Correlation and Path analysis in breeding experiments

CCS HARYANA AGRICULTURAL
UNIVERSITY HISAR
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GP 591 CREDIT SEMINAR
ANKIT DHILLON (2020A58M)
(M.Sc. Scholar)
(Genetics & Plant Breeding)
CCS Haryana Agricultural
University
Hisar (125004)

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CORRELATION AND PATH
ANALYSIS IN BREEDING
EXPERIMENTS
Credit Seminar Title

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1. WHAT IS CORRELATION ?
2. DIFFERENT TYPES OF CORRELATIONS
3. PROPERTIES OF CORRELATION COEFFICIENT
4. COEFFICIENT OF DETERMINATION
5. PROPERTIES OF COEFFICIENT OF DETERMINATION
6. METHODS OF STUDYING CORRELATION
7. PATH ANALYSIS
8. CASE STUDIES
9. CONCLUSION
CONTENTS

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• Correlation is a statistical technique which helps in analyzing
the association between two or more variables.
• It helps us in determining the degree of relationship between
two or more variables.
• But it does not tell us about cause and effect relationship.
What is correlation?

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Correlation analysis consist of two steps
Determining whether a relationship exists and, if
it does, measuring it
Testing whether it is significant

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Different types of correlations
• Simple correlation
• Multiple correlation
• Partial correlation
• Genotypic correlation
• Phenotypic correlation
• Environmental
correlation
• Linear correlation
• Non linear correlation
• Positive correlation
• Negative correlation
• No correlation
Type
1
Type
2
Type
3
Type
4

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Type 1
Positive correlation
If two related variables are such that when one increases
(decreases), the other also increases (decreases)
Eg: correlation between seed size and seed yield in wheat
(Ambika et al. 2014)
Negative correlation
If two variables are such that when one increases
(decreases), the other decreases (increases)
Eg: correlation between white rust resistance and seed yield
in mustard
(Bal et al. 2014)
No correlation
If both the variables are independent of each other
Eg: no correlation between days to maturity and primary
branches in mustard
(Lodhi et al. 2016)

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Type 2
Linear correlation
When plotted on a graph it tends to be a
perfect line
Non-Linear correlation
When plotted on a graph it is not a straight
line

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Type 3
Simple correlation
In this only two variables are studied
Multiple correlation
In this three or more variables are studied
simultaneously.
Partial correlation
we recognize more than two variables but
consider only two variables to be influencing
each other and effect of other influencing
variables being kept constant

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Type 4
Phenotypic correlation
The observable correlation between two
variables
Genotypic correlation
The heritable association between two
variables
Environmental correlation
Correlation between two variables which is
entirely due to environmental effects

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Interpretation of coefficient of correlation
When r = +1, it means there is perfect positive relationship between the variables.
When r = -1, it means there is perfect negative relationship between the variables.
When r = 0, it means there is no relationship between the variables.
When r is closer to -1 or +1 than relationship between the variables are also closer.

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Properties of coefficient of correlation
• The coefficient of correlation lies between -1 to +1.
• The coefficient of correlation is independent of change of scale and origin of
the variable x & y.
• The degree of relationship between the two variables is symmetric 𝑟𝑥𝑦= 𝑟𝑦𝑥.

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Coefficient of determination
The square of multiple correlation coefficient is called coefficient of determination which is indeed the
percent of variability explained in dependent variable because of influence of independent variable.
Coefficient of determination (𝑹𝟐
) =
R= Multiple correlation coefficient
For example If the value of R = 0.9 than R2=0.81, it means 81% of the variation in the dependent
variable has been explained by the independent variable
Explained variance
Total variance

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Properties of coefficient of determination
• Its range lies between 0 to 1
• Represented by R2
• The coefficient of determination is a measure of how well the regression line represents the
data.
• If the regression line passes exactly through every point on the scatter plot, it would be
able to explain all of the variation.
• The further the line is away from the points, the less it is able to explain.

