![• The additive variance which is the variance of breeding value is
obtained as follows
VA = (2q a )2p2 + [(q-p) a ] 22pq + (-2p a )q2
VA = 4p2q2 a 2 + (q2-2pq+p2) a 2 2pq + 4p2q2 a 2
VA = 2pq a 2 (2pq + q2 - 2pq +p2 + 2pq)
VA = 2pq a 2 (1)
VA = 2pq [a + d (q-p)] 2
• The variance of dominance deviation is
VD = (-2q2d)2 + (2pqd)2 + (-2p2d)2
VD = (2pqd)2
• Total genetic variance
VG = VA + VD
VG = 2pq [a + d (q-p)]2 + (2pqd)2
VG = 2pq a 2 + (2pqd)2](https://image.slidesharecdn.com/variance-200826124434/85/Variance-and-GE-Interactions-10-320.jpg)
Variance and GE Interactions
- 1. TOPIC: Variance GE Interactions Dr S. Shanaz Assoc. Prof Division Of AGB
- 2. VARIANCE Variation: Differences in phenotypic values of quantitative traits among individuals of a population Amount of variation is measured and expressed as variance Variance measures the variability from an average or mean The basic idea in the study of variance is its partitioning into components attributable to different causes For genetic improvement variation is important Components into which the phenotypic variance is partitioned are the same as the components of phenotypic value (P= G+E) The relative magnitude of variance components is determined by the degree of resemblance between relatives.
- 4. Components of values and corresponding variance
- 5. Important difference between components of value and variance In case of phenotypic value, each component can have positive or negative values on the other hand phenotypic variance are always positive INTANGIBLE VARIATION Amount of non genetic variation whose cause is unknown and which cannot be eliminated by experimental design
- 6. Types of Variation • Phenotypic variation (VP) is the total variation in a trait (VE + VG) • Environmental variation. (VE) is the variation among individuals that is due to their environment • Genetic variation (VG) is the variation among individuals that is due to their genes
- 7. GENOTYPE VARIANCE • Variances are obtained by squaring the values multiplying by the frequency of the genotypes concerned and summing over all the genotypes • Genotypic variance is due to additive effects of genes and non-additive effects of genes • Additive effects are connected with breeding values of the individual because parents pass their genes to their offspring not their genotype
- 8. Total genetic variation (VG) actually has two components • Additive Genetic Variation (VA) = Variation among individuals due to additive effects of genes • Dominance Genetic Variation (VD) = Variation among individuals due to gene interactions such as dominance VG = VA + VD
- 9. Genotype A1 A1 A1 A2 A2 A2 Frequencies p2 2pq q2 Assigned values a d -a Breeding values 2q a (q-p) a -2p a Dominance deviation - 2q2 d 2pqd -2p2 d Variance is obtained by squaring the values then multiplying by the frequency of the genotype concerned, and summing the three genotypes Additive and Dominace variance
- 10. • The additive variance which is the variance of breeding value is obtained as follows VA = (2q a )2p2 + [(q-p) a ] 22pq + (-2p a )q2 VA = 4p2q2 a 2 + (q2-2pq+p2) a 2 2pq + 4p2q2 a 2 VA = 2pq a 2 (2pq + q2 - 2pq +p2 + 2pq) VA = 2pq a 2 (1) VA = 2pq [a + d (q-p)] 2 • The variance of dominance deviation is VD = (-2q2d)2 + (2pqd)2 + (-2p2d)2 VD = (2pqd)2 • Total genetic variance VG = VA + VD VG = 2pq [a + d (q-p)]2 + (2pqd)2 VG = 2pq a 2 + (2pqd)2
- 11. Interaction variance • When more than one locus is under consideration the interaction deviations give rise to the interaction variance. • Variation of the interaction deviations brought about by the epistatic interactions at different loci • Two factor interactions arise from interaction of two loci, three factor from three loci etc. • In two factor interaction VI = VAA + VAD + VDD + etc
- 12. ENVIRONMENTAL VARIANCE It includes all variations of non genetic origin ; environmental variance is a source of error that reduces precision in genetic studies Environmental variance may be partitioned into • Special environmental variance (VEs) - within individual variance General environmental variance (VEg)
- 13. GENOTYPE – ENVIRONMENT CORRELATION • The correlation between genotype and environment arises when better genotypes are given better environment or vice versa. – Example: Milk yield in dairy cattle. • Normal practice of dairy husbandry is to feed cows according to their milk yield, the better genotypes being given more feed. This introduces correlation between phenotypic value and environmental deviation. • Since genotypic and phenotypic values are correlated there is a correlation between genotypic value and environmental deviation. • When G x E correlation is present, the phenotypic variance is increased by twice the covariance of genotypic values and environmental deviations • Thus, VP = VG + VE + 2 covGE • If VG and VE are estimated, the G x E correlation component 2 covGE can be estimated as 2 covGE = VP - (VG + VE) • Correlation G and E is normally neglected in experimental populations, where randomization is important part of an experimental design.
