studies in the breeding of self pollinating cereals

STUDIES IN THE BREEDINGOF SELF POLLINATING CEREALS5 . USE OF THE INCOMPLETE DIALLEL IN WHEAT BREEDING

F. G . H. LUPTON(Plant Breeding Institute, Cambridge)

With 4 figuresReceived 20 Oct. 1964

ABSTRACT

The trials described in this paper have led to the identification of a number of pro-mising parental combinations suitable for detailed pedigree selection . Although theseinclude crosses involving the highest yielding parents which would probably have beenstudied without this evidence, some of the crosses identified would not have been con-sidered had these experiments not been conducted . This information has been obtainedfrom a series of trials conducted in F2 and F3.

INTRODUCTION

Useful guidance in the choice of parents likely to give rise to high yielding progenymay be obtained by detailed consideration of the phenotypes of varieties currentlyin cultivation, special attention being directed to the known defects of these varieties .By such means improvements in simply inherited characters, such as disease resistance,or even in more complex characters such as straw strength or grain quality may beobtained. Indeed, agricultural practice has shown an improvement in the yieldingpotential of winter wheat varieties cultivated in Britain amounting to approximatelyone per cent per annum over a period of fifteen years, largely resulting from the intro-duction of hybrids involving varieties in general cultivation in Western Europe, ortheir close relatives.

When considering a crop such as winter wheat on which intensive breeding workhas been carried out for many years, it is also desirable that the breeder should explorethe possibility of widening the genetic variability within which he conducts his selectionprogramme. This involves the incorporation into the programme of varieties of widelycontrasting phenotype often obtained from areas of wheat cultivation distant fromthat in which he is working. The scope available to him for this purpose is enormous andit is therefore essential that he should be able to assess the potentialities of these alienvarieties before embarking on an extensive breeding programme based upon them .

Apart from consideration of the performance and phenotypic appearence of poten-tial parental varieties, two methods of approach are available . The first involves a con-sideration of the physiological characteristics of the varieties, and the second a geneticanalysis of their behaviour when hybridised with varieties adapted to the area in whichthe breeder is working . The physiological approach involves consideration of suchcharacters as photosynthetic activity, tillering pattern, or relative duration of differentphases in the life cycle . From a consideration of such characters, it should be possiblefor the breeder to select as parents varieties with complementary physiological attribu-

Euphytica 14 (1965) : 331-352

33 1

F. G . H. LUPTON

tes which might be combined in their offspring . There is however, a considerabledanger that the desired recombinations might not be obtained in the hybrid progeniesbecause of interactions. A considerable advance in the understanding of the inheritanceof physiological attributes will be necessary before this approach to the choice ofparents can be adopted with any confidence .

The present paper is concerned with the genetic analysis of the relative merits of agroup of varieties as potential parents for improvement in yielding capacity . The ana-lysis of diallel crosses in self pollinating species developed by HAYMAN, JINxs andMATHER provides a powerful tool for this purpose (MATHER, 1949 ; HAYMAN, 1954 ;JINKS 1954, 1956) ; earlier papers in this series have considered the application of theseprocedures in wheat breeding (WHITEHOUSE, THOMPSON & RIBEIRO, 1958 ; LUPTON,1961) . The practical application of this technique is limited, however, by the very largenumber of crosses, many of which have little potential value, which must be handled ifa reasonably wide range of parents is to be considered .

In order to avoid this difficulty, a series of incomplete diallel sets of crosses has beenmade in which potential parental varieties have been hybridised with five "tester"varieties, chosen to represent the genotypes of winter wheats generally cultivated inBritain. The tester varieties have remained constant throughout the programme andhave been crossed each year with successive groups of varieties selected either becauseof their promising performance in national trials or because they showed other fea-tures of special interest.

MATERIALS AND METHODS

Incomplete diallel sets of crosses, ignoring reciprocals, have been made in succes-sive years from 1958 to 1963 . In each year, the five "tester" varieties - Cappelle Des-prez, Heine VII, Holdfast, Hybrid 46 and Minister* -have been hybridised with suc-cessive groups of varieties or hybrid selections which were considered of interest aspossible parents. The Fl's were in each case grown in the field in the year following hy-bridization and unselected bulks were grown in yield trials in F2 and F 3 . No attemptwas made to obtain yield data in the Fl generation as the number of grains availablewas frequently limited and previous experience had shown the difficulties of interpret-ing data obtained from F l trials with very widely spaced plants. Careful observationswere made throughout the Fl generation, however, and in certain cases arrays wereeliminated at this stage on account of such characters as hybrid necrosis (HERMSEN,1963), or extreme susceptibility to disease. When it was considered desirable, crossesshowing such undesirable features were back-crossed to suitable parents and handledby conventional selection methods .

The present paper considers crosses made in 1958, 1959 and 1960 and grown inyield trials in 1961-1963 . The crosses made in 1958 involved the varieties : Flamingo,Hestbignon, Leda, Mado, Relief, Stella, Svenno, Thor and Wasatch.* The crossesinvolving the Canadian varieties Relief and Wasatch, originally included on accountof the reported resistance of these varieties to Tilletia contraversa, were removed fromthe trial series on account of their extremely weak straw, though selection in backcrosses of these varieties to strong strawed parents has continued . Trials of unselectedF2 populations of the remaining crosses were grown at Cambridge and Sprowston

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BREEDING OF SELF POLLINATING CEREALS

(Norfolk) in 1960, and of F3 populations at the same two centres in 1961 . The yielddata obtained from these trials are given in Table 1 .

The crosses made in 1959 involved the varieties : Els, Felix, Heine 110, MarisWidgeon and Peko and the unnamed selections H 1444, Halle 3435, Dolis Puri 35/4,Pseudo meridionale 122 and W 254/39 .* The crosses involving the Russian selectionsDolis Puri 35/4 and Pseudo meridionale 122, originally included on account of theresistance of these varieties to Erysiphe graminis, were discarded on account of theirvery poor weak straw. Fl plants of crosses of the variety Felix with Cappelle Desprez,Heine VII and Holdfast showed marked symptoms of hybrid necrosis at an early stageof development and died during the winter months . This variety was therefore removedfrom the trial programme, though the crosses Felix x Hybrid 46 and Felix x Minis-ter showed no signs of hybrid necrosis and have been handled by normal selectionmethods. Trials of unselected F2 populations of crosses involving the remaining va-rieties were grown at Cambridge in 1961 and of F3 populations at Headley Hall(Yorkshire), Sprowston (Norfolk) and Seale Hayne (Devonshire) in 1962 . The yielddata obtained from these trials are given in Table 4 .The crosses made in 1960 involved the varieties Bonus, Maitre Pierre, Panter,

Professeur Marchal and Viking and the unnamed selections TBn 72/3 and TB 209 .*Unselected F2 populations of crosses involving these varieties were grown in trial atCambridge in 1962. Trials of F3 populations were grown at Cambridge, Headley Hall,Sprowston and Seale Hayne in 1963 . The yield data obtained from these trials aregiven in Table 7 .

Following preliminary consideration of the results then available, a further trialwas grown in 1963 to obtain estimates of the variation in yielding capacity amongstthe progeny of those crosses which showed the greatest promise . For this purpose, anaugmented randomised block design similar to that described by LUPTON (1961) wasemployed. The parental combinations used comprised an incomplete diallel series ofthe varieties Els, Maitre Pierre, Maris Widgeon, Peko, Professeur Marchal, Viking,TBn 72/3 and TB 209 crossed with the four "tester" varieties, Cappelle Desprez,Heine VII, Hybrid 46 and Minister. 36 random selections from each cross were sownin 12 blocks. Each block contained 156 plots, comprising three selections from eachcross and one plot of each of the 12 parents. The mean yields obtained and the stand-ard errors of each parental combination are given in Figure 4 .

