# Selection indices

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Selection indices

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“The key is man’s power of accumulative selection; nature gives successive variations; man adds them up in certain directions useful to him.”----Darwin, p.35, Sixth edition of The Origin Of Species . 1920

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INTRODUCTION DEFININTIONS AND HISTORICAL BACKGROUND TYPES OF SELECTION INDICES FEATURES OF DISCRIMINANT FUNCTION ANALYSIS COMPUTATION OF SELECTION INDICES STASTICAL AND GENETICAL ASSUMPTIONS BRIEF REVIEW OF LITEATURE MERITS AND DEMERITS CONCLUSION FUTURE THRUST

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What is Selection index? It can be defined as a linear combinations of plant characters associated with yield . 1 What is discriminate function ? It is a statistical approach being used in construction of Selection index and discriminate desirable genotypes from undesirable ones based on various characters associated with yield.

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Smith(1936) was first to propose selection index based on discriminate function of Fisher (1936). Later on Hazel and Lush in 1943 also developed simultaneous selection model based on path coefficient analysis approach. 2

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Discriminate Function Fisher was first in 1936 to give this function with a purpose to discriminate individuals which belong to two different populations showing some degree of overlapping and mathematically it can be defined as Z= b 1 x 1 +b 2 x 2 +b 3 x 3 ….+b n x n Where X 1 ,X 2 ,X 3 …X n are measured variables and b 1 ,b 2 ,b 3 ,…b n are weighing coefficients b i values are estimated such that they are based on Z values. The ratio of variance between populations would be maximized the same maximized ratio leads to a set of simultaneous equations which after solution provide the desired values of b i . After that Z value is computed and its significance is tested . (Singh and Chaudhary 1973). 3

### Types of selection indices:

Types of selection indices General selection index Classical selection index Restricted selection index 4

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Hanson and Johnson (1957) were first to propose general selection index. . The construction of general selection index is based on pooled information of different populations from which b i values are estimated. Using these b i values the genotypic and phenotypic variances /co-variances are corrected then these corrected variances/co-variances are used to generate new b i values. These b i values can be applied to any population. General selection index: 5

### Classical selection index:

Classical selection index The application of discriminate function as a basis for making selection on several characters simultaneously is aimed at discriminating the desired genotypes from undesired ones on the basis of their phenotypic performance . According to Smith (1936) Selection indices involved two functions (1) The genetic worth of an individual ‘ H ’ and (2) The Phenotypic performance of various characters of plant ‘ I ’ . The coefficient of the function I are estimated such that the correlation between H and I i.e. r (H,I) is maximized. This leads to a set of simultaneous equations which upon solving give desired estimates of b i values. These indices are specific to those populations from which they have been derived. 6

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Restricted selection indices:- Certain situations may arise where in a breeder may like to effect change in means of ‘ r ’ out of ‘ p ’ characters while keeping the means of (p - r) characters unchanged. This is the case of restricted selection indices and Kempthorne and Nordskog (1959) gave solution to this problem by using lag range multiplier .In this method the estimates of b i values are obtained which maximize correlation between H and I and at the same time do not allow any change in means of (p - r) characters. It can be worked out by following formula b-[ Inn-P -1 GC(c'GP -1 GC) -1 c‘G]G.a - I where Inn is the n X n unit matrix p -1 is the inverse of phenotypic variance and covariance matrix G is the genotypic variance and covariance matrix C is coefficient vector matrix C' is transposed coefficient vector 7

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MAIN FEATURES OF DISCRIMINATE FUNCTION ANALYSIS:- It measures the efficiency of various characters combinations in selection. Selection index leads to simultaneous manipulations of several characters for genetic improvement of economic yield. (2) This technique provides information on yield components and thus helps in indirect selection for genetic improvement of yield. (3) Analysis is based on linearity and additivity. (4) Analysis involves variance and covariance. (5) Though based on path analysis it differs from it in several aspects. PATHCOEFFICIENT ANALYSIS DISCRIMINATE FUNCTION (1) It measures the cause of association between two variables. It measures the efficiency of various traits combinations in selection. (2) Analysis is based on all possible simple correlations. Analysis involves variances and co-variances. (3) Direct, indirect and residual effects are calculated for path analysis. Weight coefficients, expected genetic advance and relative efficiency are estimated. DIFFERENCES 8

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SIMILARITIES:- ( 1) Both help in determining the yield components. (2) Both based on statistical assumptions of linearity and additivity. COMPUTATION OF SELECTION INDEX:- Selection index can be constructed using one of the three models described above. Construction of selection index is based on the estimates of phenotypic and genotypic variances and co-variances of characters involved in selection index. The selection indices can be worked out from replicated data only. The construction of selection index is based on following statistical and genetical assumptions. STATISCAL ASSUMPTIONS:- (1) Random selection of parents for mating. (2) Absence of G X E interaction. (3) Linear or additive nature of component characters to be included in the index. GENETICAL ASSUMPTIONS:- (1) Diploid segregations. (2) Absence of linkage. (3) Lack of maternal effects. (4) Absence of epistatis. (5) Multiple allelism not present. All genotypes have equal survival chance . 9

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WEIGHING COEFFICIENTS: The coefficients refer to the relative importance of various characters in the index. The general form of selection index is given below I= b 1 x 1 +b 2 x 2 +b 3 x 3 +.................b n x n (where x 1 , x 2 , x 3 ......x n represent the phenotypic values of the character number 1,2,3, and n respectively and b 1 , b 2 , b 3 ....b n corresponding weights. (Singh and Chaudhary,1973) The values are calculated from series of simultaneous equations involving the appropriate phenotypic and genotypic variances and covariance. The b values are worked out separately for various selection indices involving single, double, triple and multiple traits. The simultaneous equations are solved by elimination process and b values are obtained. If there were three characters and yield the following simultaneous equations could be set with the help of appropriate variances and covariance of these traits. b 1 w 11 +b 2 w 12 +b 3 w 13 =g 1 y b 1 w 12 +b 2 w 22 +b 3 w 23 =g 2 y b 1 w 13 +b 2 w 23 +b 3 w 33 =g 3 y (where b 1 ,b 2 and b 3 are weighing coefficients. w 11 , w 22 and w 33 are phenotypic variances of character member 1,2 and 3 respectively. w 12 ,w 13 and w 23 are phenotypic covariance of character number 1-2,1-3 and 2-3 respectively. g 1 y, g 2 y and g 3 y are genotypic covariance of character number 1,2, and 3 with dependent character yield . 10

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The genetic advance for discriminant function GS 1 , is estimated separately for various selection indices involving single, double, triple and multiple traits with the help of formula Δ G=Z/Q (b 1 g 1 y + b 2 g 2 y + ….b n g n y) where Z/Q is selection intensity at 5% i.e. K(2.06); b 1 ,b 2 and b n are coefficient values for character 1,2,3 and n respectively and g 1 y,g 2 y and g n y n are the corresponding genotypic co- variances of these traits with dependent character yield. The genetic advance GS 2 by straight or direct method is calculated for the dependent character (yield only )with the help of following formula Δ G=(Z/P) ∑ ∑ a i bi G ij / √ ∑ ∑ bi bj pij where z / p is selection intensity (i), G ij symbolizes the genotypic variances and co-variances and P ij represent the phenotypic variances and co- variances. The genotypic advance of I th character( Δ ) can be calculated as per Brim et al. i= ∑b i G ij / √∑(b i G i) EXPECTED GENETIC ADVANCE 11

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The relative efficiency of selection is worked out separately for various selection indices involving single, double, triple and multiple traits with the help of formula RELATIVE EFFICIENCY= GS 1 /GS i *100 Thus apparently it is expressed as the percentage ratio of genetic advance for discriminant function (GS 1 ) to genetic advance for direct selection (GS 2 ). It measures the effectiveness of various selection indices. The relative efficiency of direct selection for yield is considered as 100%. Any selection index showing superiority over direct selection is considered important and the characters involving in such index are considered as major components of yield. Such combination of characters has to be given due weight age in selection of elite genotypes from diverse breeding populations. RELATIVE EFFICIENCY:- 12

