Biometrical Techniques in Plant Breeding

Basic Principles of Biometrical Genetics
Presented by :-
S. A. Patil
A. S. Deshmukh
Ph.D Scholar
Course No. GP-602
Vasantrao Naik Marathwada Krishi Vidyapeeth, Parbhani
College of Agriculture, Parbhani

Biometrical Genetics
Genetics: Genetics is a biological science which deals with the principles of heredity and variation.
Biometrics: The science that deals with the application of statistical concepts and procedures to
the study of biological problems is called biometrics. It is also referred to as
biometry or biostatistics.
Biometrical Genetics: A branch of genetics that utilizes various statistical concepts and
procedures to the study of genetic principles is called biometrical genetics.
Types: 1) Quantitative Genetics
2) Population Genetics
1. Quantitative Genetics: A branch of biometrical genetics which deals with the study of
polygenic or quantitative characters is known as quantitative genetics.
2. Population Genetics: It deals with the frequency of genes and genotypes in a
mendelian population.

HISTORY
Statistician/ Biometrician Contribution / concept developed
R. A. Fisher(1918) Provide initial frame of biometrics and divided genetic variance into additive,
dominance and epistatic.
Sewall Wright (1921) Developed the concept of path analysis. He also divided the genetic variance into
additive and non-additive components
Mahalanobis, P. C. (1928) Developed the concept of D2 statistics.
Smith H. F. (1936) Developed the concept of discriminant function analysis.
Comstock, R. E. and Robinson, H. F. (1948, 1952) Developed the concept of biparental mating.
Kempthorne, O. (1957) He developed three important concepts, viz. Partial diallel cross analysis, line x tester
analysis and restricted selection index
Rawlings, J. O. and Cokerham, C. C. (1962) Developed the concepts of triallel and quadriallel cross analysis
Kearsey, M. J. and Jinks, J. L. (1968) Developed the concepts of triple test cross analysis.
Freeman, G. H. And Perkins, J. M. Provided a model of stability analysis
Perkins, J. M. and Jinks, J. L. Provided a model of stability analysis
Anderson, E. (1957) He developed the concept of metroglyph analysis
Finlay, K.W. and Wilkinson, G. N. (1963) They first provided a systemic approach in 1963 for the analysis of adaption in plant
breeding.
Federer, W. T. (1956, 1961) He developed the concept of augmented design.

Basic Principles of Biometrical Genetics
 Aids to assessment of variability
 Aids to the selection of elite genotypes
 Aids to the choice of suitable parents and breeding procedures
 Aids to the assessment of varietal adaptation
Principles Biometrical Techniques
Aids to assessment of variability 1)Simple measures of dispersion (Range, standard
deviation, variance, standard error, coefficient of
variation, 2)Metroglyph analysis and 3) D2 statistics
Aids to the selection of elite genotypes Correlation analysis, path coefficient analysis and
discriminant function analysis
Aids to the choice of suitable parents and
breeding procedures
Diallel cross, partial diallel cross, line x tester cross,
triallel cross, quadriallel cross, biparental cross, triple
test cross, generation mean analysis.
Aids to the assessment of varietal adaptation Stability analysis

Aids to Assessment of Variability
 Simple measures of variability
1. Range
2. Standard deviation
3. Variance
4. Standard error
5. Coefficient of Variation
Range: Range is the difference between the lowest and the highest values present in the observations in a sample.
Standard deviation: It is the square root of the arithmetic mean of squares from the mean. OR It is the square root of
the variance
Variance: Variance is defined as the average of the squared deviation from the mean OR it is square of the standard
deviation
Standard error: It is the measure of the mean difference between sample estimate of mean and the population
parameter.
Coefficient of variation: The ratio of standard deviation of a sample to its mean expressed in percentage is called
coefficient of variation.

Metroglyph analysis
 This technique was developed by Anderson in 1957. It is a semigraphic
method.
Main Steps
1. Selection of Genotypes
2. Evaluation of Material
3. Assessment of variability
I. Plotting of glyph on the graph: A small circle by which the position of a
genotype or line is represented on the graph is called glyph.
II. Depiction of Variation : Depiction for remaining characters of each
genotype is displayed on the respective glyph by rays.
III. Construction of Index Score: The maximum and minimum score of an
individual will be 3n, and n where n is the total number of characters
included in the study.
IV. Analysis of Variation: The variation is analysed for various traits
within the group and between the groups.

ADVANTAGES AND DISADVANTAGES
Advantages:
 It helps in studying the pattern of morphological variation in large number of
germplasm lines at a time.
 This procedure is very simple and this technique can be applied to both unreplicated
as well as replicated data.
 It is useful for classification of germplasm for various characters.
Disadvantages:
 The inclusion of large number of genotypes sometimes leads to overlapping of glyphs
on the graph.

