Analysis of Polygenic Traits (GPB-602)

Quantitative genetics – study of inheritance of quantitative characters or polygenic characters in experimental populations.

1. ACHARYA N.G. RANGA AGRICULTURAL UNIVERSITY Submitted by :- P.TEJASREE TAD/2023-10 Ph.D. 1 st Year Dept. of GPBR DEPARTMENT OF GENETICS AND PLANT BREEDING Course No :- GPB-602 Course Title :- ADVANCES IN BIOMETRICAL GENETICS Submitted to :- Dr. P. Shanthi Associate Professor Dept. of GPBR 1 S.V AGRICULTURAL COLLEGE, TIRUPATI Analysis of Polygenic Traits

2. Biometrical Genetics: A branch of genetics which utilizes statistical concepts and procedures for the study of genetic principles is known as biometrical genetics. Population genetics – study of inheritance of qualitative characters with frequency of genes and genotypes in natural populations. Quantitative genetics – study of inheritance of quantitative characters or polygenic characters in experimental populations. BIOMETRICAL TECHNIQUES: Metroglyph analysis, D2 analysis, Principal Component Analysis, correlations, path coefficients, discriminant function, diallel cross, partial diallel cross, line x tester cross, triallel cross, quadriallel cross, biparental cross, triple test cross, generation mean analysis and stability analysis. APPLICATIONS OF BIOMETRICAL TECHNIQUES: In plant breeding and genetics, biometrical techniques are useful in ( i ) assessment of variability (ii) determination of yield components (iii) determination of gene action and (iv) assessment of varietal adaptation

3. List of Various Biometrical techniques used in Crop Improvement Applications/uses Biometrical techniques used 1. Assessment of variation Measures of Dispersion Components of Genetic variances Metroglyph Analysis D 2 Statistics Molecular Diversity Analysis 2. Selection of elite Genotypes Correlation Analysis Path Coefficient Analysis Discriminant Function Analysis 3. Choice of parents and breeding procedures Analysis of Several Single Crosses     Analysis of Several Three way Crosses Analysis of Several Double Crosses Analysis of Individual Cross   Diallel Cross Analysis Partial Diallel Analysis Line X tester Analysis 1. Triallel Analysis 1. Quadriallel Analysis Generation Mean Analysis Biparental Cross Analysis Triple Test Cross Analysis 4. Assessment of Varietal Adaptability Stability Analysis Models

4. Landmarks in the history of biometrical genetics Year Scientist Country Contribution/concept developed 1888 Francis Galton Britain Introduced the concept of correlation 1902 Karl pearson England Correlation coefficient 1918 R.A. Fisher England Provided initial frame of biometrics and divided genetic variance into additive, dominance and epistatic components 1908 Hardy, G.H. Britain Laid the foundation for population genetics 1908 Weinberg, W. Germany Laid the foundation for population genetics with Hardy 1921 Sewall Wright England Path coefficient analysis 1928 Mahalanobis, P.C. India Developed the concept of D 2 statistics 1935 Sewall Wright England Divided the genetic variance into additive variance and non-additive components 1936 Smith, H.F. England Developed the concept of disriminant function analysis 1949 Mather, K. England Provided scaling test and divided genetic variance into heritable fixable and heritable non-fixable 1952 Comstock, R.E. and Robinson, H.F. USA Developed the concept of biparental mating 1952 Rao, C.R. India First suggested use of D 2 statistics for assessment of diversity in plant breeding 1952 Cavalli England Provided the joint scaling test 1953 Jinks, J.L. and Hayman, B.I. England Developed the graphical approach of diallel cross analysis 1956 Federer, W.T. England Proposed augmented design 1956 Griffing , B. England Developed numerical approach of diallel cross analysis 1957 Hanson, W.D. and Johnson, H.W. England Proposed general selection index 1957 Anderson, E. England Developed the concept of metroglyph analysis 1957 Kempthorne, O. England Developed the concept of partial diallel and Line x Tester analysis 1958 Hayman, B.I. England Proposed six and five parameter models of genration mean analysis 1958 Jinks, J.L. and Jones, J.M. England Proposed three parameter model of generation mean analysis 1959 Kempthorne, O and Nordkog, A.W. England Proposed restricted selection index 1959 Dewey, O.R. and Lu, K.H. England First applied path coefficient for plant selection 1962 Rawlings, J.O. and Cockerham, C.C. Britain Developed the concept of triallel and quadriallel cross analysis 1963 Finlay, K.W. and Wilkinson, G.N. England Provided first approach for stability analysis 1966 Eberhart, S.A. and Russell, W.A. USA Developed a model for stability analysis 1968 Perkins, J.M. and Jinks, J.L. England Provided separate model of stability analysis 1968 Kearsey, M.J. and Jinks, J.L. England Provided triple test cross analysis 1971 Freeman, G.H. and Perkins, J.M. England Provided different model of stability analysis 1984 Dudley, J.W. USA Proposed theory of alleles 1997 Dudley, J.W. USA Presented review of quantitative genetics