GENETIC ANALYSIS

The data obtained from trials of unselected bulks of incomplete diallel sets ofcrosses may be analysed by a modification of the methods described by JINxs andHAYMAN, loc. cit ., although the precision of the results obtained will not be so great asthat obtained from the analysis of complete diallel sets of crosses . The analysis may,however, be used for identification of parental combinations showing non-allelicinteraction, and may also be used to obtain evidence on the relative levels of domi-nance shown by the parents involved. The variances of the arrays of yield data (Vr)

* The countries of origin and pedigrees of the varieties used as parents will be found, so far as theyare known, in the appendix . Cappelle Desprez is referred to throughout the remainder of this paperas Cappelle.

333

F. G. H. LUPTON

and their co-variances with the yields of the non-recurrent parents (Wr) are calculatedas in the case of complete diallel sets of crosses, except that the yields of the recurrentparents are not included in the calculations . It can then be shown that in the absenceof non-allelic interaction, the regression of Vr on Wr will be linear and of unit slope .In the presence of non-allelic interaction, the regression will have a slope of less thanunity, and it is commonly found that the standard error of the regression coefficient islarge .

When a significant regression is obtained, those parents whose positions on the re-gression line lie nearest to the origin of the Wr/Vr graph carry the greatest number ofdominant factors for the character being considered ; similarly, those which lie furthestfrom the origin carry the greatest number of recessive characters . As in the analysis ofcomplete diallel sets of crosses, a limiting parabola of formula Wr 2 = Vp Vr, may besuperimposed on the Wr/Vr regression line ; in the case of the incomplete diallel Vp isthe variance of the non-recurrent parental varieties . The positions on this line corres-ponding to all parents in the diallel set of crosses must lie within the arc of this para-bola. It is therefore possible to estimate the prospects of selection for improved ex-pression of the character being analysed by considering the positions of the points onthe Wr/Vr regression relative to the intersections of this regression with the limitingparabola.

In addition to the Wr/Vr analysis, further evidence on the merits of the parentalcombinations used in diallel crosses may be made, using the principles outlined byHAYMAN (1954) . This analysis provides for the sub-division of the data obtained fromtrials of diallel crosses in order to obtain estimates of the general and specific com-bining abilities of the parents and parental combinations involved.

The variation in yield performance is divided by HAYMAN into components due todifferences between the parents, and those due to dominance effects . The general com-bining ability of each parent, referred to as component "a" in HAYMAN's analysis, isdetermined from analysis of the mean yields of the arrays comprising the diallel table .The specific combining ability is derived from the interaction term in this analysis whenvariation due to arrays has been removed .

Dominance is divided by HAYMAN into three components : b l due to overall domi-nance of the crosses as a whole ; b2 due to expression of dominance by arrays with acommon parent ; and b3 due to specific dominance effects shown by individual parentalcombinations . The dominance components of each set of crosses are determined fromconsideration of the difference between the yield of each parental combination and themean of its two parents . The b, term is then determined from the deviation of the totaldominance effect from zero ; b2 is determined from the summed dominance effects ofcrosses involving each parent ; and b3 from the interaction term of the diallel table ofdominance effects. The b3 term, it should be noted, is identical with the interactionterm from the diallel table of yield data, and thus provides a check on the accuracy withwhich specific combining ability has been computed .

The data obtained from a series of trials of the same set of crosses may be combinedin a single analysis of variance . From such an analysis, the second order interaction ofspecific combining ability with trial sites or generations provides an estimate of error .This may be compared with the first order interaction terms, testing the consistency ofgeneral combining ability or of the components of dominance over trial sites and gene-

334


rations. If the first order interactions are not significant, they may be pooled with theerror term . It is frequently found, however, that these terms are significant . In suchcases, the significance of overall differences in general combining ability, or in thecomponents of dominance, must be tested by comparison with the appropriate firstorder interactions .

RESULTS

Crosses made in 1958The yield data obtained from the trials of crosses made in 1958 are given in Table 1 .

In order to obtain evidence on the relative levels of dominance shown by the parentalvarieties involved, and to identify possible cases of non-allelic interaction, the datafrom these trials have been pooled and analysed according to the techniques referredto in the previous section.

TABLE 1 . YIELD DATA FROM CROSSES MADE IN 1958 (/. CAPPELLE)

335

Flamingo Hestbignon Leda(C)

Mado(D)

Stella(E)

Svenno(F)

Starke(G)(A) (B)

F, Cambridge : 1960 107.1 99 .0 106 .9 106 .5 106 .8 90.5 95 .3[L.S.D . (P = 0.05) 11 .3]Cappelle (P) 100 .0 115 .8 101 .9 108.8 102 .6 104.8 106.5 103 .2Heine VII (0) 100 .8 103 .2 102 .9 106 .1 103 .7 107.2 96 .4 108 .7Holdfast (R) 86 .5 107.1 98 .0 100.2 101 .3 99.4 100.4 96.0Minister (S) 106 .0 91 .5 96 .0 102.2 108 .9 89.2 103 .2 87 .6Hybrid 46 (T) 103 .8 112 .6 104 .0 111 .0 105 .8 106.7 101 .8 106.6

F, Sprowston : 1960 96 .8 97 .8 95 .5 95 .8 102.7 79 .0 74 .2[L .S.D . (P = 0.05) 12.1]Cappelle (P) 100 .0 97 .3 104 .3 100.0 100 .8 102.4 97 .0 98 .6Heine VII (Q) 95 .8 97 .0 103 .7 103 .1 103.5 115 .0 86 .8 88 .9Holdfast (R) 76 .1 92 .7 87.9 85 .2 88.3 91 .6 88 .8 76.8Minister (S) 102 .8 95 .6 96.4 103 .8 101 .2 88 .0 90 .7 90.3Hybrid 46 (T) 100 .7 98 .6 93 .6 99 .8 93.8 106 .9 95 .8 93 .5

F, Cambridge : 1961 99 .4 83 .0 78 .8 105 .6 108 .2 96 .2 87 .8[L .S.D . (P = 0.05) 22.7]Cappelle (P) 100.0 91 .8 123 .5 100.6 112.1 119 .6 104 .1 104 .0Heine VII (Q) 93 .4 114 .8 97.4 106 .0 105.0 98 .7 92 .1 101 .2Holdfast (R) 68 .5 90.4 75 .5 75 .3 78 .6 84.8 80.4 78 .7Minister (S) 108 .5 115 .1 87 .4 96 .2 116 .8 104.0 87 .4 92 .9Hybrid 46 (T) 86.6 81 .4 88 .5 85 .0 100 .5 91 .3 101 .8 88 .2

F, Sprowston : 1961 93 .3 83 .5 87.5 81 .6 105 .4 78 .9 82.6[L .S .D . (P = 0 .05) 12 .11Cappelle (P) 100 .0 83 .8 87.3 89 .4 90 .3 93 .0 91 .2 83 .9Heine VII (Q) 84.0 88 .7 87.0 90.6 87 .4 90.8 76 .5 75 .1Holdfast (R) 77.8 80 .6 77.5 94.8 81 .3 92.5 78 .5 86.5Minister (S) 92.6 78 .7 80.8 89 .2 92 .7 84.8 89 .8 76.8Hybrid 46 (T) 97 .0 86 .1 89 .0 81 .1 92 .7 91 .8 86 .1 93 .4

Mean of all trials 99 .1 90.8 92 .2 97.4 105 .8 86 .1 85 .0[L.S.D . (P = 0.05) 6 .9]Cappelle (P) 100.0 97 .2 104.2 99 .7 101 .4 104 .9 99 .7 97 .4Heine VII (0) 93 .5 100 .9 97 .7 101 .4 99 .9 102 .9 87.9 93 .5Holdfast (R) 77 .2 92 .7 84.7 88 .9 87.4 92 .1 87 .0 84.5Minister (S) 102 .5 95 .2 90.1 97 .8 104.9 91 .5 92 .8 86 .9Hybrid 46 (T) 97 .0 94 .7 93 .8 94 .2 98.2 99 .2 96 .4 95 .4