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Serial No. of plants Ranking of individual plants with the help of 1 A (Sp) 1 (Gen) 1 E (P) Progeny performance of the individual plants (R1) (R2) (R3) (R4) 1 _ _ _ _ 2 _ _ _ _ 1 x 1 y 1 z 1 t 1 500 _ _ _ _ TABLE 1: COMPARISON OF SELECTION INDICES Singh (1972) Hissar x 1, y 1, z 1 and t 1 are different ranks assigned to the individuals on the basis of 1 A (Sp), 1 (Gen) ,1 E (P) and progeny performances .R 1 ,R 2 and R 3 are ranking done by 1 A (Sp), 1 (Gen) , and 1 E (P) respectively. 13

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Index Relative*r (s) values 1(Gen) 100 1a(Sp) 98 1e(p) 82 *r (s) stands for Spearman’s rank correlation TABLE 2: FIRST COMPARISON Singh (1972) Hissar 14

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TABLE 3: SECOND COMPARISON Comparison Units Mean Original Population 100 Group 1 (gen) 110.8 Group 1 (p) (e) 79.8 Singh (1972) Hissar 15

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TABLE 4: REGRESSION COEFFECTS AND STANDARD ERRORS Characters 77-78 78-79 b SE t b SE t Stover Yield X 1 0.276 0.056 4.93** 0.066 0.098 0.680 N- Uptake X 2 0.125 0.069 1.81 0.0005 0.076 0.006 P-Uptake X 3 0.053 0.057 0.92 0.272 0.113 2.39 Cob Length X 4 0.703 0.726 0.98 0.514 0.985 0.52 Cob Girth X 5 0.516 1.594 0.2 1.014 0.799 1.27 Grain Yield/cob X 6 0.142 0.088 1.61 0.030 0.105 0.29 No. of Grains/cob X 7 0.584 0.033 1.76 0.002 0.020 0.14 1000-grain wt. X 8 0.248 0.066 3.74** 0.241 0.216 1.11 Protein % in Grain X 9 1.753 1.073 1.63 1.857 2.287 0.81 Moisture% in Grain at harvest X 10 0.505 0.329 1.53 0.437 0.399 1.09 Plant height At Maturity X 11 0.102 0.047 2.14 0.072 0.086 0.83 Patel et al. ( 1987 ) I.A.R.I., New Delhi 16

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TABLE 4.1: SELECTION INDICES. Year Multiple regression equation Multiple correlation coefficient Variation explained (%) 1977-78 -39.6518+0.1867x 1 +1.7136x 5 +0.1550x 8 0.9910** 98.20 1977-78 -55.2340+0.1330x 1 +0.0180x 6 +0.3651x 8 0.9733** 94.74 1978-79 -44.5649+0.1000x 1 +0.0515x 6 +0.2367x 8 +0.6728x 10 0.9819** 96.41 1978-79 -42.1075+0.0701x 1 +0.0707x 6 +0.2073x 8 +0.6583x 10 +0.0115x 7 0.9826** 96.55 X 1 = Stover Yield X 5 = Cob Girth X 6 = Grain Yield/cob X 7 = No. of Grains/cob X 8 = 1000-grain wt. X 10 = Moisture% in Grain at harvest Patel et al. (1987) I.A.R.I., New Delhi 17

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TABLE 5: INTERGENERATION CORRELATION COEFFICIENTS (r) AND NARROW SENSE HERITABILITY (h 2 ) BETWEEN F 2 -F 3 GENERATION FOR YIELD COMPONENTS IN TWO CROSSES OF FINGER MILLET. Characters HR-911 X Indaf-9 Indaf-8 X HR-41-2 r h 2 r h 2 Plant height 0.71** 80.6 0.32 31.4 Productive tillers per plant 0.28 49.8 0.50* 10.1 Length of ear 0.92** 60.2 0.78** 55.3 Number of fingers per ear 0.46* 47.2 0.45* 27.3 Ear weight per plant 0.08 2.0 0.07 1.7 Straw weight per plant 0.10 3.2 0.26 7.3 Harvest index 0.21 10.9 0.14 3.5 Grain yield per plant 0.12 3.4 0.09 2.0 Basavaraja and Sheriff (1992) Bangalore 18

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TABLE 5.1: DISCRIMINANT FUNCTIONS, THEIR GENETIC ADVANCE (GA) AND RELATIVE EFFICIENCY (RE)OVER STRAIGHT SELECTION FOR GRAIN IN TWO CROSSES OF FINGER MILLTET. Content of index HR-911 X Indaf-9 Indaf-8 X HR-41-2 GA RE GA RE X 6 = Grain Yield Per Plant 2.52 100.0 1.18 100.00 X 1 = Plant Height 2.26 89.7 0.47 39.4 X 2 = Productive Tillers Per Plant 1.69 67.1 0.59 50.3 X 3 = Ear Weight Per Plant 1.02 40.4 0.50 42.2 X 4 = Straw weight Per Plant 0.08 3.2 0.44 37.0 X 5 = Harvest Index 0.82 32.5 0.21 17.6 X 1 + X 2 3.11 123.8 0.75 63.7 X 1 + X 3 2.54 100.8 0.65 55.5 X 1 + X 4 2.47 97.9 0.63 53.7 X 1 + X 5 2.26 89.7 0.55 46.8 Basavaraja and Sheriff (1992) Bangalore Continued 19

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TABLE 5.1: DISCRIMINANT FUNCTIONS, THEIR GENETIC ADVANCE (GA) AND RELATIVE EFFICIENCY (RE) OVER STRAIGHT SELECTION FOR GRAIN IN TWO CROSSES OF FINGER MILLTET. Content of index HR-911 XIndaf-9 Indaf-8X HR-41-2 GA RE GA RE X 2 + X 4 2.09 82.9 1.06 90.1 X 1 + X 2 + X 3 3.13 124.1 0.76 64.6 X 1 + X 2 + X 4 3.12 123.4 1.15 97.6 X 1 + X 2 + X 5 3.11 123.4 0.83 70.7 X 1 + X 3 + X 4 2.57 101.7 1.08 91.7 X 1 + X 3 + X 5 2.56 101.2 0.78 66.2 X 2 + X 3 + X 4 2.11 83.7 1.20 101.6 X 2 + X 1 + X 5 2.17 86.0 1.44 122.1 X 1 = Plant Height X 2 = Productive Tillers Per Plant X 3 = Ear Weight Per Plant X 4 = Straw weight Per Plant X 5 = Harvest Index Basavaraja and Sheriff (1992) Bangalore Continued 20

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Content of index HR-911 XIndaf-9 Indaf-8X HR-41-2 GA RE GA RE X 2 + X 3 + X 4 2.11 83.7 1.20 101.6 X 2 + X 3 + X 5 2.04 81.0 0.70 59.1 X 2 + X 1 + X 5 2.17 86.0 1.44 122.1 X 3 + X 4 + X 5 1.33 52.6 1.84 155.7 X 1 + X 2 + X 3 + X 4 3.13 124.1 1.26 106.6 X 1 + X 2 + X 3 + X 5 3.15 124.7 0.86 73.1 X 1 + X 2 + X 4 + X 5 3.12 123.5 1.59 133.6 X 1 + X 3 + X 4 + X 5 2.57 101.7 1.94 164.4 X 1 + X 2 + X 3 + X 4 + X 5 3.15 124.8 2.19 185.7 Basavaraja and Sheriff (1992) Bangalore TABLE 5.1: DISCRIMINANT FUNCTIONS, THEIR GENETIC ADVANCE (GA) AND RELATIVE EFFICIENCY (RE) OVER STRAIGHT SELECTION FOR GRAIN IN TWO CROSSES OF FINGER MILLTET. X1= Plant Height X2= Productive Tillers Per Plant X3= Ear Weight Per Plant X4= Straw weight Per Plant X5= Harvest Index 21

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TABLE 6: SELECTION INDEX, DISCRIMINANT FUNCTION, EXPECTED GENETIC ADVANCE AND REALTIVE EFFICIENCY IN ROSELLE ( Hibiscus subdariffa L. ) GENOTYPES Selection index Discriminant function Genetic advance Relative efficiency Fibre yield per plant F:W ratio Plant height 0.0400 1.26 115.6 140.4 Basal diameter 0.3288 0.76 5937 84.5 Fibre yield per plant 0.0226 1.09 100.0 121.4 Fibre-wood ratio 1.3475 0.90 82.4 100.0 Pl.ht.-bas. Dia. 0.0400+0.03288 1.47 134.9 163.7 Pl.ht.-fib. Yld. 0.0400+0.0226 1.64 152.6 185.3 Pl.ht.-F:Wratio 0.0400+1.3475 1.54 141.3 171.5 Pl. ht.--- plant height, bas. Dia.—basal diameter, fib. Yld.---- fibre yield per plant And F:W— fibre to wood ratio. C. Aruna et al.( 1989) Bapatla Continued 22