5. Plant characters are of two types, viz., oligogenic and polygenic traits. Oligogenic traits are governed by one or two genes, whereas polygenic traits are governed by several genes . Those characters which are governed by several genes are called polygenic characters and variation observed in such characters is known as polygenic variation . Polygenic characters are also known as quantitative traits . The inheritance of traits governed by several genes is termed as polygenic inheritance . Examples of oligogenic characters are colour of stem, leaf, flower, seed, pollen; leaf shape and hairiness, etc. Polygenic traits include yield, days to flower, days to maturity, seed size, seed oil content, protein content, seed weight, plant height etc. Polygenic variation

6. FEATURES OF POLYGENIC TRAITS: There are some characteristic features of polygenic characters. Continuous variation : clear cut classification of polygenic traits into different classes is not possible Transgressive segregation : appearance of transgressive segregants in F 2 or later generation is an important feature of polygenic traits. Involvement of effective and ineffective alleles : effect of individual gene is small which is not detectable. Environmental effect : The environmental variation varies from 10 to 50% for majority of polygenic traits. For some traits say yield, it is even more. The high environmental variation results in continuous variation.

7. THE MULTIPLE FACTOR HYPOTHESIS In 1906, Yule proposed that continuous quantitative variation could result from a large number of genes with small and similar effects and that these genes were transmitted according to the laws of Mendel. In 1908, Nilsson- Ehle presented experimental evidence to support the hypothesis of Yule. He studied the inheritance of seed colour in wheat ( Triticum sp.). The F2 generations from various crosses had red and white grains in the ratios of 3 : 1, 15 : 1 or 63 : 1. 1.This is also known as theory of polygenic traits . 2. This hypothesis provides explanation to the inheritance of quantitative traits which exhibit continuous variation from one extreme to another for a character. 3. In polygenic inheritance, effect of each gene is not easily detectable . 4. For polygenic traits, classification of plants into distinct clear cut classes is not possible . Analysis of polygenic characters is based on means, variances and covariances . 5. Polygenic traits exhibit transgressive segregation . 6. Multiple factor hypothesis is universally accepted for explanation of polygenic traits.

8. This (1 : 4 : 6 : 4 : 1) ratio is obtained if it is assumed that the seed colour is governed by two genes with small, similar and additive effects . The dominant alleles of the two genes produce red colour , while the recessive alleles produce no colour . The intensity of colour depends on the number of dominant alleles present. Thus genotypes R1R1 r2r2, r1r1 R2R2 and R1r1 R2r2 all will produce the same intensity of colour since they all have two dominant alleles each. Thus, NilssonEhle was able to show that certain characters are governed by genes that have small and cumulative effect . The red seeds could be grouped into the following four distinct classes: dark red, medium dark red, medium red and light red.

9. TYPES OF POLYGENIC VARIATION Phenotypic Variation : It is the total variation which is observable. It includes both genotypic and environmental components and hence changes under different environmental conditions. Such variation is measured in terms of phenotypic variance. Genotypic Variation : It is the inherent variation which remains unchanged by environmental factors This type of variation is more useful to a plant breeder for exploitation in selection or hybridization. Such variation is measured in terms of genotypic variance. The genotypic variation consists of additive dominance and environmental components. Environmental variation : it refers to non heritable variation which is entirely due to environmental effects and varies under different environmental conditions. This is uncontrolled variation which is measured in terms of error mean variance. The variation in true breeding parental lines and their F 1 hybrid is non-heritable.

10. ANALYSIS OF POLYGENIC TRAITS The analysis of such traits is based on means, variances and co-variances . Various statistical procedures which are used for the analysis of polygenic traits include simple measure of variability, tests of significance analysis of variance analysis of covariance regression analysis correlation analysis

11. 1) Simple Measures of Variability: Simple Measures of Variability include mean, range, standard deviation, variance, standard error and coefficient of variation Simple measures of variability can be worked out from both un-replicated and replicated data. Measures of Dispersion: The degree to which numerical data tend to spread about the mean value is called dispersion. Thus dispersion is a measure of variation in a sample. The measures of dispersion are also known as simple measures of variability. Arithmetic Mean: It is defined as the sum of all observations in a sample divided by their number. It is denoted by and calculated as follows. where = summation, = mean, X = observation and N = number of observations in a sample  

12. Range: Range is the difference between the lowest and the highest value present in the observations in a sample. If there are 20 observations on seed oil content in cotton, the highest value being 25% and the lowest 15%. The range will be 25-15 = 10. Standard Deviation: It is the square root of the arithmetic mean of squares of all deviations measured from the mean. It is the square root of the variance. Variance : Variance is defined as the average of squared deviations of all the individual observations from the mean. Standard deviation =