D2 STATISTICS
 The concept of D2 statistics was originally developed by P. C. Mahalanobis in 1928.
 Main Steps:
 Selection of Genotypes
 Evaluation of Genotypes
 Biometrical Analysis
i. Computation of D2 values and testing their significance: If the calculated value of D2
is higher than table value of X2 it is considered significant and vice versa.
ii. Finding out the contribution of individual character towards total divergence.
iii. Grouping of different genotypes into various clusters
iv. Estimation of average distance at (i) intra-cluster and ii) inter- cluster levels
v. Construction cluster diagram.

CLUSTER DIAGRAM
1. This number of clusters represent the number of groups in which a population can be classified on the basis
of D2 statistics.
• The distance between two cluster is the measure of the degree of diversification.
• The greater the distance between two clusters the greater the divergence and vice versa
• The genotypes falling in the same cluster are more closely related than those belonging to another cluster
OR the genotypes grouped together in one cluster are less divergent than those which are placed in different
cluster.

Advantages:
 It helps in the selection of genetically divergent parents.
 It measures the degree of diversification and determines the relative proportion of each
component character to the total divergence.
 This techniques provides reliable estimates of genetic divergence.
 A large no. of germplasm lines can be evaluated at a time for genetic diversity by this
technique.
Disadvantage:
 The analysis is difficult as it involves estimation of variances and covariances .
 The estimates are not statistically very robust as they are based on second order
statistics.
 The analysis is not possible from unreplicated data.

Comparison of Metroglyph Analysis and D2 statistics
Sr.
No.
Particulars Metroglyph
analysis
D2 Statistics
1 Statistics involved First order Second order
2 Analysis Simple Difficult
3 Analysis is possible from Unreplicated data
also
Replicated data
4 Type of Approach Semi-graphic Numerical
5 Diagram used Metroglyph Chart Cluster diagram

Aids to the Selection of Elite Genotypes
Correlaion Analysis
The term coefficient of correlation was first used by Karl pearson in 1902. It is denoted by r.
Its value lies in between -1 to 1.
Correlation: The statistics which measure the degree and direction of association
between two or more variables is known as correlation.
Types of correlation:
1. Simple correlation
2. Partial correlation
3. Multiple correlation

Simple Correlation
Simple correlation: Simple correlation refers to the association between two variables. It is
also known as total correlation or zero order correlation coefficient.
Features:
1. It involves two variables.
2. It is denoted as r12
3. It ignores effects of other independent variables.
4. It is estimated from variances and co-variances.
5. Its value is always lower than multiple correlation.
6. It is of three types, viz., genotypic ( rg12 ) , Phenotypic ( rph12 ) and environmental ( re12)

Interpretation of results of simple correlations
1. If the value of r is significant, the Association between two characters is high.
2. If the value of r bears negative (-)sign, it means that increase in the value of one character will lead to
decrease in second character. Similarly, if it bears positive (+) sign. It means that increase in one
variable will lead to increase in second character.
3. If the value of genotypic correlation coefficient (rg)is higher than phenotypic correlation coefficient
(rph), it means that there is strong association between these two characters genetically but the
phenotypic value is lessened by the significant interaction of environment.
4. If the value of phenotypic correlation coefficient (rph) is greater than genotypic correlation coefficient
(rg), it shows that the apparent association of two characters is not only due to genes, but also
favourable influence of environment.
5. If the value of environmental correlation coefficient (re) is greater than genotypic and phenotypic
correlation coefficients, it means that these two characters are showing high association due to
favourable influence of particular environment and this association may change in another locality or
with change in environment.
6. If the value of r is zero or insignificant, it means that these two characters are independent. But if the
value of rg and rph are also insignificant, it clearly indicates the independence nature of two
characters.

PARTIAL CORRELATION
Partial correlation: Partial Correlation refers to the correlation between two variables eliminating the effect of third
variable. It is denoted as r12.3. It is also known as net correlation.
Features:
1. It involves three or four variables
2. It is denoted as r12.3 or r12.34
3. It does not ignore effects of other independent variables.
4. It is estimated from simple correlations.
5. Its value is always lower than multiple correlation.
6. It is of two types, viz., first order and second order.
7. It can be calculated from un-replicated data also
Interpretation of Partial Correlation
1. If the value of partial correlation coefficient is zero. It means the simple correlation between x1and x2 is due to the
effect of another variable x3, but after eliminating the effect of x3 the two variable may be found as uncorrelated.
3. If the value of partial correlation coefficient (r12.3) is significant, it indicates true relationship between x1 and x2.

MULTIPLE CORRELATION
Multiple correlation: Multiple correlation refers to joint influence of two or more independent variables
on a dependent variable. It denoted by R1.23.
Features:
1. It involves several variables.
2. It is denoted as R1.23
3. It does not ignore effects of other independent variables.
4. It is estimated from simple correlations.
5. Its value is always higher than simple and partial correlation.
6. It is of one type only.
7. It provides estimate of coefficient of determination.
8. It is a non-negative estimate.
9. It can be calculated from un-replicated data also.
INTERPRETATION
1. If the value of multiple correlation coefficient ( R) is highly significant, it confirms that the dependent
variable was highly correlated with the various independent variables.
2. The coefficient of determination which is estimated as square of multiple correlation coefficient is
contribution of various character components towards dependent variable , say yield.