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Selection index Discriminant function Gen. adv. Relative efficiency Fibre yld. per pl. F:W ratio Bas. dia.-fib. Yld 0.328+0.022 1.33 121.7 147.8 Bas. dia.-F:W ratio 0.328+1.347 1.17 107.4 130.4 Fib.yld- F:W ratio 0.022+1.347 1.40 128.0 155.4 Pl.ht.-bas.dia.- fib. Yld. 0.040+0.328+0.022 1.83 167.8 203.7 Pl.ht.- Bas.dia.-F:W ratio 0.040+0.328+1.347 1.72 157.7 191.2 Pl.ht.- fib.yld-F:W ratio 0.04+0.022+1.347 1.89 172.4 209.3 Bas.dia.-fib.yld.-F:W ratio 0.328+0.022+1.347 1.56 145.7 176.9 Pl. ht.-bas. dia.- fib .yld.- F:W ratio 0.040+0.328+0.022+1.347 2.03 186.0 225.8 Pl. ht.--- plant height, bas. Dia.—basal diameter, fib. Yld.---- fibre yield per plant And F:W— fibre to wood ratio. C. Aruna et al. ( 1989) Bapatla TABLE 6: SELECTION INDEX, DISCRIMINANT FUNCTION, EXPECTED GENETIC ADVANCE AND REALTIVE EFFICIENCY IN ROSELLE GENOTYPES 23

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TABLE 7: GENOTYPIC CORRELATION COEFFICIENTS AMONG YIELD COMPONENTS, GINNING CHARACTERS AND FIBRE RAITS IN BIPAENTAL INTERMATED PROGENIES (BIPs) OF UPLAND COTTON ( Gossypium hirsutum L.) Char-acters Pl. ht. Boll No. Boll weight No. of Loculi/ boll No. of Seeds per locule Seed index Ginning outturn Lint index Fibre len. Fibre fine-ness Fibre mat. coeff. Yield per plant -0.19 0.092** 0.60** -0.45** 0.40** 0.17 0.40** 0.38* -0.45** 0.39* 0.31* Plant height -0.18 -0.01 0.07 -0.20* -0.03 -0.31* -0.17 0.31* -0.44** -0.40** Boll No. -0.08 -0.40** 0.16 -0.14 0.36* -0.01 -0.40** 0.25* 0.21* Boll weight 0.54** 0.98** 0.86** 0.48** 0.99** 0.46** -0.19 -0.07 No. of Loculi/ boll -0.25* -0.29* 0.19 0.21* 0.01 0.07 -0.03 No. of seeds per locule 0.39* 0.50** 0.68** -0.46** -0.43** 0.42** Tyagi.(1994) Hisar Continued 24

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Chara- cters Pl. ht. Boll No. Boll Wt. No. of Loculi/ boll No. of Seeds per locule Seed index Ginn-ing Out-turn Lint index Fibre length Fibre fine- ness Fibre mat. coeff. Seed index -0.33* 0.88** 0.37* 0.07 0.10 Ginning Outturn 0.76** -0.57** 0.47** 0.50** Lint Index 0.10 0.30* 0.32* Fibre length -0.41** -0.46** Fibre Fine-ness 0.92** Tyagi.(1994) Hisar TABLE 7: GENOTYPIC CORRELATION COEFFICIENTS AMONG YIELD COMPONENTS, GINNING CHARACTERS AND FIBRE TRAITS IN BIPAENTAL INTERMATED PROGENIES (BIPs) OF UPLAND COTTON ( Gossypium hirsutum L.) 25

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TABLE 8: MULTIPLE CORRELATION CEFFICIENTS AND SELECTION INDICES IN BIPARENTAL INTERMATED PROGENIES(BIPs) OF UPLANT COTTON( Gossypium hirsutum L.) Multiple regression equations (selection indices) R 2 R (Mul. corre. coeff.) % Contri. Y=-143.33+0.05X 1 +2.01X 2 +0.05X 3 +4.85X 4 +4.79X 5 +3.75X 6 +1.72X 7 –1.88X 8 + 0.34X 9 +0.01X 10 +10.85X 11 0.748 0.865** 74.84 Y= -123.94 +2.03X 2 +0.06X 3 +4.89X 5 + 3.62X 6 +1.66X 7 +1.56X 8 +0.49X 9 - 0.01X 10 +16.84X 11 0.740 0.861** 74.09 Y= -127.56+0.05X 1 +2.01X 2 +0.05X 3 +4.85X 4 +4.73X 5 +3.99X 6 +1.67X 7 –1.92X 8 0.745 0.863** 74.53 Y= -99.32 +2.03X 2 +0.06X 3 +4.18X 5 + 3.90X 6 +1.57X 7 +1.57X 8 0.738 0.859** 73.81 Y= -87.51 +2.11X 2 +0.08X 3 + 4.05X 6 +2.00X 7 –0.83X 8 0.712 0.844** 71.25 Y= -56.46 +0.04X 1 +2.02X 2 +0.06X 3 +3.00X 4 +5.65X 5 0.719 0.848** 71.93 Y=Yield, X 1 =Height, X2=No. of bolls, X3=Boll weight, X4=No. of loculi per boll, X5= No. of seeds per locule,X6= Seed index, X7=Ginning outturn, X8=Lint index, X9=Fibre length, X10=Fibre fineness, X11= Fibre maturity coefficient *,** Significant at 0.05 and 0.01 probability levels respectively. Tyagi.(1994) Hisar 26

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TABLE 8: MULTIPLE CORRELATION CEFFICIENTS AND SELECTION INDICES IN BIPARENTAL INTERMATED PROGENIES (BIPs) OF UPLANT COTTON ( Gossypium hirsutum L.) Multiple regression equations (selection indices) R 2 R (Multiple Correlation Coefficient) % Contribution Y= -39.05 + 0.29X 9 + 0.07X 10 +6.69X 11 0.540 0.735** 54.06 Y= -50.31 + 0.14X 1 +2.96X 4 +1.01X 5 0.159 0.399** 15.92 Y= -119.05 +4.54X 6 +4.32X 7 +2.43X 8 0.087 0.296* 8.75 Y= -3.62 +2.15X 2 +0.11X 3 0.675 0.822** 67.52 Y= 13.99 + 0.16X 1 +2.49X 4 0.034 0.186 3.43 Y=Yield, X1=Height, X2=No. of bolls, X3=Boll weight, X4=No. of loculi per boll, X5= No. of seeds per locule,X6= Seed index, X7=Ginning outturn, X8=Lint index, X9=Fibre length, X10=Fibre fineness, X11= Fibre maturity coefficient *,** Significant at 0.05 and 0.01 probability levels respectively. Tyagi.(1994) Hisar Continued 27

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TABLE 9: ESTIMATES OF COHERITABILTIY OF DIFFERENT PAIRS OF CHARACTERS IN LINSEED. Characters Days to matu. Till. per plant Pl. ht. Cap. per pl. Seeds per cap. Cap. length Cap. brea. 1000 seed wt. Seed yld./Pl. Days to flowering 0.288** 0.056 0.223 0.457 0.341** 0.354** 0.328** 0.496** 0.364** Days to maturity 0.062 0.201 0.390* 0.382** 0.316** 0.439 0.314** 0.343** Tillers per plant 0.174 0.018* 0.393 0.362 0.315* 0.272* 0.071 Plant height 0.125 0.225** 0.293 0.287* 0.338 0.226** Capsules per plant 0.340** 0.314* 0.282 0.341 0.275** Seeds /capsule 0.341** 0.358** 0.318** 0.338** Capsule length 0.295** 0.319** 0.356** Capsule breadth 0.323** 0.315** 1000 seed Wt. 0.351** Ingale (1984) Akola 28