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Methods of studying
correlation
Scatter diagram method
Spearman’s rank
coefficient of correlation
Karl pearson coefficient
of correlation

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Scatter diagram method
• A two-dimensional representation of n pairs of measurements (xi , yi ) made on two
random variables x and y, is known as a scatterplot.
• The first bivariate scatterplot showing a correlation was given by Galton in 1885.
Ref.: Gogtay et al. (2017)

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Merits and limitation of scatter diagram
Merits
• It is simple and non mathematical methods of studying correlation
between the variables.
• Making a scatter diagram usually is the first step in investigating the
relationship between two variables.
Limitation
• In this method we can not measure the exact degree of correlation
between the variables.

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Karl Pearson’s Correlation Coefficient
• Karl Pearson (1857-1936) : British mathematician and statistician.
• The extent to which two variables vary together is called covariance and its
measurement is the correlation coefficient.

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Merits and limitations of Karl Pearson’s Correlation Coefficient
Merits
• It is most popular method used for measuring the degree of relationship.
• It helps us to find the exact degree of correlation.
Limitations
• The correlation coefficient always assumes linear relationship regardless of the
fact whether assumption is correct or not.
• Takes more time to computes correlation coefficient.

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• A method to determine correlation when the data is not available in numerical form
and as an alternative, the method of rank correlation is used.
• Thus when the values of the two variables are converted to their ranks, and there
from the correlation is obtained, the correlations known as rank correlation.
• This method was developed by British psychologist Charles Edward Spearman in
1904
Spearman’s rank coefficient of correlation
D= difference in the ranks of the values of each matched pair
n= no. of pairs

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Where, m= number of times common ranks are repeated
x Rank y Rank
Var 1 3 Var 1 1 4
Var 2 7 Var 2 6 1
Var 3 6 Var 3 4 4
Var 4 4 Var 4 2 4
Var 5 5 Var 5 3 4
Var 6 1 Var 6 7 36
Var 7 2 Var 7 5 9
62
(𝑅𝑥−𝑅𝑦) 2
=
𝐷2

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Merits and limitations of Spearman’s coefficient of correlation
Merits
• This method is simpler to understand and easier to apply as compared to the Karl
pearson’s method.
• This method can be used with great advantage where the data are of a qualitative in
nature.
Limitations
• This method should not be applied where N exceeds 30 because the calculations become
tedious and require a lot of time.

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Applications of correlation in crop improvement
• Effect on selection: A positive correlation between desirable characters is favourable to the
plant breeder because it helps in simultaneously improvement of both the characters and vice
versa for negative correlation.
• Correlated response: The genetic improvement in dependent trait can be achieved by applying strong
selection to character which is genetically correlated with dependent character.
• Indirect selection: Character having low heritability can be selected through correlated character having high
heritability.

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• This was given by Sewell Wright in 1921.
• First used for plant selection by Dewey and Lu in 1959.
• Path analysis is a method of splitting correlations into different components for interpretation of effects.
• If the cause and effect relationship is well defined, it is possible to represent the whole system of variables in the form of a
diagram , known as path diagram.
Let Yield ‘Y’ of barley is the function (effect) of various components (casual factors) like number of ears per plant (𝑥1) , ear
length (𝑥2) and 100-grain weight (𝑥3) etc.
𝑥1
𝑥2
𝑥3
R
a
b
c
h
Y
r 𝑥1𝑥2
r 𝑥2𝑥3
r x1𝑥3
Some other undefined factors designated by R
Path Analysis

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• Path coefficient can be defined as ratio of standard deviation due to a given cause to the total
standard deviation of the effect.
• If Y is the effect and 𝑥1 is the cause, then
Path coefficient for the path from cause 𝑥1 to the effect Y = σ𝑥1/ σY
• A set of simultaneous equations can be written directly from the Path diagram and the solution
of these equations provides information of the direct and indirect contributions of the casual
factors to the effect.
Y = 𝑥1 + 𝑥2 +𝑥3 +R
Definition