13. Standard error : It is the measure of the mean difference between sample estimate of mean (x) and the population parameter (µ), i.e. it is the measure of uncontrolled variation present in a sample. Coefficient of Variation : A measure of variation which is independent of the unit of measurement is provided by the standard deviation expressed as percentage of mean. This is known as coefficient of variation (CV). A sample in which coefficient of variation is higher would have greater variation than the one in which it is lower - when the coefficient of variation is high the sample is less consistent. In plant breeding, phenotypic, genotypic and environmental coefficients of variation are estimated from the corresponding variances and are used for the assessment of variability. Standard error = Standard Deviation √N CV% = Standard deviation X 100 Mean

14. 2) TESTS OF SIGIFICANCE Statistical procedures which are used to decide whether the differences under study are significant or nonsignificant are known as tests of significance. The well known and commonly used tests of significance include z test, t test and F test. These tests are based on a hypothesis, called null hypothesis. NULL HYPOTHESIS: This hypothesis was given by Fisher which is denoted by H . A hypothesis of no difference is known as null hypothesis - No true difference exists in the sample result and population parameter to be tested and that the observed difference is only by chance and unimportant arising out of sampling fluctuations. In case of sample result fails to support the null hypothesis then we must conclude that something else is true. When the differences under study are significant the null hypothesis is rejected and alternate hypothesis is used, which is denoted by H 1 . Comparison of two means : When a significance of difference is to be tested between population mean and sample mean or between two sample means either z test or t- test is applied. z-Test : It is used when the sample size is large (more than 30). t-Test : It is used when the sample size is small (up to 30). It is of two types, viz., student's t and Fisher’t . Student's t : It is used when the observations are paired. Fisher's t : It is used when the observations are not paired.

15. The calculated value of z or t is compared with table at appropriate degrees of freedom. If the calculated value is greater than table value, it is considered as significant and vice versa. In plant breeding, significance of z test or t test between the selected plants and the base population indicates effectiveness of selection. 2. Comparison of Several Means : The significance of difference between several means is tested with the help of F test. It requires F value which is based on analysis of variance. The calculated value of F is compared with table value at desired level of significance and appropriate degrees of freedom. If the calculated value is greater than table value, it is considered as significant and vice versa. 3) ANALYSIS OF VARIANCE (ANOVA) : The statistical procedure which separates the total variation in to different components. It is carried out with replicated data. In Plant Breeding such analysis divides the total variation into two main parts, viz. , variation between varieties, variation within varieties i.e., environmental variation. Partitioning of phenotypic variation into genotypic and environmental Components Genotypic variance (VG) = MSt - MSe /r Environmental variance (VE) = MSe Phenotypic variance (VP) = VG + VE

16. Analysis of variance permits estimation of phenotypic, genotypic and environmental coefficients of variability . It also permits estimation of broad sense heritability and expected genetic advance under selection Where, K is the selection differential at 5% selection intensity. 4) ANALYSIS OF COVARIANCE (ANCOVA) : This statistical technique splits simultaneously the variation of two variables into various components. The total variation can be partitioned into genotypic, phenotypic and environmental covariances. The analysis of covariance is also carried out with replicated data. Genotypic covariance ( Cov.G ) = MSPt – MSP e /r Environmental Covariance ( Cov.E ) = MSP e Phenotypic covariance ( Cov.P ) = Cov G + Cov E

17. Where, MSP t= mean sum of product for treatments , MSP e = error mean covariance and r = number of replications Analysis of covariance permits estimation of coheritability . Coheritability ( xy ) = Cov.G / Cov.P x 100 Both variances and covariances are used for the estimation of: P henotypic, genotypic and environmental correlation and path coefficients D2 statistics S election indices R egression coefficient 5) REGRESSION ANALYSIS: Regression coefficient is a statistical measure of the average functional relationship between two or more variables. In regression analysis, one variable is considered as dependent and other (s) as independent. byx = ∑x y- (∑x . ∑y)/ ∑y2 –(∑y)2 bxy = ∑x y- (∑x . ∑y)/ ∑x2 –(∑x)2

18. 6) CORRELATION ANALYSIS (r) : Correlation refers to the degree and direction of association between two or more than two variables. It value lies between -1 and 1. Interpretation of results: If GCV > PCV – selection will be rewarding If PCV > GCV – selection will be mis leading If ECV > PCV, GCV – selection is ineffective r xy = Cov ( xy )/√( vx ).( vy )

19. High heritability accompanied with high genetic advance indicates that most likely the heritability is due to additive gene effects and selection may be effective . High heritability accompanied with low genetic advance indicates non- additive gene action and selection for such traits may not be rewarding . Low heritability accompanied with high genetic advance reveals that the character is governed by additive gene effects . The low heritability is being exhibited due to high environmental effects. Selection may be effective in such areas Low heritability accompanied with low genetic advance indicates that the character is highly influenced by environmental effects and selection would be ineffective .

20. Thank you Have a statistically significant day