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TABLE 10: DISCRIMINANT FUNCTIONS, EXCEPTED GENETIC ADVANCE IN SEED YIELD AND RELATIVE EFFICIENCY OF DIFFERENTSELECTION INDICES. Selection index Discriminant function G. A. Relative efficiency % X 6 seed yield 0.2418X 6 17.07 100.00 X 1 seeds /capsule 1.4422 X 1 15.09 88.38 X 2 tillers/plant 0.0343 X 2 0.99 5.84 X 3 1000 seed Wt. 0.5754 X 3 13.65 79.98 X 4 plant height 0.0664 X 4 5.54 32.45 X 5 capsules /plant 0.0149 X 5 31.81 80.91 X 6 X 1 0.8204 X 6 - 0.1677 X 1 31.86 186.62 X 6 X 2 0.8374 X 6 - 0.1351 X 2 31.72 185.71 X 6 X 3 0.6795 X 6 - 3.4547 X 3 28.61 167.65 X 6 X 4 0.7852 X 6 - 0.0573 X 4 30.33 177.64 X 6 X 5 0.5163 X 6 -0.0071 X 5 26.71 156.42 X 6 X 5 X 4 0.4591 X 6 - 0.0075 X 6 -0.0457 X 4 26.09 146.95 X 6 X 5 X 4 X 2 0.2961 X 6 - 0.0129 X 5 - 0.0384 X 4 + 2.6557 X 3 32.17 188.38 X 6 X 5 X 4 X 3 X 2 0.2910 X 6 - 0.0138 X 5 - 0.0364 X 4 + 2.77827 X 3 +0.9119 X 1 32.91 192.95 X 6 X 5 X 4 X 3 X 2 X 1 0.2691 X 6 - 0.0149 X 5 - 0.003 X 4 + 2.2226 X 3 +0.9654 X 2 - 1.3770X 1 33.16 194.17 Ingale (1984 ) Akola 29

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TABLE 11: THE EXPECTED GENETIC ADVANCE IN SEED YIELD OF SAFFLOWER FROM THE USE OF DIFFERENT SELECTION INDICES AND THEIR RELATIVE EFFICIENCIES. Sr. No. Combinations G.A. Relative efficiency % 1 X 6 yield per plant 20.12 100.00 2 X 1 Branches per plant 20.08 99.80 3 X 2 days to first flower 16.28 80,91 4 X 3 capitulum per plant 19.54 97.11 5 X 4 grain weight 24.48 121.66 6 X 5 Number of seeds per capitulum 21.16 105.16 7 x 3 + x 6 22.60 112.32 8 X 4 + X 6 26.15 131.46 9 X 5 + X 6 25.10 124.75 10 X 1 +X 2 + X 5 21.10 104.87 11 X 1 +X 3 +X 4 21.30 105.86 12 X 1 + X 3 + X 6 25.46 126.54 13 X 1 + X 4 + X 5 22.18 110.23 Joshi et al. (1985) Dhule (Continued) 31

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TABLE 11 :THE EXPECTED GENETIC ADVANCE IN SEED YIELD OF SAFFLOWER FROM THE USE OF DIFFERENT SELECTION INDICES AND THEIR RELATIVE EFFICIENCIES. Sr. No. Combinations Genetic advance Relative efficiency percentage 14 X 1 + X 4 + X 6 28.10 139.66 15 X 1 + X 5 + X 6 27.30 135.68 16 X 3 + X 5 + X 6 25.10 124.75 17 X 4 + X 5 + X 6 28.30 140.65 18 X 1 +X 3 + X 5 + X 6 22.16 110.14 19 X 1 +X 4 + X 5 + X 6 24.18 120.17 20 X 4 + X 5 + X 6 28.30 140.65 21 X 1 + X 3 + X 4 + X 6 20.18 100.29 22 X 1 +X 3 + X 5 + X 6 22.16 110.14 23 X 1 +X 4 + X 5 + X 6 24.18 120.17 24 X 1 +X 4 + X 5 + X 6 30.00 149.10 25 X 3 +X 4 + X 5 + X 6 29.08 144.53 26 X 1 +X 2 +X 3 + X 5 + X 6 45.02 223.75 X 1 =Branches per plant X 3 =capitula per plant X 5 = number of seed per capitulum X 2 = days to first flower X 4 =grain weight X 6 = yield per plant Joshi et.al . (1985) Dhule 32

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TABLE 12: SELECTION INDICES, GENETIC GAIN AND RELATIVE EFFICIENCY OF  G OVER  G’ FOR DIFFERENT COMBINATIONS OF PHYSIOLOGICALTRAITS IN NONSEGREGATING GENERATIONS OF CROSSES RH30 X RH 781 AND PRAKASH X RC 1425 OF INDIAN MUSTARD. Y- seed yield, X 1 = NAR (reproductive phase), X 2 = CGR (reproductive phase), X 3 = LAD ( reproductive phase), X 4 = LAI (reproductive phase),  G= expected genetic gain through straight selection, G’= expected genetic gain through discriminant function. Yadav and Singh (1988) Hissar Continued Selection indices  G  G ’ R.E of  G over  G’ % 0.599Y+20.80X 1 3.5 3.6 1.46 0.328Y+-0.289X 2 1.9 2.3 21.15 0.552Y+1.216X 4 6.7 7.0 3.16 0.491X 3 +20.022 X 4 132.7 140.5 5.86 0.431Y+16.506X 1 + 0.231X 2 1.9 2.2 14.16 -0.031Y+173.41X 1 +2.377X 4 6.7 7.4 10.12 0.832 Y+1.385 X 2 +0.914X 3 130.6 126.6 3.13 0.154Y+0.546 X 2 +1.342X 4 5.7 6.3 11.92 0.750Y +47.052X 1 +0.285X 2 +1.004X 3 130.7 133.1 1.86 33

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Selection indices  G  G ’ R.E. of  G over  G’ % 0.209Y+10.884 X 1 –0.218 X 2 +1.378 X 4 15.7 6.3 11.45 26.641X 1 –0.205X 2 +0.482 X 3 +20.090X 4 132.4 139.7 5.48 0.047Y+42.700X 1 –1.246X 2 +0.348X 3 +20.798X 4 134.8 136.2 1.01 0.832 Y+1.385 X 2 +0.914X 3 130.6 126.6 3.13 0.154Y+0.546 X 2 +1.342X 4 5.7 6.3 11.92 0.750 Y+47.052X 1 +0.285X 2 +1.004X 3 130.7 133.1 1.86 0.209Y+10.884 X 1 –0.218 X 2 +1.378 X 4 15.7 6.3 11.45 26.641X 1 –0.205X 2 +0.482 X 3 +20.090X 4 132.4 139.7 5.48 0.047Y+42.700X 1 –1.246X 2 +0.348X 3 +20.798X 4 134.8 136.2 1.01 Y-- seed yield, X 1 = NAR (reproductive phase), X 2 = CGR reproductive phase), X 3 = LAD ( reproductive phase), X 4 = LAI (reproductive phase)  G expected genetic gain through straight selection  G’ expected genetic gain through discriminate function Yadav and Singh (1988) Hissar TABLE 12 : SELECTION INDICES, GENETIC GAIN AND RELATIVE EFFICIENCY OF  G OVER  G’ FOR DIFFERENT COMBINATIONS OF PHYSIOLOGICAL TRAITS IN NONSEGREGATING GENERATIONS OF CROSS Prakash X RC 1425 OF I. MUSTARD. 34

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TABLE 13: EXPECTED GAIN(%) IN SEED YIELD OVER STRAIGHT SELECTION IN GROUNDNT FROM THE USE OF VARIOUS SELECTION INDICES IN MIDNAPUR LOCATION. Selection index Expected gain(%) Y=0.967 X 1 (number of pods per plant) 19.96 Y=0.953 X 2 (pod yield per plant) 17.15 Y=0.874 X 3 (100 seed weight) (g) 8.59 Y=0.911 X 4 ( harvest index) 6.66 Y=0.581 X 5 (seed yield per plant) 3.66 Y=1.040 X 1 +1.236 X 2 30.33 Y=1.117X 1 +1.140X 3 22.51 Y=0.963 X 1 +1.007 X 4 22.11 Y=0.992 X 1 +0.575 X 5 21.86 Y=0.948 X 2 +0.929 X 3 20.91 Y=0.968 X 1 +0.968 X 2 +0.929 X 3 29.83 Y=2.153 X 1 +0.936 X 2 +0.874 X 4 38.24 Bera and Das (1997) Continued 35

