Summary
This blog explains the concept and importance of genetic parameters in plant breeding, focusing on how traits are influenced by genetic and environmental factors.
It highlights the use of Randomized Complete Block Design (RCBD) to reduce experimental error and improve precision in genotype evaluation.
The article details assumptions, randomization, ANOVA, and statistical measures such as variability, variance components, GCV, PCV, heritability, and genetic advance.
Interpretation of different combinations of these parameters is discussed to guide effective selection strategies.
A solved maize example demonstrates practical calculation and interpretation of results.
Finally, the blog outlines step-by-step procedures to estimate genetic parameters using the Agri Analyze platform.
1.Introduction
In a general statistical context, a parameter refers to a numerical characteristic or attribute that describes a population.
It can be a fixed value or an unknown quantity that helps to describe or summarize a specific aspect of a population.
Genetic Parameter is a statistical measure that quantifies the genetic contributions to traits within a population of an organism.
Genetic parameter estimation in plant breeding involves quantifying various genetic components that influence traits of interest, such as yield, disease resistance or quality attributes.
These parameters provide critical insights into the genetic basis of these traits, informing breeding decisions aimed at improving crop varieties.
Genetic parameters encompass a range of measurements, including heritability, genetic variance and genetic advance.
Heritability indicates the proportion of phenotypic variation in a trait that is attributable to genetic factors, guiding breeders on the potential response to selection.
Genetic variance quantifies the variability in traits due to genetic differences among individuals, crucial for understanding trait inheritance patterns.
Genetic advance measures the expected improvement from selection, facilitating efficient breeding strategies.
Understanding these genetic parameters empowers plant breeders to develop improved cultivars tailored to specific agricultural needs, enhancing crop productivity, resilience and quality.
These parameters are estimated through statistical analyses of trait data collected from breeding experiments, utilizing methodologies such as variance component analysis and heritability estimation.
The experiments are laid in various experimental designs that ensures valid and interpretable results through randomization, replication and control. Designs range from simple completely randomized designs to complex ones like randomized complete block designs (RCBD), factorial designs and Latin squares.
These designs help isolate variable effects and understand their interactions.
2. Randomized Complete Block Design
Randomized Complete Block Design (RCBD) is a fundamental experimental design used extensively in plant breeding research to control for variability within experimental units.
In RCBD, each block contains all genotypes, with random assignment within blocks, controlling for variability and ensuring comprehensive genotype comparison. Hence, it is called "Randomized Complete Block Design."
This design reduces experimental error and enhances the precision of genotype mean comparisons by accounting for block-to-block variability.
It is essential for drawing valid inferences about genotype effects while minimizing the influence of extraneous factors.
2.1 When RCBD is used?
The RCBD is employed in agricultural research under specific conditions to achieve reliable and precise results.
Here are scenarios when RCBD is used: heterogeneous experimental units, known gradients, multiple genotypes, limited experimental units, small-scale trials etc.
2.2 Assumptions of RCBD
The RCBD operates under several key assumptions to ensure valid and reliable results: homogeneity within blocks, independence of observations, additivity of effects, random assignment, normality, equal variance, no missing data etc.
2.3 Randomization steps in RCBD
Randomization in a Randomized Complete Block Design (RCBD) is a crucial step to ensure unbiased allocation of treatments to experimental units within each block.
Here are the detailed steps for randomization in RCBD:
- Identify the Treatments
- Define the Blocks
- Assign Treatments Randomly within Each Block
- Record the Assignment
- Repeat for All Blocks
- Verify Randomization
- Create a Layout Plan
2.4 Analysis of Variance (ANOVA) for RCBD
In a RCRD, the Analysis of Variance (ANOVA) model provides a comparison by partitioning of variance due to various sources.
It is used to analyze the data and test the significance of genotype effects.