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Correlation between 𝑥1 and Y i.e r (𝑥1, Y) is defined as
r (𝑥1, Y) = Cov (𝑥1, Y)
σ𝑥1 . σY
By putting the value of Y in above equation, we get
r (𝑥1, Y) = Cov (𝑥1+x1+𝑥2 +𝑥3 +R)
σ𝑥1 . σY
= Cov (𝑥1,x1) /( σ𝑥1 . σY) + Cov (𝑥1, 𝑥2) /( σ𝑥1 . σY)
+ Cov (𝑥1, 𝑥3) /( σ𝑥1 . σY) + Cov (𝑥1,R) /( σ𝑥1 . σY)……………(1)
Where Cov (𝑥1, 𝑥1) = V(x1)
Cov(𝑥1,R) =0 ( Assumed)
Cov (𝑥1, 𝑥2) = r(x1, 𝑥2) σx1 . σ𝑥2
Thus the equation 1 becomes:
r (𝑥1, Y) = V(𝑥1)/σ𝑥1.σY + r(𝑥1, 𝑥2) σ𝑥1.σ𝑥2/ σ𝑥1.σY +r(𝑥1, 𝑥3)σ𝑥1.σ𝑥3/ σ𝑥1.σY
= σ𝑥1/σY + r(𝑥1, 𝑥2) σ𝑥2/σY +r(𝑥1, 𝑥3)σ𝑥3/σY ……………….(2)

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r (𝑥1, Y) = σ𝑥1/σY + r(𝑥1, 𝑥2) σx2/σY +r(𝑥1, 𝑥3)σ𝑥3/σY ……………….(2)
Where as per definition,
σ𝑥1/σY =a, the path coefficient from 𝑥1to Y
σ𝑥2/σY =b, the path coefficient from 𝑥2 to Y
σ𝑥3/σY =c, the path coefficient from 𝑥3 to Y
Thus
r (𝑥1, Y) = a + r(𝑥1, 𝑥2) b +r(𝑥1, 𝑥3) c …………………..(3)
The correlation between 𝑥1and Y may be partitioned into three components
(i) Due to direct effect of 𝑥1on Y which amounts to ‘a’
(ii) Due to indirect effect of 𝑥1 on Y via 𝑥2 which amounts to r(𝑥1, 𝑥2) b
(iii)Due to indirect effect of 𝑥1 on Y via 𝑥3 which amounts to r(𝑥1, 𝑥3) c

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Similarly one can work out the equations for r(𝑥2,Y), r(𝑥3,Y) and r(R,Y).
We thus finally get a set of simultaneous equations as given below
r (𝑥1, Y) = a + r(𝑥1, 𝑥2) b +r(𝑥1, 𝑥3) c …………………………………(A)
r (𝑥2, Y) = r(𝑥2, 𝑥1) a + b + r(𝑥2, 𝑥3) c …………………………………(B)
r (𝑥3, Y) = r(𝑥3, 𝑥1) a + r(𝑥3, 𝑥2) b + c …………………………………..(C)
r ( R, Y) = h
The residual effect can be obtained by the following formula
h2
= 1- a2
- b2
- c2
- 2r(𝑥1𝑥2)ab - 2r(𝑥1𝑥3)ac - 2r(𝑥2𝑥3)bc
Considering only the first three factors i.e. 𝑥1, 𝑥2 and 𝑥3, the simultaneous equations given
above can be presented in matrix notation as
r 𝑥1 Y
r 𝑥2 Y
r 𝑥3 Y
r𝑥1𝑥1 r𝑥1𝑥2 r𝑥1𝑥3
=
a
b
c
A = B.C C = B-1A