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TABLE 13: EXPECTED GAIN(%) IN SEED YIELD OVER STRAIGHT SELECTION IN GROUNDNT FROM THE USE OF VARIOUS SELECTION INDICES IN MIDNAPUR LOCATION. Selection index Expected gain(%) Y=1.242 X 1 +1.307 X 2 +0.422 X 5 38.98 Y=1.398 X 1 +1.426 X 3 +0.842 X 4 25.50 Y=0.903 X 1 +0.727 X 3 +0.509 X 5 21.19 Y=0.875 X 1 +0.928 X 4 +0.901 X 5 25.84 Y=1.686 X 2 +0.132 X 3 +2.842 X 4 37.23 Y=1.024 X 2 +0.967 X 3 +0.554 X 5 23.37 Y=0.911 X 2 +1.905 X 4 +1.142 X 5 23.10 Y=1.992 X 1 +1.127 X 2 +0.967 X 3 +0.929 X 4 39.94 Y=0.439 X 1 +1.928 X 2 +0.553 X 3 +1.573 X 5 36.94 Y=0.969 X 1 +1.298 X 2 +1.568 X 4 +1.186 X 5 45.88 Y=1.926 X 1 +0.911 X 3 +1.237 X 4 +0.444 X 5 32.27 Y=1.130 X 2 +1.371 X 3 +1.362 X 3 +0.655 X 5 27.43 Y=0.705 X 1 +1.869 X 2 +1.670 X 3 +0.890X 4 +1.537 X 5 35.29 X1 (number of pods per plant), X2 (pod yield per plant), X3 (100 seed weight) (g), X4 ( harvest index) X5 (seed yield per plant) Bera and Das (1997) 36

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TABLE 13.1: EXPECTED GAIN(%) IN SEED YIELD OVER STRAIGHT SELECTION IN GROUNDNT FROM THE USE OF VARIOUS SELECTION INDICES IN PURULIA LOCATION. Selection index Expected gain(%) Y=0.959 X 1 (number of pods per plant) 13.38 Y=0.937 X 2 (pod yield per plant) 9.00 Y=0.935 X 3 (100 seed weight) (g) 11.16 Y=0.964 X 4 (harvest index) 8.41 Y=0.916 X 5 (seed yield per plant) 7.13 Y=1.840 X 1 +1.120 X 2 26.61 Y=0.951 X 1 +0.925 X 3 17.48 Y=1.342 X 1 +0.969 X 4 18.86 Y=0.967 X 1 +0.924 X 5 17.84 Y=0.931 X 2 +0.933 X 3 14.46 Y=0.963 X 2 +0.869 X 5 14.98 Y=0.968 X 1 +0.968 X 2 +0.929 X 3 25.83 Y=1.153 X 1 +0.836 X 2 +0.974 X 4 24.39 Y=1.001 X 1 +3.655 X 2 +0.854 X 5 32.88 X1 (number of pods per plant), X2 (pod yield per plant), X3 (100 seed weight) (g), X4 ( harvest index) X5 (seed yield per plant) Bera and Das (1997) Continued 37

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TABLE 13.1: EXPECTED GAIN(%) IN SEED YIELD OVER STRAIGHT SELECTION IN GROUNDNT FROM THE USE OF VARIOUS SELECTION INDICES IN PURULIA LOCATION. Selection index Expected gain(%) Y=1.398 X 1 +1.426 X 3 +0.842 X 4 23.93 Y=0.928 X 1 +0.959 X 4 +0.904 X 5 21.36 Y=1.606 X 2 +0.232 X 3 +1.842 X 4 19.22 Y=0.982 X 2 +1.395 X 3 +0.835 X 5 19.57 Y=1.901 X 2 +0.897 X 4 +0.940 X 5 23.39 Y=0.925 X 3 +2.040 X 4 +1.503 X 5 17.69 Y=0.992 X 1 +0.928 X 2 +1.067 X 3 +2.960 X 4 27.11 Y=0.913 X 1 +0.932 X 2 +0.800 X 3 +0.038 X 5 22.63 Y=1.978 X 1 +1.098 X 2 +1.158 X 4 +1.368 X 5 43.60 Y=0.978 X 1 +0.918 X 3 +1.014 X 4 +0.859 X 5 28.34 Y=1.130 X 2 +1.173 X 3 +1.236 X 3 +0.755 X 5 38.78 Y=1.000 X 1 +0.993 X 2 +0.903 X 3 +1.044 X 4 +1.537 X 5 37.02 X1 (number of pods per plant), X2 (pod yield per plant), X3 (100 seed weight) (g), X4 ( harvest index) X5 (seed yield per plant) Bera and Das (1997) 38

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TABLE 14: GENOTYPIC COEFFICIENT OF VARIATION (GCV), EXPECTED GENETIC ADVANCE (GA)AND CORRELATION (r) IN THE SUNFLOWER GERMPLASM FOR SEED YIELD (SY) AND OIL YIELD PER PLANT(OYP*). Sr. No. Characters GCV (%) GA(%) (SY) (OYP) 1 HT 19.64 39.78 0.8506** 0.7091** 2 HD 16.67 22.44 0.7722** 0.7418** 3 HW 51.09 71.06 0.8312** 0.7148** 4 FS 30.62 40.67 0.9112** 0.8090** 5 SY/OYP 35.99 50.47 0.8819** 0.8819** HT= PLANT HEIGHT HW= WEIGHT OF HEAD SY= SEED YIELD HD= HEAD DIAMETER FS= NUMBER OF FILLED SEEDS OYP= OIL YIELD PER PLANT Patil et.al.( 1997) Dharwad 39

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TABLE 15: SELECTION INDICES, GENETIC GAIN (GG) EXPECTED FROM THEM AND THEIR RELATIVE EFFICIENCY(R.E.) AS COMPARED TO STRAIGHT SELECTION FOR SEED YIELD AND OIL YIELD IN SUNFLOWER ACCESSIONS. Sr. No. Combinations G. G. (SY) G. G. (OYP) R.E. (%) (SY) Relative Co efficiency (OYP) 1 X 6 seed yield per plant /oil yield per plant (ratio) 15.219 4.179 100.00 100.00 2 X 1 plant height 17.456 4.315 114.700 103.265 3 X 2 head diameter 11.141 2.987 73.206 71.472 4 X 3 weight of head 12.401 2.976 81.485 71.227 5 X 4 no. of filled seeds 12.852 3.184 84.451 76.198 6 X 5 oil yield per plant/ seed yield per plant 13.205 3.746 86.766 89.636 7 X 1 - X 2 17.505 4.358 115.020 104.282 8 X 1 - X 3 17.882 4.399 117.496 105.268 9 X 1 –X 4 18.125 4.483 119.098 107.276 10 X 1 - X 5 18.217 4.594 119.217 109.942 Patil et al. (1997) Dharwad Continued 40

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TABLE 15: SELECTION INDICES, GENETIC GAIN (GA) EXPECTED FROM THEM AND THEIR RELATIVE EFFICIENCY(RE) AS COMPARED TO STRAIGHT SELECTION FOR YIELD AND OIL YIELD IN SUNFLOWER ACCESSIONS. Sr. No. Combinations Genetic gain (SY) Genetic gain (OYP) Relative efficiency percentage (SY) Relative Co efficiency (OYP) 11 X 1 - X 2 - X 3 13.7660 4.4012 117.7764 105.3111 12 X 1 - X 2 - X 4 17.9247 4.4839 119.2773 107.2896 13 X 1 - X 2 - X 5 18.1531 4.5998 102.0589 110.0616 14 X 1 - X 3 - X 4 18.2721 4.4914 119.5592 107.4681 15 X 1 - X 3 - X 5 18.1960 4.5964 120.0296 109.9814 16 X 1 –X 4 - X 5 18.2676 4.5955 120.1488 109.9592 17 X 1 - X 2 - X 3 + X 4 18.3038 4.4918 120.2669 107.4794 18 X 1 - X 2 - X 3 + X 5 18.4083 4.5999 120.9539 110.0650 19 X 1 - X 2 - X 4 + X 5 18.3627 4.6002 120.6540 110.0715 20 X 1 - X 3 - X 4 + X 5 18.3142 4.5970 120.3353 109.9952 21 X 1 - X 2 - X 3 + X 4 + X 5 18.4600 4.6003 121.3238 110.0745 X 1= plant height, X 2= head diameter, X 3 = weight of head, X 4 = no. of filled seeds X 5 = oil yield per plant/ seed yield per plant X 6= seed yield per plant/oil yield per plant (ratio) Patil et al. (1997) Dharwad 4 1