Scales for Correlation Coefficients (Serale, 1965)
Sr. No. Values of Correlation Coefficient Rate or Scale
1 >0.65 Very strong
2 0.50 to 0.64 Moderately strong
3 0.30 to 0.49 Moderately weak
4 <0.30 Very weak

PATH COEFFICIENT ANALYSIS
 The concept of path coefficient was originally developed by Wright in 1921. It was first used for plant
selection by Dewey and Lu in 1959.
Path coefficient: Path coefficient analysis is simply a standardized partial regression coefficient which
splits the correlation coefficient into the measures of direct and indirect effects. OR it measures the direct
and indirect contribution of various independent characters on a dependent character.
Features:
1. Path analysis measures the cause of association between two variables.
2. Analysis of path coefficient is based on all possible simple correlations among various characters.
3. It provides information about direct and indirect effects of independent variables on dependent
variable.
4. Analysis is based on the assumptions of linearity and additivity.
5. It also estimates residual effects.
6. Path analysis helps in determining yield contributing characters and thus is useful in indirect selection.
Types:
1. Phenotypic path
2. Genotypic path
3. Environmental path

PATH DIAGRAM
 In path analysis , a line diagram which is constructed with the help of simple correlation coefficients
among various characters included under study is referred to as path diagram.
Uses:
• It depicts the cause and effect situation in a simple manner and makes the presentation of results more
attractive. It provides a visual picture of cause and effect situation.
• It also depicts the association between various characters.
• It helps in understanding the direct and indirect
contribution of various independent variables
towards a dependent variable.
• Direct effect
• Indirect effect
• Residual effect
.
.

Scales for Path Coefficients
(Lenka and Mishra, 1973)
Value of direct or Indirect effects Rate or Scale
0.00 to 0.09 Negligible
0.10 to 0.19 Low
0.20 to 0.29 Moderate
0.30 to 0.99 High
More than 1.00 Very high

INTERPRETAION OF RESULTS OF PATH ANALYSIS
1. If the correlation between yield and a character is due to direct effect of a character. It
reveals true relationship between them and direct selection for this trait will be
rewarding for yield improvement.
2. If the correlation is mainly due to indirect effects of the character through another
component trait, indirect selection through such trait will be live in yield improvement.
3. If the direct effect is positive and high but the correlation is negative, in such situation
direct selection for such trait should be practised to reduce the undesirable indirect
effect.
4. If the value of residual effect is moderate or high, it indicated that beside the characters
studied, there are some other attributes for yield.

Advantages:
1. Path analysis provides information about the cause and effect situation in understanding the cause of
association between two variables.
2. It is quite possible that trait showing positive direct effect on yield may have a negative indirect effect via
other component traits. Path analysis permits the examination of direct effect of various characters on yield
as well as their indirect effects via other component traits.
3. It provides basis for selection of superior genotypes from the diverse breeding populations.
Disadvantages:
1. Path analysis is designed to deal with variables additive effects. Its application to variables having non-
additive effects may lead to wrong results Kempthorne 1957)
2. Its computation is somewhat difficult and inclusion of many variables makes the computation more
complicated.

DISCRIMINANT FUNCTION ANALYSIS
 The use of discriminant function for plant selection was first proposed by Smith in 1936.
 Discriminant function: Desirable genotypes are discriminated from the undesirable ones,
based on the combination of various characters, this technique is known as discriminant
function analysis.
 Features:
 It measures the efficiency of various character combinations in selection. Selection index
leads to simultaneous manipulation of several characters for genetic improvement of
economic yield.
 This technique provides information on yield components and thus aids indirect selection
for the genetic improvement of yield.
 Analysis is based on the assumptions of linearity and additivity.
 Analysis involves variances and covariances.
 Selection indices are generally three types, viz. 1) Classical 2) General and 3) Restricted
 Discriminant function analysis differs from path analysis in several aspects.

Types of Selection Index
 Classical Selection Index:
This was developed by Smith in 1936. This involves several characters simultaneously
in selection index and discriminates between desirable and undesirable genotypes on the
basis of selection efficiency. This was first applied for plant selection by Smith (1936)
and later on for animal selection by Hazel (1943)
 General Selection Index: This was first proposed by Hanson and Johnson in 1957. This
is a modification of the scheme of Smith. In this model the weights for various traits
are based on the average statistics for several populations. This selection index has
wide application in plant breeding. This model has been modified by several workers to
meet their specific breeding requirements.
 Restricted Selection Index: This was proposed by Kempthorne and Nordskog in 1959.
This helps in improving a set of characters keeping the value of other characters intact.
Sometimes the restriction is put on single character and sometimes on double characters.

