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Multiplicative Models for Specific Combining Ability in Half‐diallels with Parents
Author(s) -
Piepho HansPeter
Publication year - 2013
Publication title -
crop science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.76
H-Index - 147
eISSN - 1435-0653
pISSN - 0011-183X
DOI - 10.2135/cropsci2013.04.0256
Subject(s) - diallel cross , multiplicative function , ammi , biplot , biology , mathematics , statistics , agronomy , genetics , gene–environment interaction , mathematical analysis , hybrid , gene , genotype
This paper considers multiplicative models for the analysis of half‐diallels with parents (self‐crosses) and graphical displays based on such models, including biplots. It is shown that models respecting the symmetry of the diallel two‐way classification are inherently restrictive because multiplicative terms for specific combining ability (SCA) effects are forced to have the same sign for all self‐crosses. The models are illustrated using an example from wheat ( Triticum aestivum L). Limitations of other multiplicative models for diallel analysis such as the AMMI and GGE models are also discussed. It is concluded that multiplicative models are useful for the analysis of diallels when the pattern of SCA effects can be well represented by just one or two multiplicative terms. When SCA effects have a more complex structure, however, it may be preferable to resort to classical diallel analysis.