2 gpb 621 analysis of continuous variation

Analysis of Continuous Variation
Class - 2
Dr. K. SARAVANAN
Professor
Department of Genetics and Plant Breeding
Faculty of Agriculture
Annamalai University
GPB 621 – PRINCIPLES OF QUANTITATIVE GENETICS

.
• The continuous variation can be analysed only by estimating the
biometrical quantities like
• Mean
• Variance
• Covariance etc.,
Dr. K. Saravanan, GPB, AU

.
Mean of the Distribution
(i). Arithmetic mean
• ( a first degree statistics )
x
N
• Mean = X  Where, ∑x = sum of individual observations,
N = total number of observations.
(ii). Mode – Most frequent value in the population
(iii). Median – The middle value in an array of observations
Frequency Distribution
•
• The raw data is grouped into classes and the frequency in each class is
recorded. When the data
is calculated
are expressed in a frequency distribution, the mean
fx
X 
Where, f = class frequency x = class value
N

• Measure
.
s of dispersion (Second degree statistics)
• Range
• Mean Deviation
• Standard Deviation
• Variance
• Standard Error
• Coefficient of Variation

.
• Range
• Range is the difference between the lowest and the highest value present in
the observations in a sample
• Mean Deviation or
• Mean deviation is
the mean
Mean deviation =
Average Deviation
the average of deviation of individual
 ( x x)
observations from
N
Where, x is the individual observation, = is the mean
x
 fd
Mean deviation by frequencies =
N
Where, f = class frequency, d = deviation of class value from the mean

.
• Standard
SD 
Deviation
x)2
(
 x 2

N
SD 
Variance
N  1
• Variance
• Variance is defined as the average of squared deviations of all the individual
observations from the mean.
x)2
(
 x 2

N
Variance 
N  1
fd 2
• Variance by frequencies =
N

.
Standard Error
•
• It is the measure of the mean difference between sample estimate of mean
and the population parameter
present in a sample.
(μ)i.e. it is the measure of uncontrolled
variation
Standard Deviation
SE 
N
• Coefficient of Variation
Standard Deviation
CV  X 100
Mean

.
• Higher order Degree Statistics
n(Y )3
• Skewness = 3
(n  1)(n  2)
n(n 1)(Y )4
3(n 1)2

• Kurtosis = 4
(n  1)(n  2)(n  3) (n  2)(n  3)
Where Y = Raw data
μ = Mean
σ = SD
n = Number of observations

.
Problem 1
• The height of 30 rice genotypes is given below. Workout the
biometrical quantities viz., mean, variance, standard deviation,
standard error and coefficient of variation.
Genotypes Plant height (cm) Genotypes Plant height (cm) Genotypes Plant height (cm)
1 115.9 11 102.5 21 98.6
2 120.8 12 111.5 22 107.3
3 101.2 13 125.2 23 115.6
4 106.7 14 104.9 24 128.3
5 113.3 15 87.7 25 93.7
6 110.7 16 110.6 26 108.3
7 96.9 17 102.7 27 112.6
8 117.9 18 98.3 28 100.5
9 128.1 19 120.6 29 115.4
10 97.7 20 89.7 30 96.7

.
x
N
(115.9 + 120.8 + …… + 96.7)
(a) Arithmetic mean = X 
=
=
/ 30
3239.90 / 30 = 108.00
(b) Frequency distribution mean =
fx
X 
N

.
(f)
Range Class value (x) Frequency fx d d2
fd fd2
85 - 90 87.5
90 - 95 92.5
95 - 100 97.5
100 - 105 102.5
105 - 110 107.5
110 - 115 112.5
115 - 120 117.5
120 - 125 122.5
125 - 130 127.5
Total

.
(f)
Frequency mean = 108.33
Variance by frequency distribution = 126.81
Range Class value (x) Frequency fx d d2 fd fd2
85 - 90 87.5 2 175 -20.83 433.89 -41.66 867.78
90 - 95 92.5 1 92.5 -15.83 250.59 -15.83 250.59
95 - 100 97.5 5 487.5 -10.83 117.29 -54.15 586.44
100 - 105 102.5 5 512.5 -5.83 33.99 -29.15 169.94
105 - 110 107.5 3 322.5 -0.83 0.69 -2.49 2.07
110 - 115 112.5 5 562.5 4.17 17.39 20.85 86.94
115 - 120 117.5 4 470 9.17 84.09 36.68 336.36
120 - 125 122.5 2 245 14.17 200.79 28.34 401.58
125 - 130 127.5 3 382.5 19.17 367.49 57.51 1102.47
30 3250 3804.167
mean 108.3333 fd2/N 126.81