Advantages and Disadvantages
Advantages:
1. In crop improvement programmes, discriminant function analysis
provides information on yield components and thus aids in indirect
selection for genetic improvement of yield.
2. This technique can be applied to both parental population as well as
segregating populations.
Disadvantages:
1. The construction of selection index is difficult task which requires lot of
statistical calculations.
2. Selection index is applicable to individual plant selection only. However,
family selection is not greatly improved by the use of an index.
3. Selection indices have limited applications in practical plant breeding
because of inaccuracies associated with the estimation of variances and
covariances.
4. Different estimation procedures generally provide different values when
applied to the same set of population.

Aids to the Choice of Suitable Parents and Breeding
Procedures
 Diallel Cross Analysis
 Partial Diallel analysis
 Line x Tester analysis
 Diallel Cross Analysis:
Diallel cross refers to mating of selected parents in all possible combinations and
evaluation of a set of diallel crosses is known as diallel analysis.
Types:
1. Full Diallel
2. Half Diallel

Full Diallel
In this design all possible mating among the selected parents are made in both directions i.e. direct and
reciprocals.
Features:
 Total number of single crosses in a full diallel is equal to P (P-1), where P is the number of parents used.
 Full diallel is used when (a) reciprocal differences are significant and (b) parents do not have male sterility
or self incompatibility.
 Full diallel permits estimation of maternal effects.
Half Diallel
In this design all possible crosses among the selected parents are made in one direction only
Features:
 In half diallel, parent is used either as male or as female in the mating.
 The number of single crosses required is equal to P(P-1)/2, where P is the number of parents used.
 Half diallel is used when reciprocal differences are not significant.
 It can be used when parents have male sterility and self incompatibility

Plan of crossing for a Diallel analysis
Wwww
Parents 1 2 3 4 5 6
1 * x x x x x
2 + * x x x x
3 + + * x x x
4 + + + * x x
5 + + + + * x
6 + + + + + *
Where, x, + and * = Direct crosses, Reciprocals, and Parents, respectively.

Advantages and Disadvantages of Diallel
Advantages:
1. Diallel cross is used for evaluation of several single crosses in terms of
genetic components of variance.
2. It provides information about general and specific combining ability
variances and additive(D) and (V) dominance (H) components of genetic
variance.
3. The Each parent has equal opportunity to mate and recombine with every
other parent.
4. The results obtained from diallel cross analysis have high level precision.
5. Diallel analysis helps in the selection of suitable parents for use in
hybridization programme.
Disadvantages:
1. Diallel analysis can test only a limited number of parents at a time.
2. All the assumptions of a diallel cross are seldom fulfilled.
3. Analysis of diallel cross by hand is difficult.

Partial Diallel Analysis
The concept of partial diallel mating design was developed by Kempthorne in 1957 and was further
elaborated by Kempthorne and Curnow in 1961.
Partial Diallel: Partial diallel is nothing but a modified form of a diallel cross in which only a part of all
possible crosses made among n parents is utilized for evaluation and biometrical techniques.
Features:
1. Partial diallel utilizes only a part of all possible crosses from a diallel.
2. In partial diallel, each parent is crossed to some of other parents, but not all.
3. In partial diallel, total no. of crosses is equal to ns/2,where n and s are number of parents and sample
crosses respectively.
4. Partial diallel provides information about gca and sca variances and gca effects and D and H
components.
5. Results obtained from partial diallel have lesser precision than those of diallel analysis.
Important steps:
1. Selection of Parents: The parents to be included in the study should have phenotypic diversity.
2. Affecting sample crosses: A sampling procedure is adopted to decide the number of crosses to be
effected for evaluation.

Sampling Procedure:
In partial diallel, only a part of all possible crosses made in a diallel fashion is utilized for
evaluation and analysis, therefore, sampling is important for deciding the various crosses to
be made among selected parents. The total number of sampled crosses is equal to
ns/2,where, n is the number of parents and s is the number of sampled crosses per parent or
per array.
The following three points are important for sampling
1. The s should be a whole number. It can not be in decimal fraction.
2. The s should be either greater than or equal to n/2
3. Both n and s can neither be odd nor even. If n is odd, s should be even and vice-versa.
For the purpose of sampling, first a constant K is worked out as follows
K=(n+1-s)/2 where, n and s =number of parents and sampled crosses, respectively
If n=10 and s=5, K will be = (10+1-5)/2=3
This means that in each array five crosses are to be made (s=5), and sampling is to being
after 3 arrays, i.e. from the 4th array as depicted below. In this partial diallel, only 25crosses
(10x5)/2=25 will be included.

Procedure of Sampling and Plan of Crossing in a
Partial Diallel Design
Parents P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
P1 X X X X X
P2 X X X X X
P3 X X X X X
P4 X X X X
P5 X X X
P6 X X
P7 X
P8
P9
P10
It is clear from the sampling procedure that the following 25 cross have to be made among 10 parents
P1 X P4 P2 X P5 P3 X P6 P4 X P7 P5 X P9
P1 X P7 P2 X P8 P3 X P9 P4 X P10 P6 XP10

Advantages:
1. Partial diallel provides information about gca variances and gca effects, and also on
the components of genetic variance.
2. More parent can be evaluated by this technique at a time than by diallel analysis.
3. Heritability, genetic advance and heterosis can also be estimated.
4. It can be used with open pollinated species having self incompatibility or male
sterility.
Disadvantages:
1. Each parent does not have opportunity to mate and recombine with every other parent.
2. The estimate have lesser precision than those obtained by diallel cross.