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 If the correlation coefficient between a casual factor and the effect is almost equal to its direct effect, than
correlation explains the true relationship and a direct selection through this trait will be effective.
 If the correlation coefficient is positive , but the direct effect is negative or negligible , the indirect effects
seem to be cause of correlation. In such situations, the indirect casual factors are to be considered
simultaneously for selection.
 If the direct effects are positive and high, but correlation coefficient is negative, in such conditions, direct
selection for such trait should be practiced to reduce the undesirable effects.
 The residual effect determine how best the causal factors account for the variability of the dependent factor. It
indicates that beside the character studied, there are some other attributes which contribute for yield.
Interpretation of path analysis results

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• Rice is one of the pivotal staple cereal crops.
• Hybrid rice technology has helped in breaking the yield barriers by
yielding 15-20% more than the best HYV’s.
• Information on association of characters, direct and indirect effects
contributed by each character towards yield add advantage in aiding
the selection process.
• Correlation and path analysis establish the extent of association
between yield and its components and also bring out relative
importance of their direct and indirect effects.

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Studying the character associations in
rice hybrids for yield improvement

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• Twenty one rice hybrids were evaluated in a Randomized Block
Design (RBD) with three replications.
• Statistical analyses for the above characters were done following
Singh and Chaudhary (1995) for correlation coefficient and
Dewey and Lu (1959) for path analysis.

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The results revealed that the estimates of genotypic coefficients were higher than
phenotypic correlation coefficients for most of the characters under study which indicated
strong inherent association between the characters which might be due to masking or
modifying effects of environment.

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Character
Days to 50 %
flowering
Plant height
(cm)
Panicle length
(cm)
No. of
productive
tillers plant-1
No. of filled
grains panicle-1
No. of chaffy
grains panicle-1 1000grain
weight (g)
Grain
yield plant-1
Days to 50 %
flowering
1.000
(1.000)
0.4576**
(0.5284)**
0.3580**
(0.4346)**
-0.1483
(-0.2790)*
0.3627**
(0.3689)**
0.1888
(0.1928)
0.1776
(0.1789)
-0.2212
(-0.4540)**
Plant height (cm) 1.000
(1.000)
0.4470**
(0.5641)**
-0.1870
(-1.0133)**
0.4883**
(0.4587)**
0.3178*
(0.2539)*
0.0476
(-0.0049)
-0.2586*
(-1.1903)**
Panicle length
(cm)
1.000
(1.000)
-0.2210
(-0.4341)**
0.2752*
(0.3245)**
0.4759**
(0.5683)**
0.2577*
(0.2982)*
-0.1963
(-0.6386)**
No. of
productive
tillers plant-1
1.000
(1.000)
0.0218
(-0.1951)
0.0280
(-0.1605)
0.0395
(-0.0033)
0.7125**
(0.9473)**
No. of filled
grains panicle-1
1.000
(1.000)
0.4088**
(0.3836)**
-0.0375
(-0.0613)
-0.2173
(-0.6229)**
No. of chaffy
grains panicle-1 1.000
(1.000)
0.2414
(0.2322)
-0.2250
(-0.6479)**
1000-grain
weight (g)
1.000
(1.000)
-0.0675
(-0.2357)
Grain yield
plant-1 (g)
1.000
(1.000)
** Significant at 1 per cent level * Significant at 5 per cent level
Figures in parenthesis are genotypic correlation coefficients
Blue box – positive significant
Orange box – negative significant
Estimates of phenotypic and genotypic correlation coefficients between yield and yield
component characters

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Traits Correlation (significant) Correlated with
Days to 50 per cent flowering positive plant height, panicle length and number of filled
grains per panicle
negative number of productive tillers per plant and grain
yield per plant
Plant height positive panicle length, number of filled grains per panicle,
number of chaffy grains per panicle
yield per plant
Panicle length positive number of filled grains per panicle, number of
chaffy grains per panicle and 1000 grain weight
yield per plant.
Number of productive tillers per plant positive grain yield per plant
Number of filled grains per panicle positive number of chaffy grains per panicle
negative grain yield per plant.
Number of chaffy grains per panicle Negative grain yield per plant.