Mean of Array 96 .1 94 .1 96 .4 98 .4 98 .1 92 .8 91 .5

336

W

F. G. H. LUPTON

FIG. 1 . Wr Vr graphs of crosses made in 1958

(b) Omitting Minister arrayVr

Wr

9.1 13 .642 .6 48 .820.7 29.737.0 41 .121 .7 34.525.1 33 .321 .8

38.1

Vp = 66 .0b=0.79+0.37

b = 1 .00 ± 0.20

The Wr/Vr graph obtained from consideration of pooled data derived from all thetrials is shown in Figure la . The points on this graph lie on a line of slope 0 .79 ± 0.37,which does not differ significantly from zero . This suggests the possibility of non-alle-lic interaction, and a study of the yield data in Table 1 shows that the yields obtainedfrom crosses involving the variety Minister are somewhat erratic and frequently fallbelow the mean of their parents . This observation is supported by notes made in thefield that some of the crosses involving this variety showed marked leaf necrosis inmid May, and agrees with reports of such necrosis in Minister crosses made in anearlier paper in this series (LUPTON, 1961). It therefore seems possible that non-allelicinteraction may be taking place in some of the crosses involving Minister . A recomput-ed Wr/Vr graph omitting crosses involving this variety is shown in Figure lb. Thisgraph shows a Wr/Vr regression of 1 .00 ± 0.20 and confirms the occurrence of non-allelic interaction in parental combinations involving Minister . Since the crossesinvolved were lower yielding than might have been anticipated from consideration ofthe parental performance, it is unlikely that exploitation of the interaction would be ofvalue to the plant breeder .

Consideration of the Wr/Vr relationship shown in Figure lb reveals no clear cutassociation of high yielding capacity with dominant or recessive genetic factors. Thepoints on the regression line corresponding to the two highest yielding varieties, Madoand Stella, both lie towards the middle of the graph, as does also that correspondingto the lowest yielding variety, Starke . It is therefore difficult to make useful predictionsconcerning the possibilities of obtaining high yielding segregates from any of the paren-

80

60

40

20

Dx

Cx

xB

E

30 40 60 80 y

(a) All arraysVr Wr

Flamingo

A

6.2 7.5Hestbignon B

35.1 28.7Leda

C

16.0 23.4Mado

D

28.1 40.7Stella

E

24.3 13.5Svenno

F

18.8 23.8Starke

G

19.9 19.7


tat combinations represented in this group of crosses . This difficulty is increased whena comparison is made between the Wr/Vr regressions obtained from the componenttrials. Largely as a result of the differing levels of accuracy of these trials, the figuresfor Wr and Vr obtained from them differ widely in scale. This effect can be greatlyreduced, however, by dividing the Wr and Vr figures for each trial by the error meansquare from the analysis of the appropriate yield trial . All data have therefore beenrescaled in this manner and analysed according to the procedure outlined by ALLARD(1956), as adapted by THOMPSON and WHITEHOUSE (1962) . This analysis gives the fol-lowing figures :

As in the case of the data presented by THOMPSON and WHITEHOUSE, the error termin the second part of the table is derived from the pooled data from the Dominance XArrays and Trials x Dominance x Arrays interactions .

Consideration of the upper portion of the table shows that there is a highly signi-ficant overall regression of Wr on Vr, with no evidence of heterogeneity between thetrials making up this series of experiments. The first term in the lower portion of thetable is derived from a comparison of summed Vr T Wr estimates over all varietiesbetween trials, and indicates that in spite of the rescaling of the data, the trials differsignificantly from one another in total variability . This is, however, only a reflectionof the efficiency of the rescaling process, and has little biological significance. Of muchgreater interest is the highly significant interaction between trials and arrays . Comparedwith this interaction, the differences between arrays are non-significant, so that nomeaning can be attached to the order of points along the Wr/Vr regression .

An alternative assessment of the merits of the parental combinations used in thisseries of trials may be made by comparing their general and specific combining abili-ties, following the conventional methods . This may be supplemented, as explainedabove, by estimation of the dominance effects, according to the system outlined byHAYMAN (1954) . The general combining ability of each parent is defined as the meanyield of crosses in which that parent is involved, and may be derived from the final rowof figures in Table 1 . Similarly, the specific combining ability of each parental combina-tion is defined as the mean performance of that parental combination and is derivedfrom the component figures of this block . Corresponding mean data for dominance,obtained by subtracting the mean yield of its parents from that of each hybrid, aregiven in Table 2. Statistical analysis of the data from this series of trials, gives the fol-lowing figures, the symbols in the left hand column being those of HAYMAN (1954) :

337

D.F . M.S . V.R. P.

Mean regression 1 1.7340 8 .72 0.01-0.001Heterogeneity 3 0.0816 0.41 N.S .Error 20 0.1988

Trials 3 2.3241 10.65 <0.001Dominance 1 0.3024 1 .38 N.S .Trials x Dominance 3 0.2288 1 .05 N.S .Arrays 6 0.7366 1 .03 N.S .Trials x Arrays 18 0.7153 3 .28 0.01-0.001Error 24 0.2188

F. G. H. LUPTON

From this analysis it may be seen that, with the exception of the interaction ofdominance due to parents A,B,C- x locations, the first order interactions are allsignificant when compared with the second order interaction . The significances ofdifferences in main effect have therefore been tested by comparison in each case withthe appropriate first order interaction, from which it is clear that there are significantdifferences in yielding capacity between arrays of crosses, indicating differences ingeneral combining ability between the parents concerned . There are also significantdifferences in dominance between the varieties, but it is interesting to note that thereis no evidence of significant differences in specific combining ability. As pointed outearlier, estimates of the significance of differences in this component may be obtainedeither from the interaction term of the yield data in the final block of Table 1, or fromthe corresponding term from the data for dominance effects in Table 2 . Comparisonsof array mean yields and mean dominance effects with estimates of the relevant signi-ficant differences are given in Table 3, together with figures for these data discounting

TABLE 2. DOMINANCE IN CROSSES MADE IN 1958(Mean difference in yield between crosses and mid parents expressed as % Cappelle yield)

L . S.D . (difference between cross means) 6 .9 (P = 0 .05)

338

Notation afterHAYMAN (1964) DF MS VR P

a General combining ability 11 296 .9 3.60 0.01-0.001

b 1Dominance :Overall Dominance 1 293 .4 1 .07 N.S .Dominance due to parents A,B,C- 6 69.4 1 .89 N.S .

b 2Dominance due to parents P,Q,R- 4 309 .4 3 .68 0.05-0.01

b, Interaction of dominance effects 24 52 .8 1 .40 N.S .

B(Specific combining ability)

Generations and locations 3 1639 .3 19 .9 <0.001aB G.c .a. x locations 33 82 .4 2.19 0.01-0.001b1B Overall Dominance x locations 3 273 .0 7 .25 <0.001

Dominance due to A,B,C- x loca-tions 18 36 .7 0 .97 N.S .

b 2B tDominance due to P,Q,R,- x loca-tions 12 84 .1 2 .23 0.05-0.01

b,B Interaction of dominance effects x lo-cations 72 37 .7

Flamingo Hestbignon Leda Mado Stella Svenno Starke(A) (B) (C) (D) (E) (F) (G)

Cappelle (P) -2.3 8 .8 3 .6 2.8 4 .0 6.6 4.9Heine VII (Q) 4.6 5 .6 8.6 4.4 3 .3 -1 .9 4.2Holdfast (R) 4.5 0 .7 4.1 0.1 0.6 5 .3 3 .4Minister (S) -5 .6 -6 .5 0.5 4.9 -12 .9 -1 .5 -6.8Hybrid 46 (T) -2 .2 -0 .1 -0.4 1 .0 -2.7 4 .5 4.4


TABLE 3 . YIELD DATA AND EXPRESSION OF DOMINANCE IN CROSSES MADE IN 1958 (As % CAPPELLE YIELD)

Array mean yield

Dominance

(P = 0.05)

crosses involving the variety Minister. The latter are excluded because, as has beennoted, a number of crosses involving this variety exhibited necrotic leaf yellowing inMay so that yield data obtained from them may distort estimates of combining abilityor dominance . Their elimination has in fact rendered the comparison of expressions ofdominance non-significant . This leaves, as the principal conclusion from this series oftrials, a demonstration that the variety Stella has a significantly better combiningability than any of the other varieties tested.

