multivariate genotype - environment data Analysis of multivariate genotype - environment data using Non-linear Canonical Correlation Analysis Hans Pinnschmidt Danish Institute for Agricultural Sciences Division of Crop Protection Cereal Plant Pathology Group Denmark Archived at http://orgprints.org/8021

Background Objectives BAROF WP1 data: multivariate measurements on 86 spring barley genotypes in 10 environments (2 years: 2002 & 2003, 3 sites: Flakkebjerg, Foulum, Jyndevad, 2 production systems: ecological & conventional). Objectives Multivariate characterisation of genotypes with emphasis on yield-related properties.

} derive information on factors: genotype environment G1 E1 . . . Ej . Gi variables: X1(i,j) ... Xm(i,j) parameters Xm(i)1 ... Xm(i)p Xm(j)1 ... Xm(j)p variables: yield 1000 grain weight grain protein contents culm length date of emergence growth duration mildew severity rust severity scald severity net blotch severity disease diversity weed cover broken panicles & culms lodging parameters: raw data mean/median/max./min. rank/relative values main effects interaction slopes raw data adjusted for E/G main effects/slopes (residuals) IPCA scores SD/variance } derive information on general properties, specificity, stability/variability

Non-linear Canonical Correlation Analysis (NCCA): an optimal scaling procedure suited for handling multivariate data of any kind of scaling (numerical/quantitative, ordinal, nominal).

Non-linear Canonical Correlation Analysis (NCCA) data treatment: quantitative variables (vm) were converted into ordinal variables with n categories (v11 ... v1n, ..., vm1 ... vmn).

Non-linear Canonical Correlation Analysis (NCCA) is based on multivariate contingency tables containing frequency counts. G1 . Gi E1 . . . . . . . . . Ej Vm1 . . . Vmn

Non-linear Canonical Correlation Analysis (NCCA): main “dimensions” ( principal components) are determined “loadings” of variables ( overall correlation) are computed “category centroids” are quantified “object scores” ( principal component scores) are computed

Characterisation of environments based on data adjusted for G main effects (= residuals)

Flakkebjerg 2002: high rust & 1000 grain weight late sowing Foulum 2002 conventional & Jyndevad 2003 ecological: high mildew & lodging Flakkebjerg 2003: high yield, net blotch & panicle breakage low mildew & lodging Jyndevad 2002 ecological: low yield, 1000 grain weight, weed infestation, protein content

Characterisation of genotypes based on data adjusted for E main effects (= residuals)

dimension 5 (sq. root) dimension 1 (sq. root) high yield & 1000 grain weight low protein content & lodging high mildew low net blotch & disease diversity low yield & 1000 grain weight low mildew

genotypes & environments based on: Characterisation of genotypes & environments based on: raw data data adjusted for E main effects data adjusted for G & E main effects ( G x E interaction)

low yield, 1000 grain weight, weed infestation & net blotch high mildew high rust late emergence high yield, 1000 grain weight & net blotch low mildew low rust short culms early emergence

high yield & 1000 grain weight low protein content & lodging low net blotch & disease diversity high mildew low yield & 1000 grain weight high protein content

little lodging high panicle breakage high yield & 1000 grain weight low protein content low yield & 1000 grain weight high protein content much lodging

Conclusions & outlook NCCA is an “intuitive” method good for “visualising” the main features in multivariate data of various scales. NCCA is useful for obtaining an overall orientation of G properties and E characteristics. Future work: Refinements to obtain a better synopsis of E-specific performance of G’s as related to their property profiles. Include AMMI- and clustering (biclassification) results in NCCA, organise data as environment-specific sets of variables.

Characterisation of genotype performance in individual environments based on: raw yield- and disease data disease main effects of G’s environmental disease variability of G’s (= standard deviation of E adjusted data)