- 15. What are Genotype x Environment Interactions? Differential response of genotypes to varying environmental conditions Delight for statisticians who love to investigate them The biggest nightmare for plant breeders (and some other agricultural researchers) who try to avoid them like the plague
- 16. Definition GE interaction • The G × E interaction is defined as the relative change in the performance of two or more genotypes in two or more environments. The phenomenon is reflected by the differential expression of different genotypes over environments; • Genotype can be breeds, strains or lines & environments can be nutrition, climate, housing and management etc • For example the genotype A may be superior to genotype B in the environment - I, but inferior in environment – II, when G × E interaction is present.
- 17. Why to study GE ? • To investigate relationships between genotypes and different environmental (and other) changes • To identify genotypes which perform well over a wide range of environments General adaptability • To identify genotypes which perform well in particular environments Specific adaptability
- 18. What reflects Genotype x Environment interactions?
- 19. • Under certain combination of genotype and environment, the phenotype may not be equal to the sum of these two variables but rather be smaller or larger. P < or > (G + E) • When interaction is absent the phenotype equals the sum of genotype and environment. P = (G + E) • If the ranking order of two (or more) genotypes varies from environment to environment in which they are conducted then there is G × E interaction • The best genotype in one environment is not the best in another environment.
- 20. Why do researchers conduct multiple experiments? Effects of factors under study vary from location to location or from year to year. To obtain an unbias estimate Interest in determining the effect of factors over time To investigate genotype (or treatment) x environment interactions.
- 21. • Each genotype has its specific adaptability for which the G × E interaction is responsible • When there is no interaction the best genotype in one environment will be the best in all • When the interaction between genotype and environment is present, the phenotypic value becomes P = G + E + IGE. The interaction component also makes changes in the sources of variation for the phenotypic variance and result in Vp = VG + VE + VGE. Since the variance occurring in genetically uniform groups is entirely due to environmental differences among the individual, the variance due to interaction is included with environment variance.
- 22. • Genotype – Environmental (G × E) Interaction are very important for individuals in population , reared under different conditions, where environment cannot be controlled • Experimental evidences shows that the best dairy breed sires in the temperate countries were not the best in the tropical countries. The importance of IGE was also found between countries with a high level of concentrate feeding versus pasture feeding base. The best sires in low environment level were not the best in the high environment level The G × E interaction requires additional efforts in selection of breeding stock with a general adaptability to more than one environment condition or specifically suitable for desired environmental condition. Importance of G×E interaction
- 23. In practical breeding, an important concept w.r.t G × E interaction is adaptability. In temperate climate, Zebu cattle (Bos indicus) are inferior to the various European breeds of cattle (Bos taurus). In tropical climate, Zebus are superior. The ranking of European breeds and Zebus depend upon the climate in which they are tested Ranking of bull varies according to the country in which performance of their daughters is measured.