The statistical model for ANOVA in RCBD is as under:
\[
Y_{ij} = \mu + g_i + r_j + \varepsilon_{ij}
\]
Where,
\(Y_{ij}\) = An observation of \(i^{th}\) genotype in \(j^{th}\) replication
\(\mu\) = General mean
\(g_i\) = The effect due to \(i^{th}\) genotype
\(r_j\) = The effect due to \(j^{th}\) replication
\(\varepsilon_{ij}\) = Uncontrolled variation associated with \(i^{th}\) genotype in \(j^{th}\) replication
\(i\) = Number of genotypes \((1, 2, \ldots, g)\)
\(j\) = Number of replications \((1, 2, \ldots, r)\)
Here's a brief outline of the ANOVA procedure for a RCBD:
| Source of variation |
DF |
Sum of Squares |
Mean sum of squares |
Cal. F |
| Replication |
\(r - 1\) |
\[
\sum_{j=1}^{r} Y_{.j}^2
-
\frac{\left(\sum_{i=1}^{g}\sum_{j=1}^{r} Y_{ij}\right)^2}{rg}
\]
|
\[
M_r = \frac{SS_r}{DF_r}
\]
|
\[
\frac{M_r}{M_e}
\]
|
| Genotype |
\(g - 1\) |
\[
\sum_{i=1}^{g} Y_{i.}^2
-
\frac{\left(\sum_{i=1}^{g}\sum_{j=1}^{r} Y_{ij}\right)^2}{rg}
\]
|
\[
M_g = \frac{SS_g}{DF_g}
\]
|
\[
\frac{M_g}{M_e}
\]
|
| Error |
\((r - 1)(g - 1)\) |
By subtraction |
\[
M_e = \frac{SS_e}{DF_e}
\]
|
|
| Total |
\(rg - 1\) |
\[
\sum_{i=1}^{g}\sum_{j=1}^{r} Y_{ij}^2
-
\frac{\left(\sum_{i=1}^{g}\sum_{j=1}^{r} Y_{ij}\right)^2}{rg}
\]
|
|
|
Here the null hypothesis is set as all genotypes means are equal and the alternative hypothesis is at least one genotype pair differs significantly.
Significance of the mean sum of squares due to replications (Mr) and genotypes (Mg) is tested against error mean squares (Me).
A comparison of the calculated F (Mg/Me) with the critical value of F corresponding to genotype degrees of freedom and error degrees of freedom gives the idea to accept or reject the null hypothesis.
2.5 Different statistic related to RBD design
2.5.1 Standard error of mean (SEm):
\[
SE_m = \sqrt{\frac{MSE}{r}}
\]
2.5.2 Coefficient of Variation (CV%):
\[
CV\% = \frac{\sqrt{MSE}}{\bar{Y}_{..}} \times 100
\]
2.5.3 Critical difference at 5% level of significance:
\[
CD_{0.05} = t_{(0.05,\,ne)} \times \sqrt{2} \times SE_m
\]
2.6 What if replication source of variation found significant in RCBD?
2.6.1 Reasons for Significant Replication in Plant Genotype Experiments
This includes environmental micro-variation (soil heterogeneity, microclimatic conditions, etc.,), management and cultural practices (inconsistent application of treatments, differences in planting depth and spacing etc.,),
biotic factors (pest and disease pressure, microbial activity etc.,), phenotypic plasticity (adaptive responses), measurement and sampling error (human error in measurement, instrument calibration etc.,)
2.6.2 Addressing Significant Replication in Plant Genotype Experiments
This can be achieved by improving experimental design (enhance block homogeneity, increase number of replicates etc.,),
standardize cultural practices (consistent treatment application, uniform planting techniques etc.,), control environmental factors (monitor and manage microclimate, soil management etc.,),
regular monitoring for biotic factors (pest and disease management, microbial inoculants etc.,),
refine measurement techniques (training and calibration, automated measurements etc.,)
3 CALCULATION OF SIMPLE MEASURES OF VARIABILITY
Simple measures of variability include range, standard deviation, variance, standard deviation and coefficient of variation.
These measures help in understanding the distribution and spread of data, which are essential for statistical analysis and interpreting the variability within a data set for given character.
3.1 Range
The difference between the maximum and minimum values in a data set.
Provides a quick sense of the spread of the data, but is sensitive to outliers.
Range = Maximum Value - Minimum Value
3.2 Standard Deviation (SD):
A measure of the average distance of each data point from the mean. Indicates how spread out the data points are around the mean.
A smaller SD indicates data points are close to the mean, while a larger SD indicates they are more spread out.
\[
SD = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}
\]
Where, xi is each data point, x ̅ is the mean of the data and n is the number of data points
3.3 Variance:
The average of the squared differences from the mean.