.
• Range = 87.7 to 128.3
• Variance = 118.85
• Standard deviation = 10.90
• Standard error = 1.99
• CV = (10.90/108 )x 100 = 10.09 %

V
ARIATIO.
N ASSOCIATED WITH POLYGENIC RAITS
• Phenotype = Genotype + Environment
Co-efficient of Variations
• For comparing the variability of different populations or between characters
of the same population, the estimation of co-efficient of variation is required.
The formulae for estimating the phenotypic co-efficient of variation (PCV) and
genotypic co-efficient of variation
follows.
(GCV) as suggested by Burton (1952) are as
Genotypic variance
Phenotypic variance
PCV = X 100 GCV = X 100
General mean General mean
• From Non Replicated data
GCV  SDSE
X100
PCV  SD
X100 X
X

.
• Estimation
population
of environmental variation from Non-segregating
Vp1 Vp 2
VE 
Parents population 2
Vp1 Vp 2 VF 1

VE
in
F1 is also included in the experiment 3
• Partitioning of environmental variation segregating population
(Goulden, 1952)
•
•
Segregating generations like F2, B1, B2 M2, M3 etc.,
Phenotypic variance = VF2, VB1, VB2 VM2, VM3 etc.,
Vp1 Vp 2 2VF 2
VE 
• Environmental Variance =
(Empig et el., 1972)
4
• Genotypic Variance VG = VPh - VE

.
Interpretation of Variability studies
• GCV is higher than PCV
• It indicates that there is little influence of environment on the expression of
character selection for improvement of such character will be rewarding.
PCV is higher than GCV
• It means that the apparent variation is not only due to genotypes but also due
to the influence of environment. Selection for such traits sometimes may be
misleading.
ECV is higher than PCV & GCV
•
•
• It indicates that environment is playing a significant role in the expression of
such character. Selection for the improvement of such character will be
ineffective.

.
Problem 2
• Partitioning of genotypic component from segregating generations : An
experiment was conduced with 4 generations of a cross namely P1, P2, F1
and F2. Following are the
the
data obtained for plant height from these
generations.
variances.
Workout phenotypic, genotypic and environmental
P1 72.8 70.3 73.4 71.8 70.8 73.1 72.3 71.3 72.2 71.3
P2 62.8 60.3 63.8 64.3 63.0 61.4 64.8 62.1 64.3 63.9
F1 70.3 69.3 68.3 70.1 72.1 70.8 71.3 69.8 70.4 71.2
F2 63.4 72.8 82.1 60.8 69.3 84.1 80.2 72.8 70.6 80.9
69.8 71.3 70.4 80.3 67.4 70.4 79.4 60.3 82.1 73.4
62.3 85.2 72.1 79.5 80.3 68.3 72.1 80.3 79.8 71.3

SD VARIANCE
Vp1 Vp 2 VF 1
VE 
Phenotypic variance = VF2 49.82 1.03+2.08+1.17/3 = 1.43
3
Genotypic Variance VG = VPh - VE 49.82 – 1.43 = 48.39
.
P1 72.8 70.3 73.4 71.8 70.8 73.1 72.3 71.3 72.2 71.3 1.013 1.03
P2 62.8 60.3 63.8 64.3 63 61.4 64.8 62.1 64.3 63.9 1.442 2.08
F1 70.3 69.3 68.3 70.1 72.1 70.8 71.3 69.8 70.4 71.2 1.083 1.17
F2 63.4 72.8 82.1 60.8 69.3 84.1 80.2 72.8 70.6 80.9
69.8 71.3 70.4 80.3 67.4 70.4 79.4 60.3 82.1 73.4
62.3 85.2 72.1 79.5 80.3 68.3 72.1 80.3 79.8 71.3 7.058 49.82

