Estimation of Genetic Parameters in Plant Breeding: Theory, Example and Demonstration in AgriAnalyze tool

The blog is about estimation of genetic parameters like genotypic variance, phenotypic variance, heritability, genetic advance, genetic advance as a percentage of mean, phenotypic coefficient of variation (PCV), genotypic coefficient of variation (GCV) for the RCBD trails of genotypes. (Reading time 20 mins).

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.

1.     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:

• 1.     Identify the Treatments
• 2.     Define the Blocks
• 3.     Assign Treatments Randomly within Each Block
• 4.     Record the Assignment
• 5.     Repeat for All Blocks
• 6.     Verify Randomization
• 7.     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: 

    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):

2.5.2 Coefficient of Variation (CV%):

2.5.3 Critical difference at 5% level of significance

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.

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.

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.

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.

4.4  What if genotypic variance is negative?

If σ²_g (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.

5.2 Genotypic Coefficient of Variation (GCV): Measures the extent of genotypic variability relative to the mean of the trait.

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.

1. 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.
2. 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.
3. 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

1. 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.
2. 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.
3. 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.
4. 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.

6.2 How to interpret the result of heritability in broad sense?

1.   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.

2.   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.

6.5 How to Interpret the Result of Genetic Advance as Per Cent of Mean?

1. Low Genetic Advance (0-10%): The trait is less responsive to selection. Achieving significant genetic improvement through selection alone might be challenging. It might be necessary to consider other strategies such as hybridization or improving environmental conditions.

2. 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.

3. 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.

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. Link of Dataset

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 replication

H0: There are no significant differences among means of genotypes under study.

Ha: There are no significant differences among means of replications under study.

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

7.     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). Link of Dataset

Step 2: Go with Agri Analyze site.  https://agrianalyze.com/Default.aspx Register by using email and mobile number

Step 3: Click on ANALYTICAL TOOL

Step 4: Click on GENETICS AND PLANT BREEDING

Step 5: Click on GENETIC PARAMETER ESTIMATION

Step 6: Upload the CSV file and select Genotypes, Replication and Click on Submit

Output from the analysis

References:

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.

Blog Credit:

This blog is written with great effort and due research by Praful Sondarava  (PhD Scholar, AAU) for Agri Analyze