LINE X TESTER ANALYSIS
The concept of line x tester analysis was develop by Kempthorne in 1957.
It is a modified form of top cross scheme. In case of top cross only one tester is used,
while in case of line x tester cross several testers are used.
Features:
1. Line x tester analysis involves mf crosses, where m and f are number of male and
female parents.
2. This technique can evaluate large number of germplasm lines in terms of gca and sca
variances and effects and D and H components.
3. This technique help in the selection of breeding procedures.
4. Results obtained from this technique have high level of precision.
5. Analysis is simple as compared to diallel and partial diallel analysis.
Characteristic of testers :
1. Broad Genetic Base
2. Wider Adaptability
3. Low Yield Potential
4. Low performance for other traits

Plan of Crossing for Line x Tester Cross Design
Male parents
Female m1 m2 m3 m4 m5
f1 x x x x x
f2 x x x x x
f3 x x x x x
f4 x x x x x
f5 x x x x x
f6 x x x x x
f7 x x x x x
f8 x x x x x
f9 x x x x x
f10 x x x x x

Advantages:
1. Line x tester technique helps in the selection of desirable parents and also appropriate breeding
procedure by measuring the gca and sca variances and effects and genetic components of variance
(A & D)
2. This is good technique for evaluation of large number of germplasm lines at a time in terms of
combining ability variances and effects.
3. This technique can be used even when the inbred lines have self-incompatibility or male sterility.
4. Heterosis, heritability and genetic advance can also be estimated.
Disadvantages:
1. This technique does not provide the estimates of epistatic variance.
2. In this techniques each parent does not have opportunity to mate and recombine with every other
parent, which is possible in a diallel cross.
3. With the inclusion of more no. of testers, the number of hybrids becomes too large for evaluation

Triallel analysis
 The concept of triallel and quadriallel analysis was developed by Rawlings and
Cokerham in 1962 a )
This refers to the analysis of a three-way cross.
Features:
1. Triallel analysis includes all possible three-way crosses among n parents. In
triallel analysis, total number of three-way crosses is equal to n(n-1) (n-2)/2
where n is the number of parents.
2. In triallel each cross involves three different parents.
3. It provides general and specific line effects and helps in deciding the mating order
of parents for developing superior three-way hybrids.
Main steps:
1. Making Single crosses
2. Making Three Way Crosses
4. Biometrical Analysis

Plan of Crossing for Triallel Design
Single
crosses
Male Parents
1 2 3 4 5
1x2 x x x
1x3 x x x
1x4 x x x
1x5 x x x
2x3 x x x
2x4 x x x
2x5 x x x
3x4 x x x
3x5 x x x
4x5 x x x

COMBINING ABILITY EFFECTS
 General Line Effects :
Two types of general line effects are worked out, viz., general line effect of first kind (hi) and
general line effect of second kind (gi). The former refers to the general combining ability effect of
a line used as one of the grand parents, whereas the latter refers to the general combining ability
effect of a line used as parent crossed to the single cross hybrid.
 Specific Line Effects (gi):
There are three types of specific line effects as given below
1. Two Line specific Effect of First Kind (dij): It refers to the specific combining ability effect of
a line used as one of the grand parents.
2. Two Line Specific Effect of Second Kind(sik): It refers to the specific combining ability effect
of a line when crossed as a parent to the single cross hybrid.
3. Three Line specific Effect (tijk): It refers to specific combining ability effect of a line in three-
way cross.

Advantages:
1. Triallel analysis helps in the identification of superior three-way crosses, especially in
cross pollinated crops, for the development of three-way cross hybrids.
2. This is a very good techniques for the evaluation of three way cross hybrids for genetic
components of variation.
3. This technique provides reliable information about the components of epistatic variance
and also about the order of parents for crossing to obtain superior recombinants.
Disadvantages:
1. Triallel cross analysis requires two cropping seasons for generating experimental
material only, whereas diallel cross requires one season only for this purpose.
2. In this approach more crosses have to be made than in diallel cross which adds to the
experimental cost.