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• As simple correlation does not provide the true contribution of the characters towards the
yield, these genotypic correlations were partitioned into direct and indirect effects through
path coefficient analysis.
• It allows separating the direct effect and their indirect effects through other attributes by
apportioning the correlations for better interpretation of cause and effect relationship.
• The estimates of path coefficient analysis are furnished for yield and yield component
characters.
• Among all the characters, the number of productive tillers per plant had the maximum
positive effect on grain yield followed by panicle length.
• On the other hand, negative direct effect on grain yield were recorded by number of chaffy
grains per panicle, number of filled grains per panicle, 1000 grain weight, days to 50 per
cent flowering and plant height.

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Character
Days to 50 %
flowering
Plant height
(cm)
Panicle length
(cm)
No. of productive
tillers plant-1
No. of filled
grains panicle-1
No. of chaffy
grains panicle-1
1000 grain
weight
(g)
r gy
Days to 50 % flowering
-0.0442
(-0.2080)
-0.0202
(-0.1099)
-0.0158
(-0.0904)
0.0066
(0.0580)
-0.0160
(-0.0767)
-0.0083
(-0.0401)
-0.0078
(-0.0372)
-0.2212
(-0.4540)**
Plant height (cm)
-0.0069
(0.4643)
-0.0150
(0.8786)
-0.0067
(0.4956)
0.0028
(-0.8903)
-0.0073
(0.4030)
-0.0048
(0.2231)
-0.0007
(-0.0043)
-0.2586*
(-1.1903)**
Panicle length (cm)
0.0598
(0.0535)
0.0746
(0.0694)
0.1669
(0.1230)
-0.0369
(-0.0534)
0.0459
(0.0399)
0.0794
(0.0699)
0.0430
(0.0367)
-0.1963
(-0.6386)**
No. of productive
tillers plant-1
-0.1117
(-0.4652)
-0.1409
(-1.6893)
-0.1665
(-0.7237)
0.7533
(1.6671)
0.0164
(-0.3252)
0.0211
(-0.2675)
0.0297
(-0.0055)
0.7125**
(0.9473)**
No. of filled grains
panicle-1
-0.0610
(-0.1929)
-0.0821
(-0.2398)
-0.0463
(-0.1697)
-0.0037
(0.1020)
-0.1682
(-0.5228)
-0.0688
(-0.2006)
0.0063
(0.3020)
-0.2173
(-06229)**
No. of chaffy grains
panicle-1
-0.0422
(-0.0760)
-0.0710
(-0.1001)
-0.1063
(-0.2241)
-0.0063
(0.0633)
-0.0913
(-0.1512)
-0.2233
(-0.3943)
-0.0539
(-0.0915)
-0.2250
(-0.6479)
1000-grain weight (g)
-0.0149
(-0.0297)
-0.0040
(0.0008)
-0.0217
(-0.0495)
-0.0033
(-0.0006)
0.0032
(0.0102)
-0.0203
(-0.0385)
-0.0841
(-0.1658)
-0.0675
(-0.2357)
Residual effect (Phenotypic) = 0.624
Residual effect (Genotypic) = -0.833
Figures in parenthesis are genotypic effects
Path analysis (diagonal are the direct effects and off diagonal are indirect effects)

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To find out the nature and magnitude of genetic variability, association among yield contributing
traits and direct and indirect effect of each of the component traits towards yield in germplasm
accessions of pea.

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Nineteen diverse germplasm accessions viz. VRPMR-9, VRPMR-10, VRP342, VRP-266, VRP-152,
VRP-229, VRP-360, VRP-305, VRP-401, VRP-231, VRP-200, VRP-324, PC-531, AP-1, AP-2,
VRP-38, VRP-392, VRP- 372, VRP-4 and five important commercial cultivars of pea viz. Arkel,
Kashi Nandani, Kashi Mukti, Kashi Shakti and Kashi Udai were grown manually in a randomized
block design with three replications.
The correlation coefficients were computed as per AI-Jibouri et al. (1958), while path analysis was
carried out following the method as suggested by Dewey and Lu (1959).