Crosses made in 1959

The yield data obtained from trials of crosses made in 1959 are given in Table 4 .The Wr/Vr graph obtained from the pooled data derived from all the trials is shownin Figure 2 . The points on this graph lie on a line of slope 0.79 + 0.21. This regressiondiffers significantly from zero but not significantly from unity, although, as in theprevious series of trials, there is a suggestion of non-allelic interaction . A considerationof the data in Table 4 shows once again, that the crosses involving the variety Ministerare erratic and frequently yield less than the means of their parents . Elimination of theMinister crosses gives a regression of 0 .72 + 0 .18. This regression also differs signi-ficantly from zero, but does not differ from unity, nor from the regression of 0 .79 +0.21 obtained when crosses involving Minister were included in the calculations . Eli-mination of the Minister crosses has not, therefore, eliminated the source of the non-allelic interaction . Elimination in turn of the other parents has also failed to reveal thesource of the interaction which must therefore be . ascribed to a general interactionamongst the component crosses .

Consideration of the Wr/Vr relationship shown in Figure 2 shows that, as in thecrosses made in 1958, there is no clear cut association of high yielding capacity withdominant or recessive genetic factors . It may be noted, for example, that the pointscorresponding to the highest and lowest yielding varieties, Peko and H 1444, both lieclose to the origin of the graph. Comparison of the Wr/Vr relations of the componenttrials, using the same procedure as that employed in the case of the earlier series oftrials, gives the following analysis of variance :

339

All data EliminatingMinister crosses

All data EliminatingMinister crosses

Flamingo 96 .1 96.5 -0.11 0.65Hestbignon 94 .1 95 .3 0.98 2.24Leda 96.4 96 .3 1 .88 2.28Mado 98 .4 96 .8 1 .52 1 .19Stella 98 .1 100 .0 -1 .11 0 .46Svenno 92 .8 92.8 1 .49 2.09Starke 91 .5 92 .7 1 .16 2.42

L.S.D. 2 .62 2.84 2.62 2.84

The upper portion of the table shows that there is again a highly significant overallregression of Wr on Vr, with no evidence of heterogeneity between the trials making upthe series of experiments . In contrast to the earlier set of trials, there is a demonstrationof overall dominance in this series of experiments . This confirms deductions which maybe made from a comparison of Figure lb with Figure 2 ; in the former, the Wr/Vrregression is almost tangential to the limiting parabola, while in the latter, the regres-sion line passes close to the origin of the graph .

As in the earlier set of trials, there is here a demonstration of a highly significantinteraction between trials and arrays. Compared with this interaction, the differencesbetween arrays are again non-significant .

Comparison of the general and specific combining abilities of the parental combi-nations of crosses made in 1959 may be made from consideration of the data in thefinal block of Table 4. Corresponding data for the dominance effects are given in Ta-ble 5. Statistical analysis of these data gives the following figures :

340

F. G . H. LUPTON

Notation afterHAYMAN (1954)

DF MS VR P

a General combining ability 11 856 .7 3 .49 0.01-0.001

b1Dominance :Overall Dominance 1 228 .1 0.63 N.S .Dominance due to parents A,B,C- 6 1559 .5 8.27 0.01-0 .001

b 2Dominance due to parents P,Q,R,- 4 320.0 1 .90 N.S .

b $ Interaction of dominance effects 24 80 .2 1 .55 N.S .

B(specific combining ability)

Generations and locations 3 2583 .6 10.55 <0.001aB G.c .a. x locations 33 245 .4 4.73 <0.001b1B Overall dominance x locations 3 360 .2 6.95 <0.001

Dominance due to A,B,C, x locations 18 186 .6 3.60 <0.001b 2B

Dominance due to P,Q,R, x locations 12 168 .6 3 .25 0.01-0 .001b 2B Interaction of dominance effects x lo-

cations 72 51 .8

DF MS VR P

Mean regression 1 1 .6336 15 .63 <0.001Heterogeneity 3 0.1691 1 .62 N.S .Error 20 0.1045

Trials 3 0.3590 3 .30 0.05-0 .01Dominance 1 2.8480 26.30 <0.001Trials x Dominance 3 0.1785 1 .65 N.S .Arrays 6 0.3153 0 .58 N.S .Trials x Arrays 18 0.5827 5 .38 <0.001Error 24 0.1080


TABLE 4. YIELD DATA FROM CROSSES MADE IN 1959 (% CAPPELLE)

FIG. 2 . Wr Vr graph of crosses made in 1959 (All arrays)

w

Vp = 67.6

b = 0.79 + 0 .21

341

Halle3435(A)

W 254/39

(B)

H 1444

(C)

MansWidgeon

(D)

Peko

(E)

Els

(F)

Heine110(G)

F s Cambridge : 1961 105 .6 112 .3 101 .0 121 .1 104.8 118 .1 94.0[L .S .D . (P = 0.05) 13 .5]Cappelle (P) 100.0 102 .0 115 .1 85 .4 119 .4 130 .2 131 .0 84.5Heine VII (Q) 101 .8 113 .6 129.2 81 .0 112 .1 138 .8 134 .1 103 .1Holdfast (R) 77.8 89 .8 111 .2 66 .8 106 .7 109 .8 103 .6 77.0Minister (S) 109.6 91 .0 82.5 85 .6 117 .3 124 .8 125 .8 117.6Hybrid 46 (T) 91 .8 105 .7 98 .2 87 .9 125 .2 126 .2 147 .9 109.2

F a Headley Hall : 1962 86 .8 104.1 90 .7 105 .0 109 .9 77 .0 100.5[L .S .D. (P = 0.05) 14.5]Cappelle (P) 100.0 100 .8 102 .3 76 .6 110 .0 104.5 112 .3 102.4Heine VII (Q) 111 .5 94 .8 100.1 86 .2 102 .0 91 .8 97 .3 103 .9Holdfast (R) 83 .8 98 .1 109.2 86 .2 93 .0 103 .5 91 .8 95 .4Minister (S) 93 .6 80 .3 97.0 62 .8 85 .6 103 .0 103 .0 100.8Hybrid 46 (T) 107 .6 97 .3 106 .6 79 .5 110 .0 119 .4 97 .5 100.5

F, Seale Hayne : 1962 91 .1 103 .6 111 .3 98 .5 87 .9 34.6 82 .7[L.S.D. (P = 0.05) 11 .9]Cappelle (P) 100.0 99 .4 106 .0 73 .3 107 .8 94.3 75 .2 107.1Heine VII (Q) 115 .1 100 .5 106 .5 90.9 96 .5 87.0 77 .1 94.3Holdfast (R) 80.3 92 .8 99 .0 74 .5 88 .1 95 .0 67 .5 93 .8Minister (S) 94.2 97 .5 95 .4 80.0 92 .8 97 .2 77 .8 93 .2Hybrid 46 (T) 100 .5 99 .0 100 .7 89 .3 100 .5 91 .0 91 .2 100.2

F, Sprowston : 1962 73 .8 91 .7 88 .3 88 .0 104.8 67 .2 79.4[L.S.D . (P = 0.05) 12.4]Cappelle (P) 100.0 88 .0 95 .7 81 .4 92.0 94 .0 82 .5 91 .4Heine VII (Q) 101 .1 84 .6 106 .8 77 .3 87 .5 88 .1 84 .9 79.8Holdfast (R) 76 .5 85 .6 82 .3 80.2 80 .7 92.9 74 .8 76.5Minister (S) 97.3 89 .5 98 .7 80.0 81 .3 97 .5 96 .0 97.5Hybrid 46 (T) 88 .3 91 .3 95 .6 84.8 98 .1 104.1 83 .9 89.5

Mean of all trials 89 .3 102 .9 97.8 103 .1 101 .8 74 .2 89 .1[L.S.D. (P = 0.05) 6.51Cappelle (P) 100 .0 97 .5 104 .8 79 .2 107 .3 105 .7 100 .2 96.3Heine VII (Q) 107 .4 98 .4 110 .6 83 .8 99 .5 101 .4 98 .3 95.3Holdfast (R) 79 .6 91 .6 100 .4 76.9 92 .1 100.3 84 .4 85.7Minister (S) 98 .7 89 .6 93 .4 77.1 94.2 105 .6 100.6 102 .3Hybrid 46 (T) 97 .0 98 .3 100 .3 85 .4 108 .4 110.2 105 .1 99.8

Mean of array 95 .1 101 .9 80 .5 100 .3 104 .6 97 .7 95.9

Vr Wr

Halle 3435 A 11 .2 12.2W 254/39 B 26.0 16 .7H 1444 C 9.8 14.0Marls Widgeon D 35.2 23 .3Peko E 10 .9 7 .6Els F 39 .5 40.4Heine 110 G 25.8 29.4

TABLE 5 .