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TABLE 16:SELECTION FUNCTION, EXPECTED GENETIC ADVANCE(GA) IN (gm/plant) IN GRAIN YIELD PER PLANT AND RELATIVE THEORETICAL EFFICIENCY (in%) OF SELECTION INDICES IN SOYBEAN. Selection function GA RE(%) 0.760X 6 = Seed yield per plant 1.57 100.00 0.012 X 1 = Plant height 0.38 21.20 0.003 X 2 = Hundred seed weight (g) 0.01 00.63 0.101 X 3 = Number of pod per plant 1.29 82.16 0.030 X 4 = days to maturity 0.36 22.94 1.090 X 5 = number of primary braches per plant 1.02 64.96 0.001 X 1 +0.760 X 6 1.57 100.00 0.254 X 2 +0.130 X 3 1.50 96.15 0.010 X 2 +0.760 X 6 1.56 99.68 0.030 X 3 +0.628 X 6 1.59 101.92 -0.005 X 4 +0.768 X 6 1.57 100.00 0.350 X 5 +0.670 X 6 1.67 106.00 Singh and Dalal (1979) Jabalpur Continued 42

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TABLE 16:SELECTION FUNCTION, EXPECTED GENETIC ADVANCE IN (gm/plant) IN GRAIN YIELD PER PLANT AND RELATIVE THEORETICALEFFICIENCY (in%) OF DIFFERENT SELECTION INDICES IN SOYBEAN. Selection function GA RE(%) -0.006 X 1 +0.217 X 2 +0.136 X 3 1.48 95.12 0.208 X 2 +0.141 X 3 -0.027 X 4 1.49 96.00 0.125 X 3 -0.052 X 4 +0.132 X 5 1.41 90.32 -0.007 X 4 +0.334 X 5 +0.691 X 6 1.59 101.92 -0.002 X 1 +0.159 X 3 -0.096 X 4 1.61 103.20 X6= Seed yield per plant X1= Plant height X2= Hundred seed weight (g) X3= Number of pod per plant X4= days to maturity X5= number of primary braches per plant Singh and Dalal (1979) Jabalpur Continued 43

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TABLE 16: SELECTION FUNCTION, EXPECTED GENETIC ADVANCE(G.A.) IN (gm/plant) IN GRAIN YIELD PER PLANT AND RELATIVE THEORETICAL EFFICIENCY in% OF DIFFERENT SELECTION INDICES IN SOYBEAN. Selection function GA RE(%) 0.014 X 2 +0.343 X 5 +0.677 X 6 1.59 101.92 0.306 X 2 +0.160 X 3 +0.073 X 5 1.62 103.84 0.196 X 2 +0.103 X 3 +0.298 X 6 1.64 105.12 0.021 X 3 +0.225 X 5 +0.613 X 6 1.60 102.40 -0.007 X 2 -0.008 X 4 +0.328 X 5 +0.694 X 6 1.59 101.92 0.052 X 3 -0.003 X 4 +0.052 X 5 +0.567 X 6 1.66 106.41 0.194 X 2 +0.101 X 3 +0.018 X 5 +0.301 X 6 1.64 105.12 0.000 X 1 +0.210 X 2 +0.128 X 3 -0.021 X 4 +0.198 X 5 1.50 96.15 0.00 X 1 +2 X 2 +0.065 X 3 +0.051 X 4 -0.23X 5 +0.172X 5 +0.519X 6 1.62 105.84 X6= Seed yield per plant X1= Plant height X2= Hundred seed weight (g) X3= Number of pod per plant X4= days to maturity X5= number of primary braches per plant Singh and Dalal (1979) Jabalpur 44

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TABLE 17 : EXPECTED GENETIC ADVANCE AND RELATIVE EFFICIENCY(R.E.) %, (THEORETICAL ) OF DIFFERENT SELECTION INDICES IN POOLED F 2 . POPULATION OF SOYBEAN. Selection Functions Genetic advance R.E. (%) Seed Yield X 4 6.53 100 -1.892X 1 (Days to Maturity) 36.86 564 1.937X 2 ( Primary Branches) 99.29 1520 23.892X 3 (Pods/plant) 841.28 12883 0.969X 5 (100 seed weight) 2.04 31 0.237X 6 (Oil Content) 1.10 17 -2.181X 1 + 1.978 X 2 34.16 523 - 1.885X 1 + 0.971X 5 36.61 561 - 1.888X 1 + 0.228X 6 36.76 563 2.224 X 2 +1.008 X 5 14.18 217 8.895 X 3 +6.850 X 4 826.70 12660 7.753 X 3 +0.973 X 5 841.56 12887 4.006 X 3 +0.242X 6 841.26 12883 6.813 X 4 +1.088X 5 56.39 864 Mannur et al. ( 1991) Dharwad Continued 45

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TABLE 17: EXPECTED GENETIC ADVANCE AND RELATIVE EFFICIENCY% (THEORETICAL ) OF DIFFERENT SELECTION INDICES IN POOLED F 2 POPULATION OF SOYBEAN. Selection Functions Genetic advance Relative efficiency(%) 6.813X 4 +1.088X 5 56.53 866 11.209 X 3 + 6.717X 4 +1.116X 5 862.98 13216 6.815X 4 + 1.086X 5 +4.689X 6 56.2 870 - 2.468X 1 + 1.666X 2 + 6.514X 4 29.86 457 - 2.155X 1 + 2.231X 2 +1.009X 5 35.37 5642 - 2.176X 1 + 1.981X 2 +0.277X 6 35.86 549 1.950X 1 +6.809X 4 + 1.090X 5 6.72 103 2.229X 2 + 1.004X 5 +3.187X 6 14.48 222 2.240X 2 + 2.294X 3 + 1.608X 5 6.80 104 5.825 X 2 + 0.968X 5 —0.035X 6 386.99 5914 1.953 X 2 +6.811X 4 +1.065X 5 +0.049X 6 6.76 103 11.292 X 3 +6.719 X 4 +1.114X 5 +0.025X 6 863.14 13218 X1=Days to Maturity ,X2 = Prim. Branches X3=Pods/plant , X4=Seed Yield X5=100 seed weight, X6= Oil Content Mannur et al. (1991) Dharwad Continued 46

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TABLE 17.1: VARIANCE, MEAN AND RANGE IN PARENTS AND F 2 POPULATION OF SOYBEAN . Character Mean Range variance VGF 2 P 1 P 2 F 2 P 1 P 2 F 2 Days to maturity 82.8 98.0 92.0 80-98 94-118 74-162 84.2 Primary branches 4.8 9.0 7.9 3-9 6-13 1-22 10.4 Pods per plant 45.2 157.0 130.0 26-110 90-325 10-850 8179.9 Seed yield per plant 14.5 1.0 4.6 8-27 0.6-1.6 0.5-22.0 13.3 100-seed weight 13.9 0.6 2.8 10.8-18.0 0.45-0.65 1.0-9.05 0.7 Oil content 19.1 9.4 13.6 17.0-22.0 8.2-9.8 10.4-18.5 19.9 VGF 2 =genotypic variance in F 2 Mannur et al. (1991) Dharwad 47

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TABLE 18: THE PARTIAL REGRESSION COEFFICIENTS AND THE CORRESPONDING STANDARD ERRORS IN THE MULTIPLE REGRESSION EQUATIONS FITTED WITH ALL THE CHARCTERS. Character Partial regression coefficient Days to flowering 0.378*  0.174 Duration of flowering 0.039  0.170 Days to maturity 0.373*  0.186 Plant height 0.109*  0.043 Primary branches 0.091  0.072 Secondary branches 0.856**  0.227 Pods per plant 0.071**  0.009 Seeds per pod 2.288  1.675 100-seed weight 1.913*  0.833 Harvest index 1.720**  0.242 Protein content 1.693  1.153 a= -179.26 Sandhu et al. (1995) FARIDKOT 48