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To find the nature of correlation among various
characters and their direct and indirect influence
on seed cotton yield of Gossypium hirsutum L.

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• During kharif (2018) 20 cotton genotypes were evaluated in Randomized
Complete Block Design with three replications and spacing of 90×30 cm.
• Correlation coefficients between different characters were worked out as per
Singh and Narayanan (1993). Phenotypic correlation coefficients were
further partitioned into direct and indirect effects by path analysis as
suggested by Dewey and Lu (1959).

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PH NM NS SLG SLFPH INL NBP BW UHML FS MIC GOT SI LI SCY
PH 1.000 0.379** 0.573** 0.285* 0.592** 0.124 0.389** 0.218 -0.104 -0.137 0.084 0.166 0.333** 0.283* 0.299*
NM 1.000 0.105 -0.140 0.295* -0.153 0.002 0.004 -0.077 0.172 0.015 -0.297* 0.041 -0.150 0.082
NS 1.000 0.319* 0.399** 0.109 0.483** 0.344** -0.047 0.017 0.023 0.021 0.344** 0.055 0.501**
SLG 1.000 0.124 0.251* 0.260* 0.314* -0.039 -0.087 0.147 0.086 0.274* 0.094 0.230
SLFPH 1.000 0.258* 0.237 0.215 -0.109 -0.052 0.237 0.120 0.058 0.179 0.031
INL 1.000 0.491* 0.116 -0.114 -
0.328*
-
0.088
0.195 0.371 0.188 0.535**
NBP 1.000 0.431** -0.107 -0.046 -
0.050
0.295* 0.487** 0.311* 0.520**
BW 1.000 -
0.331**
0.137 -
0.237
0.331 * 0.134 0.242 0.209
UHML 1.000 0.243 -
0.027
-0.226* -0.053 -0.086 0.002
FS 1.000 -
0.125
-
0.366**
-0.074 -0.221 -0.162
MIC 1.000 -0.104 -0.114 0.022 -0.038
GOT 1.000 0.016 0.780** 0.057
SI 1.000 0.330* 0.495**
LI 1.000 0.142
Phenotypic correlation among 15 character in advanced lines of cotton (Gossypium hirsutum L.)

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TRAIT CORRELATION (SIGNIFICANT) CORRELATED WITH
SEED COTTON YIELD POSITIVE plant height (0.299), no. of sympodia per plant (0.501), inter nodal length (0.535), no. of bolls per
plant (0.520) and seed index (0.495)
PLANT HEIGHT POSITIVE No. of monopodia per plant (0.379), no. of sympodia per plant (0.573), sympodial length at ground
level (0.285), sympodial length at fifty per cent of plant height (0.592), no. of bolls per plant (0.389),
seed index (0.333) and lint index (0.283).
NUMBER OF MONOPODIA POSITIVE sympodial length at 50% of plant height (0.295).
NUMBER OF SYMPODIA POSITIVE sympodial length at ground level (0.319), sympodial length at 50% of plant height (0.399), no. of
bolls per plant (0.483), boll weight (0.344) and seed index (0.344).
SYMPODIAL LENGTH AT GROUND
LEVEL
POSITIVE internodal length (0.251), No. of bolls per plant (0.260), boll weight (0.314) and seed index (0.274).
SYMPODIAL LENGTH AT 50%
PLANT HEIGHT
POSITIVE inter-nodal length (0.258).
NUMBER OF BOLLS POSITIVE boll weight (0.431), ginning outturn (0.295), seed index (0.487) and lint index (0.311).
BOLL WEIGHT POSITIVE Ginning outturn (0.331).
UPPER HALF MEAN
LENGTH (UHML)
NEGATIVE ginning outturn (-0.226).
FIBRE STRENGTH NEGATIVE ginning outturn (- 0.366).
GINNING OUTTURN POSITIVE lint index (0.780).
SEED INDEX POSITIVE lint index (0.330)
INTERNODAL LENGTH NEGATIVE fibre strength.