It measures the dispersion of data points. It's the square of the standard deviation.
\[
\text{Variance} = \frac{\sum (x_i - \bar{x})^2}{n - 1}
\]
3.4 Coefficient of Variation (CV):
The ratio of the standard deviation to the mean, expressed as a percentage.
It standardizes the measure of variability by comparing the standard deviation relative to the mean. Useful for comparing the degree of variation between different data sets,
especially those with different units or widely different means.
\[
CV\% = \left( \frac{SD}{\bar{x}} \right) \times 100
\]
4. Variance Components
In the context of plant breeding and genetics, ANOVA (Analysis of Variance) is often used to partition the observed variance into different components:
phenotypic variance, genotypic variance, and environmental variance.
These components are crucial for understanding the underlying variability and for estimating the respective coefficients of variation.
4.1 Phenotypic Variance (\(\sigma_p^2\)):
It represents the total observable variance in a trait. Includes both genetic and environmental components and is derived from the total mean square in ANOVA.
\[
\sigma_p^2 = \sigma_g^2 + \sigma_e^2
\]
Where,
\(\sigma_p^2\) = Phenotypic variance
\(\sigma_g^2\) = Genotypic variance
\(\sigma_e^2\) = Error variance
4.2 Genotypic Variance (\(\sigma_g^2\)):
It represents the portion of the total variance attributed to genetic differences among genotypes. It is derived from the mean square between genotypes in ANOVA.
\[
\sigma_g^2 = \frac{M_g - M_e}{r}
\]
Where,
\(\sigma_g^2\) = Genotypic variance
\(M_g\) = Genotypic mean sum of square of the character
\(M_e\) = Error mean sum of square of the character
\(r\) = Number of replications
4.3 Environmental Variance (\(\sigma_e^2\)):
It represents the portion of the total variance attributed to environmental differences affecting genotypes. It is derived from the mean square within genotypes (error mean square) in ANOVA.
\[
\sigma_e^2 = M_e
\]
4.4 What if genotypic variance is negative?
If σ2g (genotypic variance) is negative, it indicates that the calculated value is not feasible since variance, by definition, cannot be negative.
This situation typically arises due to small sample size, large experimental error, incorrect data or calculation etc.
To address this issues increase replications, improve experimental design, re-evaluate data etc.
In summary, a negative genotypic variance suggests the need for a reassessment of the experimental design, data quality and analysis methods.
5. COEFFICIENTS OF VARIATION
5.1 Phenotypic Coefficient of Variation (PCV):
Measures the extent of phenotypic variability relative to the mean of the trait.
\[
PCV(\%) = \sqrt{\frac{\sigma_p^2}{\bar{X}}} \times 100
\]
Where,
\(\bar{X}\) = General mean of the character under study
\(\sigma_p^2\) = Phenotypic variance
5.2 Genotypic Coefficient of Variation (GCV):
Measures the extent of genotypic variability relative to the mean of the trait.
\[
GCV(\%) = \sqrt{\frac{\sigma_g^2}{\bar{X}}} \times 100
\]
Where,
\(\bar{X}\) = General mean of the character under study
\(\sigma_g^2\) = Genotypic variance
GCV and PCV were categorized as low, moderate and high as follows:
| Range |
Category |
| 0–10% |
Low |
| 10–20% |
Moderate |
| 20% and above |
High |
5.3 How to Interpret the Relative Values of GCV, PCV and ECV?
The relative values of Genotypic Coefficient of Variation (GCV), Phenotypic Coefficient of Variation (PCV), and Environmental Coefficient of Variation (ECV) provide insights into the sources and magnitude of variability within a genetic population.
- GCV is High Compared to PCV: PCV typically exceeds or equals GCV since it includes both genetic and environmental variance.
If GCV surpasses PCV, this suggests a calculation error; review for accuracy.
- PCV is High Compared to GCV: PCV is higher than GCV, indicating substantial environmental influence on the trait.
The difference suggests significant environmental variance.Despite genetic variability, breeders must minimize environmental effects to select effectively based on genetic potential.
- ECV is Higher than GCV: The trait is heavily influenced by environmental factors, with minimal genetic variability. Phenotypic selection may be difficult.
