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All four methods yielded consistent approximations of the exact values.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Abstract<\/jats:title>\n                    <jats:p>Genomic prediction models, such as genomic best linear unbiased prediction (GBLUP), use genomic data to improve the accuracy of estimated genetic values. As the number of genotypes and traits increases, the exact calculation of prediction error variances (PEVs) and reliabilities becomes computationally infeasible due to the need to invert the coefficient matrix of the mixed model equations, whose dimension increases directly with the number of individuals and traits. The objective of this study was to evaluate the applicability of the Monte Carlo (MC) sampling method to approximate PEVs and reliabilities in a multiple-trait GBLUP framework relevant to hybrid breeding. The MC method avoids direct matrix inversion by repeatedly sampling genetic values from their assumed distributions to approximate PEVs. We applied the MC method using four previously published formulas to approximate PEVs and reliabilities. All formulas produced consistent estimates of PEVs and reliabilities, with convergence rates depending on the formula, the level of reliability, and the MC sample size.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1007\/s00122-026-05336-0","type":"journal-article","created":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T14:18:13Z","timestamp":1787926693000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximating prediction error variances and reliabilities in a multiple-trait genomic prediction model using Monte Carlo sampling"],"prefix":"10.1007","volume":"139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-3088-3430","authenticated-orcid":false,"given":"Antero","family":"Heikkil\u00e4","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ismo","family":"Strand\u00e9n","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin H.","family":"Lidauer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Klaus","family":"Nordhausen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sara","family":"Taskinen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,28]]},"reference":[{"key":"5336_CR1","doi-asserted-by":"publisher","unstructured":"Alemu A, \u00c5strand J, Montesinos-L\u00f3pez OA, Isidro y S\u00e1nchez J, Fern\u00e1ndez-G\u00f3nzalez J, Tadesse W, Vetukuri RR, Carlsson AS, Ceplitis A, Crossa J, Ortiz R, Chawade A (2024) Genomic selection in plant breeding: key factors shaping two decades of progress. 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