QUADRIALLELANALYSIS
The concept of Quadriallel analysis was developed by Rawlings and Cokerham (1962b)
Quadriallel analysis: A Quadriallel cross refers to the analysis of double cross hybrids which are the first
generation progeny of a cross between unrelated F1 hybrids.
Features:
 It involves all possible double crosses among n parents. The total no. of crosses is equal to n(n-1) (n-2) (n-3)/8
where n is the number of parents.
 Each cross involves four different parents.
 It provides information about additive (D), dominance (H) and epistatic variances.
 It measures one, two, three and four lines average effects and helps in deciding the mating order of parents for
development of superior double cross hybrids in cross pollinated crops.
 More crosses than diallel and triallel have to be made, ie 630 among in 10 Parents.
Important steps:
1. Making Single Crosses
2. Making Double Crosses
4. Biometrical analysis

Plan of Crossing for Quadriallel Design
Single
crosses
12 13 14 15 23 24 25 34 35 45
12 * x x x
13 * x x x
14 * x x x
15 * x x x
23 + + * x
24 + + * x
25 + + * x
34 + + + *
35 + + + *
45 + + + *
Where, X, * and + = Direct crosses, selfings and reciprocal crosses. Selfings
and reciprocal are not required for quadriallel analysis.

INTERPRETATION OF RESULTS
Singh and Chaudhary (1985)
1. The one line average effect accounts for the total additive effects Thus, if the gene
action is primarily of additive type, the estimates of one line effects are sufficient to
predict the hybrid performance.
2. The two line average effects represent non additive type of gene action.
3. The three line average effects are the function of additive x dominance interaction
including all three factors or higher order interactions except all dominance types.
4. The average four line effects represent dominance x dominance interactions and all
three factor interactions, except all additive types.
5. The effects arising due to the arrangement of lines are exclusively the results of
dominance effects or interactions involving dominance components.

Advantages:
1. Quadriallel cross analysis helps in the identification of superior double cross hybrids,
especially in cross pollinated crops, for the development of commercial hybrids.
2. This technique provides additional information on epistatic components of variance as
does the triallel analysis
3. This also provides information about the order in which parents should be crossed to
obtain superior segregants.
Disadvantages:
1. This technique requires one additional crop season for generating experimental
material than diallel analysis
2. This adds to the cost of experiments as more number of crosses have to be made in
this design as compared to diallel cross and triallel crosses.
3. Triallel and quadriallel cross analysis can evaluate less number of inbred lines at a
time as compared to diallel, partial diallel and line x tester cross analyses.

Biparental Cross
The concept of biparental cross or biparental mating was originally developed by
Comstock and Robinson (1948, 1952).
In this technique, plants are randomly selected in F2 or subsequent generation of a cross
between two pure lines having contrasting characters and the selected plants are crossed
in a definite fashion.
Important Steps:
1. Selection of Parents
2. Making Original Cross
3. Growing F1 and F2 Progeny
4. Making Crosses in F2
5. Evaluation of Crosses

MAIN FEATURES
1. This technique involves F2, P1 and P2 generations of a single cross to develop material for testing
2. It requires three crop seasons for generating experimental material and fourth season for
evaluation.
3. This technique provides information about additive and dominance components of genetic
variance.
4. This techniques helps in the choice of breeding procedure for genetic improvement of polygenic
characters.
5. Analysis is based on second order statistics. Moreover, analysis is more difficult than generation
mean analysis.
6. Biparental crosses include full sib and half sib progenies in the mating programme.
DESIGNS OF BIPARENTAL MATING:
1. North Carolina Design I (NCD I)
2. North Carolina Design II (NCD II)
3. North Carolina Design III (NCD III)

NORTH CAROLINA DESIGN I (NCD I)
This design is also known as Nested design.
Important Steps :
1. Selection of Plants
2. Mating Procedure
3. Number of Crosses
4. Variance
Features:
1. Each male is mated to a different set of females.
2. Each set consists of f crosses, where f is the number of female plants.
3. Variance between males provides an estimated of D.
4. Variance among females provides estimated of H & D.
5. Influenced by the presence of maternal effects.
6. Requires 10-12 times more area than design 3.
7. This is the least powerful design

Plan of Crossing for North Carolina Design I
Set I Set II
m1 x f1 m3xf9 m1 x f1 m3 x f9
X f2 X f10 X f2 X f10
X f3 X f11 X f3 X f11
X f4 X f12 X f4 X f12
m2 x f5 m4x f13 m2x f5 m4 x f13
X f6 X f14 X f6 X f14
X f7 X f15 X f7 X f15
X f8 X f16 X f8 X f16

NORTH CAROLINA DESIGN II ( NCD II)
This design is also known as factorial design. This design is similar to line x tester analysis.
Important steps:
1. Selection of Plants
2. Mating Procedure
4. Variance
Features:
1. Each male is mated to the same set of females.
2. Each set consists of mf crosses, where m and f denote number of male and female plants.
3. Variances due to males and female provide an estimate of D.
4. Variance due to male x female provides an estimate of H.
5. Influence by the presence of maternal effects.
6. Requires 2-4 times more area than design 3.
7. This is an intermediate design

Plan of Crossing for North Carolina Design II
Males Female
f1 f2 f3 f4
m1 x x x x
m2 x x x x
m3 x x x x
m4 x x x x
m5 x x x x
m6 x x x x

NORTH CAROLINA DESIGN III (NCD III)
This design involves backcrossing in F2 .
Important Steps:
1. Selection of parents
2. Mating procedure
4. Variance
Features:
1. Each male is mated to both parents of original cross.
2. Each set consists of 2m crosses, where m is the number of male plants used in a set
3. Variance due to male provides an estimate of D.
4. Variance due to male x female provides an estimate of H.
5. Not affected by the presence of maternal effects.
6. Requires much less area than design 1 and 2.