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PH NM NS SLG SLFPH IND NBP BW UHML FS MIC GOT SI LI rSCY
PH -0.1438 -0.0546 -0.0824 -0.0411 -0.0851 -0.0178 -0.0560 -0.0314 0.0149 0.0198 -0.0120 -0.0239 - 0.0479 -0.0407 0.2988*
NM 0.0687 0.1810 0.0191 -0.0253 0.0535 -0.0276 0.0004 0.0007 -0.0139 0.0312 0.0027 -0.0537 0.0075 -0.0272 0.0819
NS 0.2423 0.0446 0.4228 0.1349 0.1685 0.0459 0.2044 0.1455 -0.0200 0.0072 0.0095 0.0090 0.1454 0.0232 0.5010**
SLG -0.0096 0.0047 -0.0107 -0.0336 -0.0042 -0.0086 -0.0087 -0.0106 0.0013 0.0029 0.0049 -0.0029 -0.0092 -0.0032 0.2303
SLFPH -0.0300 -0.0150 -0.0202 -0.0063 -0.0507 0.0131 -0.0120 -0.0109 0.0055 0.0026 -0.0120 -0.0061 -0.0029 -0.0091 0.0314
IND 0.0474 -0.0585 0.0417 0.0985 -0.0988 0.0383 0.1881 0.0444 -0.0438 -0.1258 -0.0339 0.0748 0.1424 0.0722 0.5350**
NBP 0.0296 0.0002 0.0368 0.0198 0.0181 0.0374 0.0762 0.0328 -0.0081 -0.0035 -0.0038 0.0225 0.0371 0.0237 0.5201**
BW 0.0174 0.0003 0.0274 -0.0250 0.0172 0.0092 0.0343 0.0797 -0.0264 0.0109 -0.0189 0.0264 0.0107 0.0193 0.2085
UHML -0.0139 -0.0103 -0.0063 -0.0053 -0.0146 -0.0153 -0.0143 -0.044 0.1338 0.0325 -0.0037 -0.0302 -0.0071 -0.0115 0.0022
FS 0.0164 -0.0205 -0.0020 0.0103 0.0062 0.0391 0.0055 -0.0163 -0.0289 -0.1192 0.0149 0.0436 0.0088 0.0263 -0.1616
MIC 0.0033 0.0006 0.0009 -0.0058 0.0093 -0.0035 -0.0020 -0.0093 -0.0010 -0.0049 0.0392 -0.0041 -0.0044 0.0009 -0.0377
GOT -0.0001 0.0002 0.0000 0.0000 -0.0001 -0.0001 -0.0002 -0.0002 0.0001 0.0002 0.0000 -0.0005 0.0000 -0.0004 0.0567
SI 0.0719 0.0089 0.0742 0.0592 0.0125 0.0802 0.1051 0.0289 -0.0115 -0.0159 -0.0245 0.0035 0.2159 0.0712 0.4953**
LI -0.0006 0.0003 -0.0001 -0.0002 -0.0004 -0.0004 -0.0007 -0.0005 0.0002 0.0005 0.0000 -0.0017 -0.0007 -0.0022 0.1423
Phenotypic path analysis for 15 yield, yield attributing and fibre quality traits in advanced lines of cotton (Diagonal
are direct effects and off diagonal are indirect effects)
Orange colour indicates negative direct effect
Blue colour indicates positive direct effects
Residual effect = 0.663, ** Significant at 1% (p = 0.01)

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53
• Path analysis revealed that no. of sympodia per plant (0.422) had highest direct
effect on seed cotton yield.
• Traits like plant height, sympodial length at ground level, sympodial length at
50% plant height, fibre strength, ginning outturn and lint index showed
negative direct effect on seed cotton yield.
• No. of monopodia per plant, no. of sympodia, inter-nodal distance, no. of bolls
per plant, boll weight, UHML, micronaire, seed index exhibited low levels of
direct effect on seed cotton yield.
• In conclusion, seed cotton yield being a complex polygenic character, direct
selection based on these traits would not yield fruitful results.