Introducing new genetic material could help increase genetic variability and improve selection efficiency for the trait.
5.4 How to Interpret Combination of Values of GCV and PCV
-
High GCV and High PCV:
This indicates that the trait is strongly influenced by genetic factors, but environmental factors also play a significant role. Despite the environmental influence, the high genetic variability suggests good potential for improvement through selection. Focus on stabilizing the environment to harness the genetic potential effectively. Breeders can make significant progress by selecting superior genotypes.
-
High GCV and Low PCV:
This suggests that the trait is predominantly influenced by genetic factors, with minimal environmental impact. The high genetic variability is not masked by environmental effects. This is an ideal situation for breeders. Selection will be highly effective since the phenotypic performance directly reflects the genetic potential.
-
Low GCV and High PCV:
This indicates that the trait is largely influenced by environmental factors, with little genetic variability. The high phenotypic variability is mostly due to environmental effects. Selection might be less effective due to the low genetic variability. Breeders may need to focus on improving environmental conditions or management practices to reduce the environmental variance. Additionally, exploring wider genetic bases or introducing new germplasm could be considered to increase genetic variability.
-
Low GCV and Low PCV:
This suggests that the trait is relatively stable with minimal influence from both genetic and environmental factors. The lack of variability might indicate that the trait is either highly conserved or has reached a selection plateau. Limited scope for improvement through selection. Breeders might need to introduce new genetic material to increase variability. Alternatively, focus could shift to other traits with higher variability and potential for improvement.
6. Heritability and Genetic advance
Heritability and Genetic advance are important selection parameters.
Heritability estimates along with the genetic advance are normally more helpful in predicting genetic gain under selection than heritability estimates alone.
However, it is not necessary that a character showing high heritability will also exhibit high genetic advance.
6.1 Estimation of Heritability in a broad sense (h2b)
It is the proportion of phenotypic variability that is due to genetic reasons.
It is a good index of transmission of characters from parents to their offspring.
It includes all genetic variance components (additive, dominance, and epistatic variances).
$$
h_b^2 = \frac{\sigma_g^2}{\sigma_p^2} \times 100
$$
Heritability percentage is categorized as
| 0–30 % |
Low |
| 30–60 % |
Moderate |
| 60 % and above |
High |
6.2 How to interpret the result of heritability in broad sense?
-
Low Heritability (0–30%):
A low percentage of phenotypic variation in the trait is due to genetic factors.
Most of the observed variation is likely due to environmental influences.
Selective breeding for this trait might be less effective because genetic differences
contribute minimally to the trait's expression. Instead, focus on optimizing
environmental conditions to improve the trait.
-
Moderate Heritability (30–60%):
A moderate percentage of phenotypic variation is due to genetic factors.
Both genetics and environment play significant roles in influencing the trait.
Selective breeding can lead to moderate improvements in the trait.
Genetic gains can be achieved, but it is also essential to manage environmental
factors to fully express the genetic potential.
-
High Heritability (60% and above):
A high percentage of phenotypic variation is due to genetic factors.
Most of the variation in the trait can be attributed to genetic differences
among individuals. Selective breeding is highly effective for this trait.
Significant genetic improvements can be made, and the trait is less influenced
by environmental factors.
6.3 Estimation of Genetic Advance (GA)
Genetic advance refers to the improvement in a trait achieved through selection.
It depends on the selection intensity, heritability, and phenotypic standard
deviation of the trait. The expected genetic advance (GA) can be calculated
for each character by adopting the following formula at 5% selection intensity
using the constant ‘K’ as 2.06.
$$
GA = K \times h_b^2 \times \sigma_p
$$
Where,
GA = Genetic advance
K = Standardized selection differential, (K = 2.06 at 5% selection intensity)
h2b = Heritability in the broad sense
σp = Phenotypic standard deviation
6.4 Estimation of Genetic advance expressed as per cent of mean
The genetic advance expressed as per cent of the mean was estimated as follows:
$$
GA\ (\% \text{ of mean}) = \frac{GA}{\bar{X}} \times 100
$$
Where,
GA = Expected genetic advance
X̄ = Mean of character understudy
The genetic advance as per cent mean was categorized as
| 0–10 % |
: Low |
| 10–20 % |
: Moderate |
| 20 % and above |
: High |
6.5 How to Interpret the Result of Genetic Advance as Per Cent of Mean?
-
Low Genetic Advance (0–10%):
The trait is less responsive to selection.