Plan of Crossing for North Carolina Design III
Males P1 P2 Males P1 P2
Set I Set III
m1 x x m1 x x
m2 x x m2 x x
m3 x x m3 x x
m4 x x m4 x x
m5 x x m5 x x
Set II Set IV
m1 x x m1 x x
m2 x x m2 x x
m3 x x m3 x x
m4 x x m4 x x
m5 x x m5 x x

COMPARISON OF THREE DESIGNS OF BIPARENTAL CROSS
Sr.
No.
Particulars NCD I NCD II NCD III
1. Mating of each selection male plant
to
Different group of
females
Same group of females P1 and P2
2. Efficiency Least powerful Intermediate Most Powerful
3. Populations involved F2 only F2 only F2 , P1 and P2
4. The variance is due to Males and females Males, females and males x
females
Males and males x
females
5. Area required Highest Medium Lowest
6. Estimates obtained D and H D and H D and H
7. Total crosses made f mf 2m
8. Maternal effect Observed Observed Not Observed
9. Additive variance (D)obtained from Males Males and Females Males
10 Dominance variance (H) obtained
from
Females Males x females Males x females

Triple Test Cross Analysis
The concept of triple test cross (TTC) analysis was proposed by Kearsey and Jinks in 1968.
In triple test cross, each randomly selected F2 plant is crossed to the inbread parents (P1 and P2)of the original cross
and their F1
Features:
1. This design involves P1, P2, F1, and F2 generations of a single cross in developing experimental material.
2. This technique requires 4 crop seasons for complete study. Three crop seasons are required for the development
of breeding material and the fourth one for the evaluation of material.
3. The analysis is based on second order statistics, therefore, calculation is more difficult than generation mean
analysis.
4. This design provides test for non-allelic interaction, which is one of the assumptions.
5. This evaluates the above material in terms of genetic components of variation.
Important steps:
1. Making single cross
2. Raising F1 progeny
3. Making back crosses
4. Evaluation of material
5. Biometrical analysis

Plant of Crossing for Triple Test Cross Design
Males Female Plants
P1 P2 F1
m1 x x x
m2 x x x
m3 x x x
m4 x x x
m5 x x x
m6 x x x
m7 x x x
m8 x x x
m9 x x x
m10 x x x
m11 x x x

Comparison of Triple Test Cross and North Carolina Design III
Sr. No. Particulars Triple Test cross NCD III
1 Populations
involved
P1, P2,F1 and F2 of a cross P1, P2 and F2 of a cross
2 Mating of selected
F2 plants with
P1,P2 and F1 of the cross P1 and P2 of the cross
3 Test of epistasis Applicable Not applicable
4 Analysis is based
on
P1, P2, F1 and F2 generations P1, P2, and F2 generations
5 Area required More Less
6 Estimates obtained D and H D and H
7 Total crosses made 3n 2n

Advantages:
1. Triple test cross provides reliable information about the presence or absence of
epistasis in addition to the estimates of additive genetic variance and dominance
variance.
Disadvantages:
1. In this design the main problem is the choice of contrasting pair of inbreed lines to get
the reliable estimates of additive genetic variance.
2. This techniques takes more time for evaluation of parents than diallel analysis,
3. This biometrical technique is not in common use in plant breeding unlike diallel,
partial diallel and line x tester analysis.

Generation Mean Analysis
The concept of generation mean analysis was developed by Hayman (1958) and Jinks and
Jones (1958) for the estimation of genetic components of variation.
Analysis of this technique is based on six different generations of a cross, viz, parents
(P1 , P2), their( F1, F2) and back crosses (B1, B2)
IMPORTANT STEPS:
1. Selection of Parents for Crossing
2. Raising F1 and Making Backcrosses
3. Evaluation of material
The biometrical analysis is done according to the model of generation mean analysis. The
biometrical analysis consist of two main steps 1) testing of epistasis and 2) estimation of
gene effects and variances.
 Scaling test
 Joint scaling test

SCALING TEST
Scaling Test: In the generation mean analysis, the test which determines (1) the presence or absence of non-
allelic interactions and (2) their type is known as scaling test.
Mather 1949 has given 4 types of tests viz., A, B, C. and D
When backcrosses are absent and F3 population is available, the D scale test is applied.
The standard error of A, B, C. and D. is worked out by taking the square root of respective variances and ‘t’
values are calculated by dividing the effects of A, B, C and D by their respective standard error.
The calculated ‘t’ values of these four tests are compared against 1.96 which is the table value of ‘t’ a 5
% level of significance. If the calculated values of these scales is higher than 1.96, it is considered
significant and vice versa.. The significance of these four scales indicates the presence of epistasis.
The type of epistasis is revealed by the significance of specific scale as given in following Table.
The Interpretation of Results of Scaling Test
Sr. No. Significance Reveals / Indicates
1 A and B scales Presence of all three types of epistasis, viz., A x A, A x D and D x D
2 C Scale Dominance x Dominance of epistasis (j)
3 D Scale Additive x Additive type of epistasis (i)
4 C and D scales Additive x Additive type of epistasis (i)
and Dominance x Dominance of epistasis (j)