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• Correlation simply measures the association of characters but it doesn’t
indicates the relative contribution of causal factors to yield.
• The component characters are themselves interrelated and often affect their
direct relationship with seed yield.
• Path coefficient analysis permits the separation of the direct effects from
indirect effects through other related characters by partitioning the correlation
coefficient.
• Correlation and path analysis both are very effective techniques for crop
improvement through indirect selection for yield.
Conclusion

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@sonulangaya
Acquaah, G. (2009). Principles of plant genetics and breeding. John Wiley & Sons.
Aman, J., Bantte, K., Alamerew, S. and Sbhatu, D.B. (2020). Correlation and path coefficient analysis of yield and yield components of quality protein maize (Zea mays L.)
hybrids at Jimma, western Ethiopia. International Journal of Agronomy, 9(6): 51-57
Ambika, S. Manonmani, V., and Somasundaram, G. (2014). Review on effect of seed size on seedling vigour and seed yield. Research Journal of Seed Science, 7(2): 31-38.
Asuero, A.G., Sayago, A. and Gonzalez, A.G. (2006). The correlation coefficient: An overview. Critical reviews in analytical chemistry, 36(1): 41-59.
Babu, V.R., Shreya, K., Dangi, K.S., Usharani, G., and Shankar, A.S. (2012). Correlation and path analysis studies in popular rice hybrids of India. International Journal of
Scientific and Research Publications, 2(3): 1-5.
Bal, R. S. and Kumar, A. (2014). Studies on the epidemiology of white rust and Alternaria leaf blight and their effect on the yield of Indian mustard. African Journal of
Agricultural Research, 9(2): 302-306.
Barrett, J.P. (1974). The coefficient of determination—some limitations. The American Statistician, 28(1):19-20.
Chaudhary, B.D. and Singh, R.K. (1985). Biometrical methods in quantitative genetic analysis. Kalyani publishers.
55
References:

UNIVERSITY HISAR
@sonulangaya
Fisher, RA (1918). The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society. 52: 399–433.
Gogtay, N.J. and Thatte, U.M. (2017). Principles of correlation analysis. Journal of the Association of Physicians of India, 65(3): 78-81.
Kearsey, M.J., Pooni, H.S., and Joshi, A. (1997). The Genetical Analysis of Quantitative Traits. Journal of Genetics, 76(1): 93-96.
Lodhi, B., Avtar, N.T.R. and Singh, A. (2016). Genetic variability, association and path analysis in Indian mustard (Brassica juncea). Journal of Oilseed Brassica, 1(1): 26-31.
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Pujer, S.K., Siwach, S.S., Sangwan, R.S., Sangwan, O., and Deshmukh, J. (2014). Correlation and path coefficient analysis for yield and fibre quality traits in upland cotton
(Gossypium hirsutum L). Journal Cotton Research Development, 28(2): 214-216.
Rodgers, J.L. and Nicewander, W.A. (1998). Thirteen ways to look at the correlation coefficient. The American Statistician, 42: 59–66.
Shruti, H.C. Sowmya, J.M. Nidagundi, R. Lokesha, B. Arunkumar and Shankar M. Murthy. (2020). Correlation and path coefficient analysis for seed cotton yield, yield
attributing and fibre quality traits in cotton (Gossypium hirsutum L.).International Journal of Current Microbiology and Applied Sciences. 9(2): 200-207.
Weldon, K.L. (2000). A simplified introduction to correlation and regression. Journal of Statistical Education: Vol. 2000.
56

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For any queries, feel free to contact:
Ankit Dhillon
M.S. Genetics & Plant Breeding
CCS HAU, HISAR, (125004)
Mail address: ankitdhill@gmail.com
Contact no.: +918901133524
57

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