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TABLE 18.1: DISCRIMINATE FOUNCTION,GENETIC ADVANCE,ANDRELATIVE EFFICIENCY OF DIFFERENT FUNCTIONS IN PEGION PEA Sr. No. Discriminant Function Genetic Advance Relative efficiency (%) 1 b 1 x 1 2.48 187.87 2 b 2 x 2 1.32 100.00 3 b 3 x 3 1.09 82.57 4 b 4 x 4 0.95 71.96 5 b 5 x 5 0.47 35.60 6 b 6 x 6 0.44 33.33 7 b 7 x 7 0.25 18.93 8 b 1 x 1 +b 2 x 2 3.13 237.12 9 b 1 x 1 +b 3 x 3 2.88 218.18 10 b 1 x 1 +b 4 x 4 2.84 215.15 11 b 1 x 1 +b 2 x 2 +b 3 x 3 3.46 262.12 X 1 = secondary branches,X 2 = seed yield per plant,X 3 = pods per plant X 4 =harvest index, X 5 =days to maturity,X 6 = plant height & X 7 = 100 seed weight. Sandhu et al. (1995) FARIDKOT Continued 49

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TABLE 18.1: DISCRIMINATE FOUNCTION,GENETIC ADVANCE(G.A.), AND RELATIVE EFFICIENCY OFDIFFERENT FUNCTIONS IN PEGION PEA Sr. No. Discriminant Function G.A. Relative efficiency 12 b 1 x 1 +b 2 x 2 +b 4 x 4 3.41 258.33 13 b 1 x 1 +b 2 x 2 +b 5 x 5 3.23 244.69 14 b 1 x 1 +b 2 x 2 +b 3 x 3 +b 4 x 4 3.70 380.30 15 b 1 x 1 +b 2 x 2 + b 3 x 3 +b 5 x 5 3.58 271.21 16 b 1 x 1 +b 2 x 2 + b 3 x 3 +b 6 x 6 3.50 265.15 17 b 1 x 1 +b 2 x 2 + b 3 x 3 +b 7 x 7 3.46 262.12 18 b 1 x 1 +b 2 x 2 + b 3 x 3 +b 4 x 4 +b5x 5 3.84 290.00 19 b 1 x 1 +b 2 x 2 + b 3 x 3 + b 4 x 4 +b 6 x 6 3.76 284.84 20 b 1 x 1 +b 2 x 2 + b 3 x 3 + b 4 x 4 +b 7 x 7 3.72 281.81 21 b 1 x 1 +b 2 x 2 + b 3 x 3 + b 4 x 4 +b 5 x 5 +b 6 x 6 3.88 293.93 22 b 1 x 1 +b 2 x 2 + b 3 x 3 + b 4 x 4 +b 5 x 5 +b 7 x 7 3.84 290.00 23 b 1 x 1 +b 2 x 2 + b 3 x 3 +b 4 x 4 +b 5 x 5 +b 6 x 6 +b 7 x 7 3.89 294.69 X 1 = secondary branches X 2 = seed yield per plant: X 3 = pods per plant X 4 =harvest index; X 5 = days to maturity; X 6 = plant height &X 7 = 100 seed weight. Sandhu et al. (1995) FARIDKOT 50

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TABLE 19: SELECTION INDEX, DISCRIMINANT FUNCTION, EXPECTED GENETIC ADVANCE(G.A.)AND RELATIVE SELECTION EFFICIENCY(R.S.E.) IN CLUSTER BEAN. Selection index Discriminant function G.A. R. S. E. (%) X 1 0.047 2.04 67.6 X 2 0.214 0.94 31.2 X 3 0.101 0.64 21.2 X 4 0.465 3.02 100.0 X 1 X 4 0.047+0.465 3.65 120.7 X 2 X 4 0.214+0.465 3.17 104.7 X 3 X 4 0.101+0.465 3.09 102.2 X 1 X 2 X 4 0.047+0.214+0.465 3.77 124.7 X 1 X 3 X 4 0.047+0.101+0.465 3.71 122.6 X 2 X 3 X 4 0.214+0.101+0465 3.23 106.9 X 1 X 2 X3 X 4 0.047+0.214+0.101+0.465 3.82 126.5 X 1 = pods per plant X 2 =pods per cluster X 3 =1000seed weight (g) X 4 =seed yield per plant (g) Choudhary and Joshi ( 1996) Mandor (Jodhpur) 51

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TABLE 20: HERITABILITY(h 2 ), PHENOTYPIC (r P ) AND GENOTYPIC (r g ) CORRELATION OF COMPONENT CHARACTER WITH YIELD (x 7 ) IN CHICKPEA. Character ^ h 2 r P r R ^ h 2 (r g ) Days to 50% flowering (X 1 ) 90.1 -0.05 -0.08 0.07 Days to maturity (X 2 ) 57.5 -0.05 -0.06 0.03 Plant height (X 3 ) 63.2 0.07 -0.05 0.03 Primary branches per plant (X 4 ) 14.2 0.38 0.34 0.05 Pods per plant (X 5 ) 398.4 0.71* 0.68* 0.27 100-seed weight (X 6 ) 92.5 0.06 0.04 0.03 Significant at 1%level. Samal and Jagadev (1996) Keonjhar (Orissa) 52

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TABLE20.1 : RELATIVE EFFICIENCY OF SELECTION INDICES OVER DIRECT SELECTION FOR SEED YIELD IN CHICKPEA . No. of characters in selection index Relative efficiency (%) Group-1 Group-2 Group-3 Group-4 Mean 1 58.9 5.4 100.0 100.0 66.1 2 58.9 6.6 100.9 100.0 66.6 3 60.1 8.3 100.9 100.1 67.4 4 62.1 27.9 101.3 100.1 72.9 5 67.6 29.3 101.5 101.2 74.9 6 67.7 67.7 101.5 101.2 84.5 7 101.7 101.7 101.7 101.7 101.7 Mean 68.2 35.3 101.1 100.6 76.3 Samal and Jagadev ( 1996) Keonjhar (Orissa) 53

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TABLE 21: SELECTION INDICES AND THEIR RELATIVE EFFICIENCY IN DETERMINATE PIGEONPEA LINES. Best character combinations among group of characters Index score Expected genetic advance Relative efficiency (%) Grand Mean (G.M) r g value with seed yield Seed yield (1m 2. .g) X 1 -199.31 -60.47 100.00 143.60  21.98 -- Primary branches per plant X 2 -33.53 -18.60 30.75 17.06  1.56 0.44* 100-seed weight (g) X 3 90.91 8.61 14.23 8.83  0.25 0.05 Racemes per plant X 4 183.09 77.35 127.90 34.50  4.29 0.48* Flowers per plant X 5 121.86 60.31 99.73 339.46  1.73 0.45* Pods per plant X 6 124.74 61.77 102.14 58.98  7.77 0.57 Days to flowering X 7 394.60 36.64 60.58 83.56  1.73 0.51* Days to maturity X 8 -166.39 -24.51 40.52 150.45  2.01 0.44 Plant height (cm) X 9 330.19 66.52 109.99 138.40  0.03 0.74** Paul and Bajpai (2000) Pantnagar Continued 54

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TABLE 21: SELECTION INDICES AND THEIR RELATIVE EFFICIENCY IN DETERMINATE PIGEONPEA LINES. Best character combinations among group of characters Index score Expected genetic advance Relative efficiency(%) X 1 + X 4 + X 6 108.52 78.37 129.58 X 1 + X 4 + X 9 313.96 82.16 135.86 X 1 + X 5 + X 6 + X 9 377.49 90.67 149.92 X 1 + X 4 + X 5 + X 6 230.39 98.89 163.52 X 1 + X 4 + X 5 + X 9 435.83 101.93 168.53 X 1 + X 3 + X 4 + X 5 + X 9 526.74 102.29 169.14 X 1 + X 4 + X 5 + X 6 + X 7 624.99 105.46 174.38 X 1 + X 4 + X 5 + X 6 + X 9 560.58 119.18 197.07 X1= Seed yield (1m 2. g) ,X2 =Primary branches per plant,X3=100-seed weight (g) X4=Racemes per plant, X5=Flowers per plant,X6= Pods per plant X7=Days to flowering, X8=Days to maturity, X9= Plant height (cm) Paul and Bajpai .(2000) Pant nagar Continued 55