342

F. G . H. LUPTON

DOMINANCE IN CROSSES MADE IN 1959(Mean difference in yield between crosses and mid parents, expressed as % Cappelle yield)

L.S.D. (differences between cross means) 6 .5 (P = 0.05)

From this analysis it may be seen that all the first order interactions are significantwhen compared with the second order interaction . The significances of difference inmain effect have therefore been tested by comparison with the appropriate first orderinteractions. Such comparisons show that there are highly significant differences inyielding capacity between arrays of crosses, indicating differences in general combiningability. There is also evidence of differences in expression of dominance amongst theparents A,B,C-, but not between the tester varieties P,Q,R- . There is, however, noevidence of differences between parental combinations in specific combining ability .

The mean data for yield and dominance expression are given in Table 6, together

TABLE 6. YIELD DATA AND EXPRESSION OF DOMINANCE IN CROSSES MADE IN 1959 (AS Y. CAPPELLE YIELD)

with estimates of significant differences . From this table it will be seen that the Pekoarray significantly outyields the remainder, indicating a higher general combining abi-lity of crosses involving this variety ; the H 1444 array is very much lower yielding thanany of the others considered. With regard to dominance, the most interesting fea-tures are the Els array, with a dominance expression considerably greater than the re-mainder, and the H 1444 array which exhibits transgressive segregation for lowyielding capacity. It should also be noted that the dominance expression of the highyielding Peko array is significantly greater than all arrays except that of Els . It there-fore appears that the greatest promise in this group of crosses is shown by those in-volving the variety Peko ; the high expression of dominance shown by the Els crossessuggests that these are also worth careful study . It is of interest to note that these two

Array mean yield Dominance

Halle 3435 95 .1 2 .1W254/39 101 .9 2.1H 1444 80.5 -16.7Marls Widgeon 100.3 0.5Peko 104 .6 5.4Els 97 .7 12.3Heine 110 95.9 3 .0

L.S.D. (P = 0 .05) 2.4

Halle3435(A)

W 254/39

(B)

H 1444

(C)

MarlsWidgeon

(D)

Peko

(E)

Els

(F)

Heine110(G)

Cappelle (P) 2 .9 3 .3 -19 .7 5 .7 4 .8 13 .1 1 .7Heine VII (Q) 0 .0 5 .4 -18 .7 -5 .7 -3 .2 7 .5 -3 .0Holdfast (R) 7 .1 9 .1 -11 .8 0.7 9 .5 7 .5 1 .3Minister (S) -4.4 -7 .4 -21 .1 -6 .6 5 .3 14 .2 8 .3Hybrid 46 (T) 5.1 0.3 -12 .1 8 .3 10.7 19 .4 6.8


varieties are normally grown as spring wheats. The significance of this observation willbe more fully discussed in a later section .

Crosses made in 1960The yield data obtained from trials of crosses made in 1960 are given in Table 7,

and the Wr/Vr graph obtained from the pooled data from these trials is shown inFigure 3a. The points on this graph lie on a straight line of slope 0.66 ± 0.15 ; this

TABLE 7. YIELD DATA FROM CROSSES MADE IN 1960 (% CAPPELLE)

* Treated as missing plot owing to poor germination .

343

Bonus

(A)

MaitrePierre(B)

Panter

(C)

Prof.Marchal

(D)

Viking

(E)

TBn 72/3

(F)

TB 209

(G)

F, Cambridge : 1962 99 .5 101 .1 91 .5 110 .2 103 .2 104 .2 97 .8[L.S.D. (P = 0.05) 14 .01Cappelle (P) 100 .0 (77 .0)* 107 .8 93.0 112 .0 94 .3 117.8 104.9Heine VII (Q) 96 .9 111 .9 110 .7 72.8 112 .3 88 .8 105 .2 110.5Holdfast (R) 80 .9 102 .5 94 .0 82.4 107 .6 96 .0 96.7 94.2Minister (S) 108 .1 103 .3 106 .1 102.6 107 .4 97 .0 113 .1 113 .8Hybrid 46 (T) 96 .6 107 .3 110 .5 108.2 118 .1 86 .1 115.3 118 .2

F, Cambridge : 1963 67 .3 89.4 74 .4 101 .1 92 .8 86 .8 84 .8[L .S .D . (P = 0.05) 10.6]Cappelle (P) 100 .0 87.5 89 .9 75 .1 96.2 81 .3 91 .1 83 .8Heine VII (Q) 78 .4 87.7 87 .5 69 .6 96.4 91 .2 88 .5 80.3Holdfast (R) 67 .3 67.6 78 .7 63 .3 80.8 71 .9 66 .1 75 .5Minister (S) 90 .6 88 .8 91 .8 84.9 88 .0 90 .3 90.7 90.8Hybrid 46 (T) 95 .6 83 .5 90 .0 79 .3 86.5 91 .4 94.1 98 .4

F, Headley Hall : 1963 100 .8 92 .0 81 .5 103 .7 102 .6 100 .2 97.5[L.S.D . (P= 0.05) 10.5]Cappelle (P) 100 .0 100 .2 104 .8 95 .7 98 .8 112.1 97 .0 102 .8Heine VII (Q) 94 .2 97 .0 94 .0 75 .8 106 .0 91 .4 97 .5 86 .8Holdfast (R) 82 .3 89 .5 85 .8 79 .6 96 .7 92 .4 89.1 95 .8Minister (S) 106 .2 98 .8 90 .6 92.7 95 .0 96 .8 111 .2 95 .2Hybrid 46 (T) 93 .4 100.6 98 .4 96.8 101 .8 89 .6 101 .0 93 .2

F, Seale Hayne : 1963 92 .5 102 .8 86.7 106 .8 105 .2 94 .8 102.6[L .S.D . (P = 0.05) 10.9]Cappelle (P) 100.0 88 .3 103 .8 82 .1 101 .6 104.2 89 .0 98.5Heine VII (Q) 81 .3 87 .5 102 .9 81 .1 92 .2 101 .6 94 .7 103.5Holdfast (R) 82.5 98 .8 90 .0 85 .2 98 .5 92.4 85 .1 101 .6Minister (S) 93 .9 93 .1 106 .5 82 .6 96 .8 99 .0 90 .7 107.5Hybrid 46 (T) 103 .5 97 .8 105 .0 100 .8 104 .8 103 .6 96 .6 106.3

F, Sprowston : 1963 98 .0 97 .0 92 .0 116 .0 106.0 105 .1 100 .5[L .S.D. (P = 0.05) 9 .11Cappelle (P) 100 .0 106 .1 101 .0 94 .8 113 .0 103 .9 97 .4 107 .4Heine VII (Q) 102.1 101 .0 99 .7 83 .6 115 .2 105 .8 107 .4 100 .5Holdfast (R) 88 .8 97 .8 94 .4 84.1 99 .9 99 .8 91 .3 95 .5Minister (S) 106.5 105 .2 100 .0 92 .3 106 .1 101 .5 102 .1 103 .6Hybrid 46 (T) 104.2 99 .1 98 .8 101 .0 111 .0 89 .3 100.6 104 .0

Mean of all trials 91 .6 96 .5 85 .2 107 .6 102 .0 98 .2 96 .6[L .S .D. (P = 0.05) 4 .9]Cappelle (P) 100.0 95 .5 101 .5 88 .1 104 .3 99 .2 98 .5 99.5Heine VII (Q) 90.6 97 .0 98 .9 76 .6 104 .4 95 .8 98 .7 96.3Holdfast (R) 80.4 91 .2 88 .6 78 .9 96 .7 90 .5 85 .7 92.5Minister (S) 101 .1 97.8 99 .0 91 .0 98 .7 96 .9 101 .6 102 .2Hybrid 46 (T) 98 .7 97 .7 100.5 97 .2 104.4 92 .0 101 .5 104.0

Mean of array 95 .8 97 .8 86.4 101 .7 94 .9 97 .2 98.9

FIG . 3 . Wr Vr graphs of crosses made in 1960

W.

