/2019 GE Chapter(1)

28/28

Wright, A.C. and R.E. Gaunt. (1992). Disease-yield relationship in barley. I. Yield, dry matter accumulation andyield-loss models. Plant Pathology41: 676-687.

Zhu, H., Briceo, G., Dovel, R., Hayes, P.M., Liu, B.H., Liu, C.T., and S.E. Ullrich. (1999). Molecular breedingfor grain yield in barley: an evaluation of QTL effects in a spring barley cross. Theoretical and AppliedGenetics