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TABLE 21: SELECTION INDICES AND THEIR RELATIVE EFFICIENCY IN DETERMINATE PIGEONPEA LINES. Best character combinations among group of characters Index score Expected genetic advance Relative efficiency (%) X 1 + X 3 + X 4 + X 5 + X 6 + X 7 715.90 105.81 174.96 X 1 + X 3 + X 4 + X 5 + X 6 + X 9 651.49 119.49 197.58 X 1 + X 4 + X 5 + X 6 + X 7 + X 9 955.18 124.69 206.17 X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 9 901.84 118.84 196.50 X 1 + X 4 + X 5 + X 6 + X 7 + X 8 + X 9 788.78 122.26 202.15 X 1 + X 4 + X 5 + X 6 + X 7 + X 8 + X 9 1046.09 124.19 206.16 X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 + X 9 879.69 122.56 202.65 X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 + X 9 1296.44 123.59 204.36 X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 + X 8 +X 9 1130.04 121.14 200.30 X 1 = Seed yield (1m2.g) ,X 2 =Primary branches /plant,X 3 =100-seed weight (g) X 4 =Racemes / plant,X 5 =Flowers /plant,X 6 = Pods / plant, X 7 =Days to flowering, X8=Days to maturity, X9= Plant height (cm) Paul and Bajpai .(2000) Pant nagar 56

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TABLE 22: DISCRIMINANT FUNCTIONS FOR SUCROSE PERCENT AND THEIR EXPECTED GENETICGAIN(%) OVER STRAIGHT SELECTION IN SUGARCANE. Discriminant function b value Expected genetic gain (%) over straight selection. b 1 Y 1 (Y 1 = Length of Inter node in cm) -0.394 -38.04 b 2 Y 2 (Y 2 = Brix % Juice) 1.004 -6.26 b 3 Y 3 (Y 3 = Purity percentage) 0.267 -24.78 b 4 Y 4 (Y 4 = C.C.S. percent) 1.005 -1.86 b 5 Y 5 (Y 5 = Sucrose percent) 0.834 0.00 b 4 Y 4 + b 5 Y 5 0.150,0.955 13.49 b 1 Y 1 + b 2 Y 2 + b 4 Y 4 -0.076,0.376,0.638 8.09 b 1 Y 1 + b 2 Y 2 + b 3 Y 3 + b 5 Y 5 -0.081,0.080,-0.015,0.7533 1.01 b 1 Y 1 + b 2 Y 2 + b 4 Y 4 + b 5 Y 5 -0.080,0.205,0.17,0.810 18.23 b 2 Y 2 + b 3 Y 3 + b 4 Y 4 + b 5 Y 5 0.177,0.022,0.308,0.503 4.83 b 1 Y 1 + b 2 Y 2 + b 3 Y 3 + b 4 Y 4 + b 5 Y 5 -0.076,0.215,0.178,0.465,0.813 43.54 Punia et. al. ( 1982) Hisar 57

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TABLE 23: PROMISING SELECTION INDICES FOR CURED LEAF YIELD, NICOTINE (X) AND NICOTINE(L) IN TOBACCO WITH HIGHER RELATIVE EFFICIENCY AS COMPARED TO DIRECT SELECTION. Sr. No. Selection index Relative efficiency(%) Genetic advance A. Selection indices for cured leaf yield 1 -0.057X 6 + -637.6888 X 14 + 110.7632 X 16 319.49 @ 201.46 2 -0.0562 X 6 +4.1829 X 12 – 649.9598 X 14 + 111.7708 X 16 319.12 201.86 3 -2.24 X 8 + 7.52 X 12 – 432.78 X 14 + 74.47 X 16 251.63 159.17 4 7.149 X 12 – 429.75 X 14 + 73.971 X 16 251.07 157.82 5 -1.5035 X 8 – 407.507 X 14 + 71.853 X 16 243.73 154.17 X 5 = leaf area plant; X 6 = Fresh leaf yield; X 8 = percent loss in weight; X 12 = reducing sugars (L); X 13 =nicotine (X); X 14 =nicotine (L) X 15 =reducing sugars/nicotine (X); X 16 = reducing sugars/ nicotine(L) *genetic advance (through direct selection) figures for the three dependent characters were as follows: Cured leaf yield: 63.26 Nicotine (X) : 0.24 Nicotine (L) : 0.25 @ suggested for adoption in selecting for yield. V. Devanand, et al .(2003) Bangalore Continued 58

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Sr. No. Selection index Relative efficiency (%) Genetic advance B. Selection indices for nicotine (X) 1 0.0003 X 6 – 0.010 X 12 + 3.29 X 14 –0.565 X 16 386.74 0.943 2 0.0003 X 6 +3.27 X 14 – 0.5634 X 16 386.53 @ 0.945 3 -0.025 X 12 + 1.964 X 14 – 0.336 X 16 298.01 0.729 4 -0.007 X 8 + 1.876 X 14 – 0.327 X 16 290.14 0.710 5 1.882 X 14 – 0.328 X 16 289.93 0.709 TABLE 23: PROMISING SELECTION INDICES FOR CURED LEAF YIELD, NICOTINE (X) AND NICOTINE(L) IN TOBACCO WITH HIGHER RELATIVE EFFICIENCY AS COMPARED TO DIRECT SELECTION. X 5 = leaf area plant; X 6 = Fresh leaf yield; X 8 = percent loss in weight; X 12 = reducing sugars (L); X 13 =nicotine (X); X 14 =nicotine (L) X 15 =reducing sugars/nicotine (X); X 16 = reducing sugars/ nicotine (L) *genetic advance (through direct selection) figures for the three dependent characters were as follows: Cured leaf yield: 63.26 Nicotine (X) : 0.24 Nicotine (L) : 0.25 @ suggested for adoption in selecting for yield. V. Devanand, et al .(2003) Bangalore Continued 59

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Sr. No. Selection index Relative efficiency (%) Genetic advance C. Selection indices for nicotine (L.) 1 0.0 X 5 + 0.0 X 6 –0.02 X 8 +0.017 X 12 +0.13 X 15 – 0.04 X 16 121.33 0.307 2 0.0 X 5 + 0.0 X 6 -0.02 X 8 + 0.18 X 13 + 0.005 X 15 –0.03 X 16 120.61 0.304 3 0.0 X 5 - 0.09X 8 +0.15 X 12 + 0.15 X 13 – 0.04 X 16 120.28 0.304 4 0.0 X 5 + 0.02 X 12 – 0.03 X 15 –0.039 X 16 118.89 0.300 5 0.0 X 5 + 0.015 X 12 + 0.118 X 13 –0.012 X 15 – 0.0328 X 16 119.56 0.302 6 0.0 X 5 + 0.21 X 13 –0.03 X 16 118.51 0.299 X 5 = leaf area plant; X 6 = Fresh leaf yield; X 8 = percent loss in weight; X 12 = reducing sugars (L); X 13 =nicotine (X); X 14 =nicotine (L) X 15 =reducing sugars/nicotine (X); X 16 = reducing sugars/ nicotine (L) *genetic advance (through direct selection) figures for the three dependent characters were as follows: Cured leaf yield: 63.26 Nicotine (X) : 0.24 Nicotine (L) : 0.25 @ suggested for adoption in selecting for yield. V. Devanand, et al .(2003) Bangalore TABLE 23: PROMISING SELECTION INDICES FOR CURED LEAF YIELD, NICOTINE (X) AND NICOTINE(L) IN TOBACCO WITH HIGHER RELATIVE EFFICIENCY AS COMPARED TO DIRECT SELECTION. 60

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LIMITATIONS: Selection indices are not as effective as yield alone in spite of making extra efforts for their estimation. The calculations becomes still complicated when the index is extended to cover many component characters ( Falconer 1960) (2) Selection index is applicable to individual plant selection only. However family selection is not greatly improved by the use of an index. ( Falconer 1960). (3) accuracies in estimation of variances and co-variances restricts the application of selection indices in practical plant breeding. (4) Different weights are provided by different workers in estimation procedures to same set of populations and hence the index becomes more inconsistent for same populations. 61

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CONCLUSION: The genotypically constructed index was more effective than the phenotypic index. The characters with high heritability and genotypic correlation will be more important for achieving higher efficiency. Selection index comprising of different combinations of different characters provides information on most important set of characters which bring about higher genetic advance. 62

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There is need to standardize the procedure for assigning weights to different characters in different crops so that applicability of the technique can be increased . FUTURE THRUST 63

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