.
:
Problem 3 ESTIMATION OF PCV AND GCV – Non replicated Data
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
G1 79.67 82.00 112.00 70.45 19.00 16.67 20.60 116.05 6.93 3.01
G2 62.67 66.00 96.00 67.33 18.33 16.33 18.20 96.85 5.23 3.21
G3 76.67 79.00 109.00 65.19 15.47 13.47 21.73 120.16 7.81 2.42
G4 84.67 88.00 118.00 65.87 15.60 13.60 21.17 112.22 7.94 2.60
G5 85.33 87.67 117.67 62.71 18.20 16.20 22.67 131.84 9.75 2.50
G6 84.33 88.00 118.00 70.09 16.73 14.73 22.47 95.68 9.50 2.56
G7 70.33 74.00 104.00 69.54 14.60 12.60 22.83 115.72 8.06 8.08
G8 70.33 74.00 104.00 61.01 14.40 47.80 21.27 120.86 8.12 2.14
G9 82.67 86.00 116.00 69.45 17.73 15.73 21.30 162.80 7.16 3.08
G10 91.67 95.00 125.00 82.34 18.73 16.73 22.20 110.56 7.23 2.33
G11 92.67 97.00 127.00 73.44 18.53 16.53 23.17 107.32 6.28 2.70
G12 98.67 100.00 130.00 76.45 10.80 8.80 28.33 130.13 9.15 2.17
G13 101.33 105.00 135.00 74.31 16.54 14.53 20.27 145.92 5.99 2.14
G14 110.33 114.00 144.00 97.66 15.47 13.47 21.27 138.28 7.16 2.38
G15 84.33 88.00 118.00 70.09 16.73 14.73 22.47 95.68 9.50 2.56

ESTIMATION
. OF PCV AND GCV – Non replicated Data
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
G1 79.67 82.00 112.00 70.45 19.00 16.67 20.60 116.05 6.93 3.01
G2 62.67 66.00 96.00 67.33 18.33 16.33 18.20 96.85 5.23 3.21
G3 76.67 79.00 109.00 65.19 15.47 13.47 21.73 120.16 7.81 2.42
G4 84.67 88.00 118.00 65.87 15.60 13.60 21.17 112.22 7.94 2.60
G5 85.33 87.67 117.67 62.71 18.20 16.20 22.67 131.84 9.75 2.50
G6 84.33 88.00 118.00 70.09 16.73 14.73 22.47 95.68 9.50 2.56
G7 70.33 74.00 104.00 69.54 14.60 12.60 22.83 115.72 8.06 8.08
G8 70.33 74.00 104.00 61.01 14.40 47.80 21.27 120.86 8.12 2.14
G9 82.67 86.00 116.00 69.45 17.73 15.73 21.30 162.80 7.16 3.08
G10 91.67 95.00 125.00 82.34 18.73 16.73 22.20 110.56 7.23 2.33
G11 92.67 97.00 127.00 73.44 18.53 16.53 23.17 107.32 6.28 2.70
G12 98.67 100.00 130.00 76.45 10.80 8.80 28.33 130.13 9.15 2.17
G13 101.33 105.00 135.00 74.31 16.54 14.53 20.27 145.92 5.99 2.14
G14 110.33 114.00 144.00 97.66 15.47 13.47 21.27 138.28 7.16 2.38
G15 84.33 88.00 118.00 70.09 16.73 14.73 22.47 95.68 9.50 2.56
MEAN 85.04 88.24 118.24 71.73 16.46 16.80 22.00 120.00 7.72 2.93
SD 12.63 12.64 12.64 8.97 2.18 8.83 2.15 19.17 1.35 1.46
SQRT(15) 3.87 3.87 3.87 3.87 3.87 3.87 3.87 3.87 3.87 3.87
SE 3.26 3.26 3.26 2.32 0.56 2.28 0.56 4.95 0.35 0.38
PCV 14.85 14.32 10.69 12.51 13.26 52.55 9.78 15.97 17.51 50.00
GCV 11.01 10.62 7.93 9.28 9.84 38.98 7.26 11.85 12.99 37.09

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2 gpb 621 analysis of continuous variation

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