80-

60

4o-

10

344

F. G. H. LUPTON

10 40 60 80 \/

regression differs significantly from zero but not from unity, although there is again asuggestion of non-allelic interaction . Examination of Figure 3 shows that the point onthe Wr/Vr regression corresponding to the variety Panter lies at some distance fromthe best straight line drawn through the remaining varieties . Furthermore, inspectionof the yield data in Table 7 reveals that although some of the crosses involving Pantershow negative heterosis, the cross of Panter with Hybrid 46 significantly outyields themean of its parents. This suggests the possibility that non-allelic interaction may occurin the cross of Panter with Hybrid 46. This hypothesis was investigated by com-puting the Wr/Vr regressions obtained when crosses involving Panter or Hybrid 46 aredisregarded . These have slopes of 1 .10 * 0.21 and 0.94 ± 0.13 respectively, both val-ues approximating very closely to the unit slope expected in the absence of non-allelicinteraction, and thus confirming the occurrence of such interaction in the cross ofPanter with Hybrid 46 . As this cross also significantly outyields its mid-parent it ispossible that selection within it may give rise to high yielding progeny . Figure 3b shows.the Wr/Vr relationships obtained after the elimination of the non-allelic interactionoccurring in the cross of Panter with Hybrid 46 . This graph shows that, although thereis no clear cut association of high yielding capacity with dominant or recessive geneticfactors, there is a tendency for the points corresponding to the higher yielding varietiesto lie near the origin of the graph, and conversely, for the points corresponding to thelower yielding varieties to lie at some distance from the origin . This suggests that highyielding capacity is in general inherited as a dominant character in this group of crosses .Attention may also be drawn to the suggestion of curvature shown by the distribution

(a) All arraysVr

Wr(b) Omitting Hybrid 46 array

Vr Wr

Bonus A 7.6 19.9 15 .0 26 .3Maitre Pierre B 14 .8 29 .4 32.8 52 .9Panter C 68 .9 52.5 48 .7 58 .6Professeur Marchal D 13 .8 16.4 22 .1 20.2Viking E 10.4 18 .4 13 .6 36 .4TBn 72/3 F 43.5 52 .6 56 .7 65 .2TB 209 G 21 .2 36 .7 24.0 42 .0

Vp = 76.1 Vp = 93 .0b = 0.66 ± 0 .15 b = 0.94 f 0.13


of points along the Wr/Vr graph in Figure 3b. This curvature is similar to that re-ported by HILL (1964) and suggests linkage between the factors determining yield .

Comparison of the Wr/Vr relations of the component trials, using the same pro-cedure as previously, gives the following analysis of variance :

The upper portion of this table shows that there is again a highly significant overallregression of Wr on Vr with no evidence of heterogeneity between the trials makingup the series of experiments. The lower part of the table shows that there are againhighly significant interactions of dominance expression and arrays with trial sites .When compared with the appropriate interactions, neither overall dominance nordifferences between arrays is significant.

Comparison of the general and specific combining abilities of the parents andparental combinations involved in crosses made in 1960 may be made from the datain the final block of Table 7 . Corresponding data for the dominance effects are givenin Table 8. Statistical analysis of these data gives the following figures :

345

Notation afterHAYMAN (1954)

D.F. M.S . V.R. P

a General combining ability 11 532 .7 8 .75 <0.001

b1Dominance :Overall Dominance 1 53 .9 0 .35 N.S .Dominance due to parents A,B,C- 6 176 .9 2 .98 0.05-0.01

b2Dominance due to parents P,Q,R- 4 65 .1 0.76 N.S .

b a Interaction of dominance effects 24 70.8 2 .51 0.01-0 .001

B(specific combining ability)

Generations and locations 4 1732.6 28 .5 <0.001ab G.c .a. X locations 44 60.8 2.16 <0.001b1B Overall dominance x locations 4 153 .4 5 .16 0.01-0.001

Dominance due to A,B,C- x loca-tions 24 59.4 2 .11 0.01-0.001

b2B Dominance due to P,Q,R- x loca-tions 16 85 .3 3 .03 <0.001

b 3B Interaction of dominance effects x lo-cations 96 28 .1

DF M.S. V.R . P

Mean regression 1 3 .0392 30 .0 <0.001Heterogeneity 4 0.0109 0 .11 N.S.Error 24 0.1013

Trials 4 4.3274 36.8 <0.001Dominance 1 0.7905 2.2 N.S .Trials x Dominance 4 0.3658 3 .1 0.05-0.01Arrays 6 1.2299 1 .9 N.S .Trials x Arrays 24 0.6511 5 .5 <0.001Error 29 0.1174

F. G. H. LUPTON

TABLE 8 . DOMINANCE IN CROSSES MADE IN 1960

(Mean difference in yield between crosses and mid parents, expressed as % Cappelle yield)

L.S.D. (differences between cross means) 4.9 (P = 0 .05)

From this analysis it may be seen that, as in the previous series of crosses, all thefirst order interactions are significant when compared with the second order interac-tion ; the significances of differences in main effect have therefore been tested by com-parison with the corresponding first order interactions . These comparisons show thatthere are significant differences between the varieties in general combining ability,and differences in dominance between the parents A,B,C-, though not between thetester varieties, P,Q,R-. There is also evidence of significant differences betweenparental combinations in specific combining ability, though elimination of the Hybrid46 and Panter arrays reduces the mean square due to specific combining ability to51 .3 and 43.2 respectively .

The mean data for yield and dominance expression are given in table 9, from whichit will be seen that the Professeur Marchal array significantly outyields the re-mainder, while the Panter array is the lowest yielding . The crosses involving Profes-seur Marchal are thus likely to be the most promising, while considerable promise isshown by the TB 209 array, which has a mean yield equivalent to that of CappelleDesprez and a high expression of dominance . These predictions agree well with thosemade after consideration of the Wr/Vr regressions . The possible value of selectionwithin the cross showing non-allelic interaction, Panter x Hybrid 46, has not beendemonstrated, however, though the significant differences in specific combining abili-ty which have been found invite a careful perusal of the data in Tables 7 and 8, from

TABLE 9. YIELD DATA AND EXPRESSION OF DOMINANCE IN CROSSES MADE IN 1960 (As % CAPPELLE YIELD)

346

Array mean yield Dominance

Bonus 95 .8 3 .0Maitre Pierre 97 .8 2.3Panter 86 .4 -3 .3Professeur Marchal 101 .7 0.8Viking 94.9 -3 .2TBn 72/3 97.2 1 .0TB 209 98.9 3 .5

L.S.D. (P = 0.05) 2.2

Bonus MaitrePierre

Panter

Prof.Marchal

Viking TBn 72/3 TB 209

(A) (B) (C) (D) (E) (F) (G)

Cappelle (P) -0 .1 3 .2 -4.5 0 .5 -1 .8 -0.6 1 .2Heine VII (Q) 5 .9 5 .3 -11 .3 5 .3 -0 .5 4 .3 2 .7Holdfast (R) 5 .2 0 .1 -3 .9 2 .7 -0 .7 -3 .6 4 .0Minister (S) 1 .5 0 .2 -2.1 -5 .6 -4 .6 1 .9 3 .3Hybrid 46 (T) 2 .5 2 .9 5.2 1 .2 -8 .3 3 .1 6 .3


which it will be seen that this cross significantly outyields and shows a significantlyhigher level of dominance than the remaining crosses in the Panter array .

