{"doi":"10.2135/cropsci2006.09.0564","title":"Modeling Additive × Environment and Additive × Additive × Environment Using Genetic Covariances of Relatives of Wheat Genotypes","abstract":"<jats:sec><jats:title>ABSTRACT</jats:title><jats:p>In self‐pollinated species, the variance–covariance matrix of breeding values of the genetic strains evaluated in multienvironment trials (MET) can be partitioned into additive effects, additive × additive effects, and their interaction with environments. The additive relationship matrix A can be used to derive the additive × additive genetic variance–covariance relationships among strains, Ã. This study shows how to separate total genetic effects into additive and additive × additive and how to model the additive × environment interaction and additive × additive × environment interaction by incorporating variance–covariance structures constructed as the Kronecker product of a factor‐analytic model across sites and the additive (A) and additive × additive relationships (Ã), between strains. Two CIMMYT international trials were used for illustration. Results show that partitioning the total genotypic effects into additive and additive × additive and their interactions with environments is useful for identifying wheat (<jats:italic>Triticum aestivum</jats:italic> L.) lines with high additive effects (to be used in crossing programs) as well as high overall production. Some lines and environments had high positive additive × environment interaction patterns, whereas other lines and environments showed a different additive × additive × environment interaction pattern.</jats:p></jats:sec>","journal":"Crop Science","year":2007,"id":599202,"datarank":0.6394019815561974,"base_score":4.2626798770413155,"endowment":4.2626798770413155,"self_citation_contribution":0.6394019815561974,"citation_network_contribution":0.0,"self_endowment_contribution":0.6394019815561974,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":70,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1535704,"name":"José Crossa","orcid":null,"position":1,"is_corresponding":false},{"id":1535705,"name":"Paul L. 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The additive relationship matrix A can be used to derive the additive × additive genetic variance–covariance relationships among strains, Ã. This study shows how to separate total genetic effects into additive and additive × additive and how to model the additive × environment interaction and additive × additive × environment interaction by incorporating variance–covariance structures constructed as the Kronecker product of a factor‐analytic model across sites and the additive (A) and additive × additive relationships (Ã), between strains. Two CIMMYT international trials were used for illustration. Results show that partitioning the total genotypic effects into additive and additive × additive and their interactions with environments is useful for identifying wheat (<jats:italic>Triticum aestivum</jats:italic> L.) lines with high additive effects (to be used in crossing programs) as well as high overall production. Some lines and environments had high positive additive × environment interaction patterns, whereas other lines and environments showed a different additive × additive × environment interaction pattern.</jats:p></jats:sec>","is_dataset_classified":null,"base_score":4.2626798770413155,"endowment":4.2626798770413155,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21097893","pmcid":null,"openalex_id":"https://openalex.org/W2015297877","authors":[],"funders":[],"total_grants":0,"fwci":4.1072,"citation_percentile":0.931201,"influential_citations":0,"citation_trend":[{"year":2012,"count":4},{"year":2013,"count":6},{"year":2014,"count":3},{"year":2015,"count":6},{"year":2016,"count":1},{"year":2017,"count":2},{"year":2018,"count":4},{"year":2019,"count":3},{"year":2020,"count":6},{"year":2021,"count":2},{"year":2022,"count":8},{"year":2023,"count":3},{"year":2024,"count":3},{"year":2025,"count":5},{"year":2026,"count":2}],"oa_status":"closed","license":"http://onlinelibrary.wiley.com/termsAndConditions#vor","oa_locations":[{"url":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.2135%2Fcropsci2006.09.0564","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/pdf/10.2135/cropsci2006.09.0564","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/full-xml/10.2135/cropsci2006.09.0564","host_type":"publisher"},{"url":"https://acsess.onlinelibrary.wiley.com/doi/pdf/10.2135/cropsci2006.09.0564","host_type":"publisher"},{"url":"https://doi.org/10.2135/cropsci2006.09.0564","host_type":"journal"}],"fields_of_study":["Genetics and Plant Breeding","Genetic and phenotypic traits in livestock","Genetic Mapping and Diversity in Plants and Animals"],"mesh_terms":[],"keywords":["Additive model","Interaction","Gene–environment interaction","Feed additive","Additive genetic effects","Biology","Generalized additive model","Main effect","Covariance","Kronecker product","Mixed model","Additive function","Analysis of covariance","Genotype","Mathematics","Statistics","Genetics","Kronecker delta","Heritability","Food science","Agronomy","Gene"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-07-28T19:45:16.244820Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}