Achieving significant genetic improvement through selection alone might be challenging.
It may be necessary to consider other strategies such as hybridization or improving environmental conditions.
-
Moderate Genetic Advance (10–20%):
The trait shows a reasonable response to selection.
Selection can lead to noticeable improvements in the trait.
A balanced approach of selection and environmental management can be effective.
-
High Genetic Advance (20% and above):
The trait is highly responsive to selection.
Significant genetic gains can be achieved through selection.
This trait is a prime candidate for intensive selection programs to achieve rapid improvement.
6.6 Combining The Results of Heritability (Broad Sense) And Genetic Advance (As Percent of Mean)
Combining heritability (broad-sense heritability) and genetic advance as percent of mean (GAM)
provides a more comprehensive understanding of the potential for improvement of traits in a breeding program.
This combination helps in identifying traits that are not only genetically controlled but also responsive to selection.
-
High hb2 (60% and above) and High GAM (20% and above):
This combination indicates that the trait is largely controlled by genetic factors and is highly responsive to selection.
The environmental influence is minimal. This is the ideal scenario for breeding programs.
Significant genetic improvements can be made through selective breeding as this trait may be governed by additive gene actions.
-
High hb2 (60% and above) and Low GAM (0–10%):
The trait is largely controlled by genetic factors, but it shows a low response to selection.
This may be due to a lack of genetic variability within the population or genetic saturation.
Even though the trait has high heritability, the low genetic advance suggests that selection alone might not result in significant improvements.
Consider introducing new genetic variability into the population, such as through hybridization or mutation breeding.
-
Low hb2 (0–30%) and High GAM (20% and above):
The trait is heavily influenced by environmental factors, yet it shows a high response to selection.
This is an uncommon combination and may indicate that specific environmental conditions or management practices are amplifying the genetic response.
Selection can still lead to significant improvements, but understanding and controlling the environmental factors is crucial.
Focus on identifying and optimizing the environmental conditions that enhance the trait’s expression.
-
Low hb2 (0–30%) and Low GAM (0–10%):
The trait is largely influenced by environmental factors and shows a low response to selection.
This indicates that both genetic control and selection effectiveness are limited.
Breeding for this trait will be challenging as neither genetics nor selection is expected to yield significant improvements.
Focus on improving environmental management and cultural practices to enhance the trait.
7. Solved Example
Dataset: The experiment was laid in Randomized Complete Block Design with three replications in maize (Zea mays L.) by using 30 genotypes.
The data were observed from each replication by randomly selected plants for days to 50% flowering.
| Genotypes |
Replications |
Genotype Total |
Genotype Mean |
| R1 |
R2 |
R3 |
| G1 |
66 |
75 |
75 |
216.00 |
72.00 |
| G2 |
68 |
75 |
76 |
219.00 |
73.00 |
| G3 |
70 |
75 |
80 |
225.00 |
75.00 |
| G4 |
70 |
81 |
86 |
237.00 |
79.00 |
| G5 |
72 |
68 |
74 |
214.00 |
71.33 |
| G6 |
66 |
72 |
80 |
218.00 |
72.67 |
| G7 |
59 |
63 |
74 |
196.00 |
65.33 |
| G8 |
66 |
69 |
79 |
214.00 |
71.33 |
| G9 |
72 |
80 |
78 |
230.00 |
76.67 |
| G10 |
64 |
66 |
83 |
213.00 |
71.00 |
| G11 |
84 |
72 |
74 |
230.00 |
76.67 |
| G12 |
60 |
64 |
75 |
199.00 |
66.33 |
| G13 |
62 |
68 |
65 |
195.00 |
65.00 |
| G14 |
63 |
72 |
75 |
210.00 |
70.00 |
| G15 |
73 |
81 |
70 |
224.00 |
74.67 |
| G16 |
58 |
84 |
70 |
212.00 |
70.67 |
| G17 |
77 |
82 |
86 |
245.00 |
81.67 |
| G18 |
64 |
69 |
75 |
208.00 |
69.33 |
| G19 |
82 |
82 |
84 |
248.00 |
82.67 |
| G20 |
72 |
74 |
75 |
221.00 |
73.67 |
| G21 |
75 |
80 |
78 |
233.00 |
77.67 |
| G22 |
70 |
76 |
82 |
228.00 |
76.00 |
| G23 |
76 |
83 |
82 |
241.00 |
80.33 |
| G24 |
77 |
76 |
75 |
228.00 |
76.00 |
| G25 |
77 |
83 |
70 |
230.00 |
76.67 |
| G26 |
76 |
84 |
86 |
246.00 |
82.00 |
| G27 |
83 |
68 |
72 |
223.00 |
74.33 |
| G28 |
61 |
75 |
84 |
220.00 |
73.33 |
| G29 |
67 |
78 |
60 |
205.00 |
68.33 |
| G30 |
67 |
70 |
78 |
215.00 |
71.67 |
| Replication Total |
2097 |
2245 |
2301 |
|
| Grand Total |
6643 |
7.1 Analysis of Variance
Null hypothesis for genotypes and replications
H0: There are no significant differences among means of genotypes under study.
