Structuring Genotype X Environment Interaction by Regression Techniques

In multienvironment trials, where a series of tests are conducted across numerous environmental circumstances, the structure of genotype-by-environment interaction is a key topic. This paper suggests a generalisation of joint regression analysis for cases where the response (for example, yield) is non-linear across environments and can be written as a second (or higher) order polynomial or another non-linear function. After identifying the common form regression function for all genotypes, we offer a selection approach based on the modification of two tests: I a test for parallelism of regression curves; and (ii) a test for coincidence for those regressions. When After the parallelism hypothesis has been disproved, groupings of genotypes with parallel (or coincident) responses should be identified. The Scheffé multiple comparison approach for regression coefficients in secondorder polynomials allows genotypes to be classified into two categories: upwardfacing concavity (i.e. potential yield rise) and downwardfacing concavity (i.e. potential yield decline) (i.e. the yield approaches saturation). Theoretical findings for genotype comparison and genotype selection are proven with an example of yield from a non-orthogonal series of experiments with winter rye (Secale cereale L.). To show that our meteorology is completely applicable to We randomly wiped 10% of the data from incomplete data sets, which are typical in multi-environment experiments. The parallelism of regression curves hypothesis was rejected, which is expected in multienvironment trials with genotype-environment interaction. The key difference between the two genotype subgroups with parallel responses is that one had upward-facing concavity (i.e. prospective yield growth) and the other had downward-facing concavity (i.e. yield growth). methods saturation), which breeders can use to help them choose genotypes. The method provided in this work is generic and can be applied to any set of experiments in multi-environment trials or just to two-way categorised data.

Author (s) Details

Dulce Gamito Santinhos Pereira
Departamento de Matemática, Escola de Ciências e Tecnologia, Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho 59, 7000-671 Évora, Portugal.

Paulo Canas Rodrigues
Department of Statistics, Federal University of Bahia, Salvador, Brazil.

Prof. Dr. Iwona Mejza
Poznan University of Life Sciences, Dept. of Mathematical and Statistical Methods, ul. Wojska Polskiego 28 – 60-637 – Poznań, Poland.

Prof. Dr. Stanislaw Mejza
Poznan University of Life Sciences, Dept. of Mathematical and Statistical Methods, ul. Wojska Polskiego 28 – 60-637 – Poznań, Poland.

João Tiago Mexia
FCT/UNL, Centro de Matemática e Aplicações, 2829-516, Caparica, Portugal.

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