shifted multiplicative model- NAVDEEP SINGH JAMWAL

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Navdeep Singh Jamwal A-2011-40-005 Shifted Multiplicative Model


Introduction Genotype x environment interaction (GEI) is the variation caused by the joint effects of genotypes and environments (Dickerson, 1962). Distinction between cross over interactions (COI) and Non cross over interactions (NCOI) is failed due to GEI Cross over interaction results in the rank change of genotypes over different environments. GEI complicate identification of superior genotype for range of environment If GEI is high, Breeding gain is smaller.

Importance of GEI:

Importance of GEI Range Broad genetic background Narrow genetic background Wide range of distinct environment Low heritability due to GEI and unreliable ranking of genotypes across environments Maximizing genetic variation among environment s and significant means between testing environments Uniform environments Maximizing genetic variation and significant means between testing genotypes Useless

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Shifted multiplicative model is developed by Seyedsadr & Cornelius (1992) It is a tool to analyze the separability of Genotypic effects from environment effects Environment effects from genotypic effects Complete separabilty Gregarious and Namkoong (1986) Separability defined one property which is that if cultivar effect is separable from environment effect than there are no rank changes from one environment to another.

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Mean of ith genotype in jth environment Shift parameter Constraints for ith genotype Constraint for jth environment Residual error Scaling constant for axis k K = 1 Primary effect (significant) = 2 Secondary effect (non-significant) = 3 Tertiary effect (non-significant)

Requirements of SHMM:

Requirements of SHMM Condition for absence of significant genotypic rank change interaction SHMM adequate for fitting data Primary effect should have same signs of environments Condition for absence of significant environment rank change interaction SHMM adequate for fitting data Primary effects of genotypes should have same signs Condition for absence of significant genotypic and environment rank change interaction SHMM adequate for fitting data Primary effects of genotype and environment should have same signs.

Analysis of Variance (ANOVA):

Analysis of Variance (ANOVA) Source d.f . 1. Genotype g-1 2. Site s-1 3. Genotype X Site (g-1)(s-1) 4. Pooled error s(r-1)(g-1) SHMM 5. Primary effects 6. Secondary effects 7. Tertiary effect 8. Remainder

SHMM Studies :

SHMM Studies Cornelius et al. (1993) used SHMM clustering to group 41 winter wheat ( Triticum aestivum L.) genotypes into non-COI clusters from a multisite trial data that included seven environments. Crossa et al. (1993), using the SHMM model, clustered 59 international sites into five non-COI groups and concluded that the procedure appears useful in identifying subsets of sites with negligible genotypic COI. Crossa et al. (1995) used the SHMM model for clustering five irrigation levels in two years (10 environments) and results were compared with the conventional cluster analysis using the Euclidean distance as the criterion. The SHMM clustering strategy formed more homogeneous non-COI subsets of sites than the conventional clustering strategy.

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CASE STUDY Data of 41 wheat genotypes evaluated in randomized complete block design in four replications in the year 1985 at each of the seven Locations at Kentucky

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Clustering First step of is to make the dendrogram by complete linkage with distance defined as Residual Sum of Square Total 40 clusters Nine clusters formed By fitting the SHMM1 No or insignificant COI

SHMM1 fitted to data (good fit):

SHMM 1 fitted to data (good fit) Non Cross over interactions

SHMM1 fitted to data (Poor fit):

SHMM 1 fitted to data (Poor fit)

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Unconstraint least square fit of SHMM 1 to data Cross over interactions

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Constraint least square fit of SHMM 1 to data

Differences in clusters:

Differences in clusters Point of intersection toward left Point of intersection toward right Parallel regression lines Constrained sol. Pt. of intersection moved towards left

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Response of eight high yielding cultivars in five clusters

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Response of unclustered six cultivars

Importance of SHMM:

Importance of SHMM Categorization of locations with similar environments helps breeders to efficiently utilize resources and effectively target germplasm. Useful tool to breeder in making decision on release of cultivar It helps in selection, testing and identifying superior genotypes Subsets of environments represent similar selection environments facilitate the exchange of germplasm

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