Ha: There are no significant differences among means of replications under study.
Correction Factor
\[
CF = \frac{\left(\sum_{i=1}^{g} \sum_{j=1}^{r} Y_{ij}\right)^2}{rg}
= \frac{6643^2}{60}
= 490327.21
\]
General Mean (GM)
\[
GM = \frac{GT}{rg} = \frac{6643}{60} = 73.81
\]
Total Sum of Squares
\[
Total\ SS = \sum_{i=1}^{g} \sum_{j=1}^{r} Y_{ij}^2 -
\frac{\left(\sum_{i=1}^{g} \sum_{j=1}^{r} Y_{ij}\right)^2}{rg}
\]
\[
= 66^2 + 75^2 + \cdots + 78^2 - 490327.21
\]
\[
= 4459.79
\]
Genotype Sum of Squares
\[
Genotype\ SS = \frac{\sum_{i=1}^{g} Y_{i.}^2}{r} -
\frac{\left(\sum_{i=1}^{g} \sum_{j=1}^{r} Y_{ij}\right)^2}{rg}
\]
\[
= \frac{216^2 + 219^2 + \cdots + 215^2}{3} - 490327.21
\]
\[
= 1914.46
\]
Replication Sum of Squares
\[
Replication\ SS = \frac{\sum_{j=1}^{r} Y_{.j}^2}{g} -
\frac{\left(\sum_{i=1}^{g} \sum_{j=1}^{r} Y_{ij}\right)^2}{rg}
\]
\[
= \frac{2097^2 + 2245^2 + 2301^2}{30} - 490327.21
\]
\[
= 740.62
\]
Error Sum of Squares
\[
Error\ SS = Total\ SS - Replication\ SS - Genotype\ SS
\]
\[
= 4459.79 - 740.62 - 1914.46 = 1804.71
\]
Mean Square for All Sources
\[
Replication\ MS = \frac{Replication\ SS}{Replication\ DF}
= \frac{740.62}{2} = 370.31
\]
\[
Genotype\ MS = \frac{Genotype\ SS}{Genotype\ DF}
= \frac{1914.46}{29} = 66.02
\]
\[
Error\ MS = \frac{Error\ SS}{Error\ DF}
= \frac{1804.71}{58} = 31.12
\]
Calculated F for Replication and Genotype
\[
F_{Replication} = \frac{370.31}{31.12} = 11.90
\]
\[
F_{Genotype} = \frac{66.02}{31.12} = 2.12
\]
ANOVA Interpretation
Here Cal F for Genotype (2.12) Table F (0.05,251) (1.66), we reject the null hypothesis of no difference between the means of the genotypes.
Observed difference is found significant at 5% level of significance and also highly significant at 1% level of significance.
This suggest the calculation of critical difference for genotypes to identify the significantly differing pairs.
Here Cal F for replication (11,90) Table F (0.05,2,58) (3.16), we accept the null hypothesis.
This means there is significant difference among the replications in terms of the response variable.