Yield Distribution Trial, 1963The mean yields, obtained from the yield distribution trial grown in 1963 are given

in Figure 4 together with their standard deviations . Application of Bartletts test forhomogeneity indicates that there are highly significant differences in yield variancebetween the selections from different parental combinations x2 31 = 69.79, (P < 0 .001)though there is no evidence of differences in variance between plots of the parentalvarieties x 211 = 8.31, (P 0.5-0 .7) . The assessment of the relative merits of the parental

111

FIG . 4. Yield distribution of parental combinations (as % Cappelle yield)

347

Els xCappelle 86.0126.3 Ix Heine II 95-5t 22 .6x Minister 96.5±23.4xhl96rid 46 115 .0±23.2

Maitre Pierre x Cappelle 105.5313 .6xHeineML 113 .0±16 .5xMinister 116 .5* 17 .3xH4brid 46 118 .0±15 .8

Mans Widgeon xCappelle 115 .0120.9.Heine ml 104.0±19 .7xMinister 114 .5±18 .2x-i xid46 105.Ot13 .9

I}ko x Cappelle 1oq.0*25.3x Heine $L 111 .0119 .7x Minister 103.5±22 .6x HI,rtd 46 107.0±17 .8

Prof . Marshal x Cappelle 114 .5218.0xHeineM 116 .5±15.1xMinister 1200±25.7x11 rid46 123.0±26 .6

Vkin xCappelle 117 .0±19 .0x1geine MI 110.0±21 .6xMinister 116 .0*2L2'x hybrid 46 114 .0113 .9

TBn72/3 %Cappelle 104.0±16 .9xHeine.M 112 .0±18 .3xMti ster 118.5±22 .4,Rbrtd4 .6 124.5±17 .2

TB 209 .Cappelle 104 03184xHeine A 96.5±16 .4xMinister 111 .0±19 .1xHybi1d 46 118.0± 19 .1

F. G . H. LUPTON

combinations involved in this experiment involves the simultaneous consideration ofthe mean yield and variance of each parental combination . This is most convenientlyeffected by means of a graphical representation as given in Figure 4 . The distancesbetween the inner marks on the horizontal lines on this figure indicate the standarddeviations for yield of each parental combination, and the distance between the outermarks the 5 % Ficudial limits. The arrow in the middle of each horizontal line indicatesthe mean yield of the parental combination concerned . The crosses of greatest promiseare therefore those corresponding to the' horizontal lines which extend furthest to theright .

It will be seen from Figure 4 that the parental combinations showing the most pro-mise are Els x Hybrid 46, Professeur Marchal x Minister and Professeur Marchalx Hybrid 46. Other crosses showing promise are Maris Widgeon x Cappelle, Pekox Cappelle, Viking X Cappelle, Viking x Minister, TBn 72/3 x Minister, TBn 72/3x Hybrid 46 and TB 209 x Hybrid 46. These assessments are, of course, completelyindependent of those made from considerations of general and specific combiningabilities, or of array variances and co-variances. It is therefore interesting and en-couraging to note the close agreement between the crosses predicted by the methodsconsidered in this paper. It is also interesting to note the good performance of the selec-tions from the crosses involving the two spring wheat varieties Els and Peko, thoughthe yields of these two varieties, were much depressed due to the severe conditionsduring the winter of 1962/63 .

DISCUSSIONTo be effective, a system of cross prediction must be capable of identifying parental

combinations which are likely to give rise to progeny showing transgressive segrega-tion for the character under consideration . Proof of the efficiency of such a system can,however, only be obtained from a long term breeding programme involving many yearsselection within those crosses which show the greatest promise. It is therefore impos-sible at this early stage to give any objective assessment of the usefulness of the sys-tems of cross prediction considered in this paper . Some indication of the value of thesystems may however be obtained by comparing the results derived from the contrast-ing systems used, and also by observing the extent to which crosses of known valuehave been identified.

Three methods of cross prediction have been employed in the experiments described .The first involved an assessment of the dominance relationships of the factors deter-mining yielding capacity, as revealed by calculation of array variances and co-varian-ces. On the whole, this approach has not yielded much useful information, largely onaccount of the variability in dominance relationships between seasons and trial sites .This variability is surprising as the W,/V, regression coefficients obtained from thecomponent trials of each series of experiments approached in most cases to unity . Thesituation is, however, very similar to that reported by THOMPSON and WHITEHOUSE(1962) in relation to wheat quality and suggests a marked effect of environment on thedominance relationships of the genes determining yield, although they remain additiveunder the varying conditions of trial to which they have been exposed . A similar in-stance in relation to yielding capacity was observed by the author (LUPTON 1961), whoreported that yield was inherited as a dominant character in one trial of unselected F 2

348


populations of wheat, and as a recessive in an adjacent trial of the same material . Inthis case it was possible to explain the apparent anomaly. The first trial was sown ata high seed rate and the second at a wider spacing ; supplementary analysis showedthat grain weight and number of grains per ear were inherited as dominant characters,while tillering capacity, of great importance in a widely spaced trial, was inherited asa recessive genetic character. Similar interactions of dominant and recessive charactersmay explain the observations reported in the present paper, as a result of which nouseful predictions could be made from the W r/Vr graphs obtained from the trials ofcrosses made in 1960. The evidence of non-allelic interaction in this material, and theidentification of the parental combination in which it occurred is one of the clearestexamples of such identification on record, and it will be of great interest if usefulselections can be obtained from the cross concerned . When the Wr/Vr regressionremaining after the elimination of this cross is considered, some information concern-ing dominance relationships may be deduced, though this should be considered withsome reserve, as there is again evidence of interaction with environment . It thusappears that, apart from its use in the identification of crosses showing non-allelicinteraction, there is little to be gained from consideration of the variance/co-variancerelationships of arrays of crosses when selecting for parental combinations likely togive rise to high yielding progeny .

The second method of cross prediction involved analysis of the general and specificcombining abilities of the parents and parental combinations and of the degree ofdominance shown by arrays of crosses involving each of the parents . In the absence ofsignificant differences in expression of dominance between arrays of crosses, estimatesof general combining ability of parental varieties give a direct measure of the yieldingcapacities of the patents concerned. In each of the series of crosses reported, however,significant differences in dominance were observed, so that the differences in generalcombining ability give useful information which could not have been obtained fromyield trials of the parents without consideration of the hybrid populations . As with theWr/Vr analyses, highly significant differences were found between generations and trialsites, and the interactions of trial sites with combining ability and dominance werein all cases significant . When compared with these first order interactions, significantvarietal differences in general combining ability and in dominance were, however, found .Useful predictions may therefore be based on the total figures obtained from each setof trials. In making these predictions, it should be remembered that the data in Tables1, 4 and 7 refer to the mean yields obtained from each parental combination and not tothe highest yielding selections which may be obtained from them .

A conspicuous feature of these data is the almost complete absence of significantdifferences in specific combining ability . This indicates a general consistency of per-formance of the parental varieties when hybridised with the five tester varieties, andimplies an overall consistency of performance of these varieties as parents provided thatthe tester varieties are adequately representative of the population of wheat varietiesfrom which they have been selected. This matter is clearly open to criticism though thetester varieties have been chosen with considerable care to represent the genotypes ofwheat varieties cultivated in Britain, bearing in mind the need to restrict their numbersso as to keep as low as possible the total number of crosses to be handled .

349

F. G. H. LUPTON

A further feature of interest in the combining ability analysis is the wide variation indominance. As has been noted, it is upon these differences that the value of the analy-sis depends, and particular importance is attached to the high expression of dominanceseen in the arrays of the spring wheat varieties Els and Peko . The cross of Peko withCappelle Desprez, also noted as particularly promising in the yield distribution trial,has been extensively handled at this Institute for a number of years and has given riseto a number of promising selections, in spite of marked defects in the phenotype ofPeko. In consequence of the results of the trials described in this paper, a programme isalso being developed based on the variety Els. It must be realised however that thehigh promise shown by unselected bulk trials of crosses between spring and winterwheats may be misleading, especially if the plant establishment in the bulks is reducedduring severe weather . The surviving hardy plants may then grow with restricted com-petition from their neighbours so that the bulk population shows little depression inyield due to the severe weather compared with that suffered by the spring wheat parentwith which it is compared in estimating dominance .