JOINT SCALING TEST
Joint Scaling Test: This test permits any combination of the six population at a time . Moreover, joint scaling test also
provides estimates of three genetic parameters viz., m, d and h. This test also provides test for the model if more than
three families are available.
MODELS OF GENERATION MEAN ANALYSIS
1. Six Parameter Model
2. Five Parameter Model
3. Three Parameter Model
Six Parameter Model: This method was first suggested by Hayman (1958) for the estimation of various genetic
components from the generation mean analysis.
Features:
1. The analysis of this model is based on six generations, viz., P1,P2, F1, F2, B1 and B2 of the single cross.
2. Six parameters, viz., mean(m), additive gene effects (d), dominance gene effects(h), and three types of non-
allelic gene interactions, Viz., additive x additive (i) and Additive x dominance (j) and dominance x dominance
(l) are estimated.
3. This model provides information about all three types of non-allelic gene interactions, i.e. i, j, and l .
4. It requires two crop season for generation of material and third season for testing.
5. Testing of this method with x2 test is not possible.

FIVE PARAMETER MODEL
This procedure is also given by Hayman (1958), this model is used when backcross progenies (B1
and B2) are not available and instead F3 is available.
Features:
1. Analysis is based on five populations, P1, P2, F1, F2 and F3 generations of the single cross.
2. Five parameters, Viz., m, d, h, i and l are estimated.
3. This model does not provide information about additive x dominance type of epistasis.
4. Requires three crop seasons for generating of material and fourth season for evaluation and
thus is more expenses.
5. This model provides x2 test for testing of the model.
This model does not provide information about additive x dominance type of gene interaction

THREE PARAMETER MODEL
This method was proposed by Jinks and Jones (1958).
This is used in the absence of epistasis (non-allelic interactions)
Features:
1. This model is used when epistasis is absent.
2. Analysis of this model is based on six generations, viz., P1, P2, F1, F2, B1, and
B2 generations of the single cross.
3. It provides estimates of three parameters viz., m, d and h.
4. It requires two crop seasons for generating material and third season for
testing.
5. This does not provide x2 test for testing of model.

INTERPRETATION OF RESULTS
The interpretation of the genetic components of variance is as follows.
1. If additive genetic is high reliance should be placed on mass selection in self
pollinated species and synthetic breeding in cross pollinated species.
2. If the dominance (especially over-dominance) variance is predominant, the
breeding objective should be towards development of hybrids for
commercial purpose.
3. If the epistatic variance is relatively high, more reliance should be placed on
selection between families and lines.
4. If all the genetic components are of equal magnitude, either composite or
population improvement programme should be taken up for the development
of superior lines with several desirable genes.

Aids to the assessment of varietal adaptation
Stability analysis: The performance of genotype mainly depends on environmental conditions. Estimation of
phenotypic stability ,which involves regression analysis , has proved to be a valuable techniques for assessing the
response of various genotypes under changing environmental conditions. The evaluation of genotype-
environmental interactions gives an idea of the buffering capacity of the population under study. The low
magnitude of genotype environmental interactions indicates consistent performance of a population over variable
environments. In other words, it shows high buffering ability of the population.
Stability analysis is done from the data of replicated trials conducted over several locations or for several
years on the same location or both.
The stability analysis consist of following steps:
1. Location or environment wise analysis or variance.
2. Pooled analysis of variance for all the locations/environments. If G x E interaction is found significant, the
stability analysis can be carried out using one of the four models.
3. Finlay and Wilkinson model
4. Eberhart and Russell model
5. Perkins and Jinks model
6. Freeman and Perkins model.

ADVANTAGES OF STABILITY
1. Stability analysis helps in understanding the adaptability of crop varieties over a
wide range of environmental conditions and in the identification of adaptable
genotypes.
2. The use of adaptable genotypes for general cultivation over wide range of
environmental conditions helps in achieving stabilization in crop production over
locations and years.
3. Use of stable genotypes in the hybridization programme will lead to development
of phenotypically stable high potential cultivars of crop species.
4. Yield stability is genetically controlled, as has been shown for maize (Scott, 1967)
and hence selection for yield stability can be effective.
5. Stability analysis is an important tool for plant breeders in predicting response of
various genotypes over changing environments.

literature cited
 Biometrical Techniques in Plant breeding by P. Singh and S. S. Naryanan
 Quantitative Genetics by P. Singh

Biometrical Techniques in Plant Breeding

Biometrical Techniques in Plant Breeding

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