Calculation of SEm
\[
SE_m = \sqrt{\frac{MSE}{r}} = \sqrt{\frac{31.12}{3}} = 3.22
\]
Coefficient of Variation (CV%)
\[
CV(\%) = \frac{\sqrt{MSE}}{\bar{X}} \times 100
= \frac{\sqrt{31.12}}{73.81} \times 100 = 7.557
\]
Critical Difference (CD) at 5%
\[
CD_{0.05} = t_{(0.05,58)} \times \sqrt{2} \times SE_m
= 2.001 \times 1.414 \times 3.22 = 9.12
\]
7.2 Estimation of Simple Measures of Variability and Variance Component
Genotypic Variance
\[
\sigma_g^2 = \frac{M_g - M_e}{r}
= \frac{66.02 - 31.12}{3} = 11.63
\]
Phenotypic Variance
\[
\sigma_p^2 = \sigma_g^2 + \sigma_e^2
= 11.63 + 31.12 = 42.749
\]
Phenotypic Coefficient of Variation
\[
PCV(\%) = \sqrt{\frac{\sigma_p^2}{\bar{X}}} \times 100
= \sqrt{\frac{42.749}{73.81}} \times 100 = 8.858
\]
Genotypic Coefficient of Variation
\[
GCV(\%) = \sqrt{\frac{\sigma_g^2}{\bar{X}}} \times 100
= \sqrt{\frac{11.63}{73.81}} \times 100 = 4.62
\]
Heritability (%) in Broad Sense
\[
\frac{\sigma_g^2}{\sigma_p^2} \times 100
= \frac{11.63}{42.749} \times 100 = 27.21
\]
Genetic Advance
\[
GA = K \times h_b^2 \times \sigma_p
= 2.06 \times 27.21 \times \sqrt{42.749} = 3.665
\]
Genetic Advance as Percent of Mean
\[
GA(\%\,of\,mean) = \frac{GA}{\bar{X}} \times 100
= \frac{3.665}{73.81} \times 100 = 4.9658
\]
8. Conclusion:
- Low GCV and low PCV for days to 50% flowering indicate low variability.
The lack of variability might indicate that the trait is either highly conserved or has reached a selection plateau.
- Heritability is < 30 indicated more influence of environment in the inheritance of the trait
- Low heritability coupled with low genetic advance as per cent of mean indicate the selection would not be rewarding due to environmental fluctuations
Steps to perform analysis of Genetic Parameter Estimation in Agri Analyze:
Step 1: To create a CSV file with columns for Genotype, replication and trait (DFF).
| Genotype |
Replication |
Yield |
| G1 |
R1 |
66 |
| G2 |
R1 |
68 |
| G3 |
R1 |
70 |
| G4 |
R1 |
70 |
| G5 |
R1 |
72 |
| G6 |
R1 |
66 |
| G7 |
R1 |
59 |
| G8 |
R1 |
66 |
| G9 |
R1 |
72 |
| G10 |
R1 |
64 |
| G11 |
R1 |
84 |
| G12 |
R1 |
60 |
| G13 |
R1 |
62 |
| G14 |
R1 |
63 |
| G15 |
R1 |
73 |
| G16 |
R1 |
58 |
| G17 |
R1 |
77 |
| G18 |
R1 |
64 |
| G19 |
R1 |
82 |
| G20 |
R1 |
72 |
| G21 |
R1 |
75 |
Step 2: Click on ANALYTICAL TOOL -> GENETICS AND PLANT BREEDING -> GENETIC PARAMETER ESTIMATION
Step 3: Upload the CSV file and select Genotypes, Replication and Click on Submit
Step 4: Open link https://www.agrianalyze.com/GeneticParameterEstimation.aspx (For first time users free registration is mandatory)
Step 5: Link Here to download sample file Sample File Download
Step 6: Click submit, pay a nominal fee, and download the output report with detailed interpretation.
Output Report:
Link of the output report
Video Tutorial:
Link of the Youtube Tutorial
Reference
Gomez, K. A., & Gomez, A. A. (1984). Statistical Procedures for Agricultural Research. John wiley & sons. 25-30.
Singh, P. and Narayanan, S.S. (1993) Biometrical Techniques in Plant Breeding. New Delhi, India: Kalyani Publishers.
The blog is written by:
Praful Sondarava, PhD Scholar, Department of Agricultural Statistics, AAU, Anand