The transgressive segregation for low yielding capacity shown by certain arrays ofcrosses is remarkable . In the case of H 1444 array this probably arises since H 1444 isderived from an interspecific cross involving rye (Secale cereale) and is known to becytologically unstable . No explanation of the occurrence of this phenomenon in thecase of the Panter and Viking crosses is available, however, though it was noted thatthe Fl's and F2's of the crosses of Panter with Cappelle Desprez, Heine VII andHoldfast showed symptoms of necrotic leaf yellowing in early summer. The absence ofsuch necrosis in the crosses with Hybrid 46 and Minister indicates that this is a case ofhybrid necrosis, as reported by HERMSEN (1963). It may also be associated with thenon-allelic interaction shown in the cross of Panter with Hybrid 46 .

The third method of crop prediction involved estimates of mean yield and yieldvariance of a number of the more promising parental combinations . Owing to therequirements in space and labour involved in handling a trial of this type, it wasnecessary to reduce very considerably the number of parental combinations grown inthis part of the programme. Furthermore, it was not possible to repeat the trial over anumber of sites and seasons, nor was it possible to handle more than 36 random selec-tions from each parental combination . Despite these serious limitations, it was possi-ble to demonstrate highly significant differences in yield variance between the crossesstudied, and when these were considered in conjunction with the mean yields obtainedfrom the crosses concerned, to obtain useful indications of the parental combinationsmost suitable for further study . As has been mentioned, these predictions are based onparameters which are distinct from those determined in the first two methods of cropprediction . It may however be claimed that the two sets of prediction are to some extentassociated, since varieties with widely separated points on the W r/Vr regression differ inrespect of many genes so that crosses between them are likely to have larger yieldvariances than crosses between varieties with adjacent points on the W r/Vr regression .It is nevertheless interesting to note the close agreement between cross-predictionsmade on the basis of yield variance estimation and those based on the other systemsdiscussed.

No discussion of the value of predictions based on the analysis of diallel crosseswould be complete without reference to the practical aspects of the work, with parti-

350


cular reference to the considerable labour and expense involved in the conduct of aseries of experiments such as those described in this paper . On the one hand, it may beargued that if a complex series of trials is necessary for the identification of promisingparental combinations, then no expense should be spared in their conduct . At the otherextreme it may be claimed that trials of this sort are an unnecessary extravagance, andthat the plant breeder should be able to select his crosses by detailed consideration ofthe parental material available to him without recourse to experimental hybridisations .In practice, a compromise has to be reached between these extreme views, and theexperiments described here represent an attempt to arrive at such a compromise . Inthe first place, in spite of the loss in sensitivity involved, no attempt has been made toestimate yields in the Fl generation, and trials have been confined to unselected bulksin F2 and F3 . Secondly, complete diallel sets of crosses have been discarded in favour ofincomplete sets, so that the range of parental material studied may be extended . Evenso, a trial of a 7 x 5 variety incomplete diallel, including the parental varieties, com-prises 47 treatments, and requires a 7 x 7 lattice square for convenient handling . Anyincrease in the size of the diallel set increases the number of treatments to a level whichcannot conveniently be handled over a range of localities . These considerations effecti-vely restrict the size of the set of crosses which may be handled as unselected bulks . Ashas already been mentioned, further restrictions have to be placed on the range ofcrosses which may be considered when estimates of yield variance are undertaken .Nevertheless the yield variance trial described in this paper involved the handling andharvesting of over two thousand plots . Extension or replication of a trial of this sizemust be considered with some reserve .

The author would like to express his thanks to Dr . G. D . H. BELL, Director of thePlant Breeding Institute, for his continued interest in this work, to Dr . J . L. JINKS andDr. J . T . WALKER for advice on the statistical analysis and helpful discussions and toMESSRS. R. H. OLIVER and J. D. B . CHAMBERS for their technical assistance .

REFERENCES

1 . ALLARD, R. W., 1956 . The analysis of genetic-environmental interactions by means of diallelcrosses. Genetics 41 : 305-318 .

2. HAYMAN, B. I ., 1954(a). The theory and analysis of diallel crosses. Genetics 39 : 789-809.3. HAYMAN, B. I ., 1954(b) . The analysis of variance of diallel tables . Biometrics 10 : 235-244.4. HERMSEN, J . G. TH., 1963 . The genetic basis of hybrid necrosis in- wheat . Genetica 33 : 245-287.5 . HmL, J., 1964 . Effects of correlated gene distributions in the analysis of diallel crosses . Heredity

19 : 27-46.6. JINKS, J. L., 1954. The analysis of continuous variation in a diallel cross of Nicotiana rustica

varieties. Genetics 39 : 767-788 .7. JINKS, J. L., 1956. The F2 and back cross generations from a set of diallel crosses . Heredity 10 :

1-30.8. LuPTON, F. G. H ., 1961 . Studies in the breeding of self pollinating cereals 3 . Further studies in

cross prediction . Euphytica 10 : 209-224.9. MATHER, K., 1949. Biometrical Genetics. Methuen, London.10. THOMPSON, J. B. and WHIrEHOUSE, R . N. H ., 1962. Studies in the breeding of self pollinating

cereals 4 . Environment and the inheritance of quality in spring wheats . Euphytica 11 : 181-196.11 . WHITEHOUSE, R. N. H., THOMPSON, J. B. and RIBEIRO, M. A. M. do V., 1958 . Studies on the

breeding of self pollinating cereals 2 . The use of a diallel cross analysis in yield prediction .Euphytica 7 : 147-169 .

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APPENDIX

Pedigrees and countries of origin of varieties testedTester Varieties

Pedigree Country of Origin

Cappelle Desprez Hybride du Joncquois x Vilmorin 27 FranceHeine VII Hybride a courte paille x Svalof Kron GermanyHoldfast Yeoman X White Fife BritainHybrid 46 Benoist 40 x other hybrids BritainMinister Benoist 40 x Professeur Delos Belgium

Varieties used in crosses made in 1958Flamingo (Tassilo x Kron) x Heine IV GermanyHestbignon (Desprez 80 x Professeur Delos) Belgium

x (Bastard II x Professeur Delos)Leda Jubilegem x Zanda BelgiumMado Juliana x Hybride du Joncquois HollandRelief Hussar x Utah 26 U.S.A .Stella (Desprez 80 x Professeur Delos) Belgium

x (Bastard II x Professeur Delos)Svenno Selection from Karn I SwedenThor W 11376 x W 11556 SwedenWasatch Ridit x Relief Canada

Varieties used in crosses made in 1959Els

Cross involving Erli, Lichti and T. carthlicum GermanyFelix

(Tassilo X Carsten) x (Carsten x Marquillo) GermanyHeine 110

Chinese 166 x unnamed hybrids GermanyMaris Widgeon

Holdfast x Cappelle Desprez BritainPeko

Peragis x Heine Kolben GermanyH 1444

Stamm 44 x Secale cereale GermanyHalle 3435

Unknown GermanyDolis Puri 35/4

Unknown U.S.S.R .Pseudo-meridionale 122 Unknown U.S .S.R .W 254/39

Jubilegem x Holdfast Britain

Varieties used in crosses made in 1960Bonus

Alba x Carstens Dikkopf V HollandMaitre Pierre

Druchamp x Yga Blondeau FrancePanter

Panser III x Alter BelgiumProfesseur Marshal

(Hybride du Joncquois x Professeur Delos) Belgiumx (Bastard II x Professeur Delos)

Viking

Single plant selection x Hybride du Joncquois DenmarkTBn 72/3

Franc Nord x (Holdfast x Squareheads Master) BritainTB 209

(CI 12633 x Holdfast) x (Minister)s Britain

studies in the breeding of self pollinating cereals

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