{'fraction_non_alphanumeric': 0.01710654936461388, 'fraction_numerical': 0.0039100684261974585, 'mean_word_length': 5.279141104294479, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
295 Parameter estimation under genomic selection


 Genetic parameters are important in animal breeding for many tasks, including as input to a model for genetic evaluation, to estimate genetic gain due to selection, and to estimate correlated response due to selection on major traits. Before the genomic era, parameter estimation was facilitated by sparse structure of mixed model equations. Methods such as AI REML with sparse matrix inversion or MCMC via Gibbs sampling could estimate parameters for populations exceeding 1 million animals. With genomic selection (GS) and single-step GBLUP, the genomic matrices are mostly dense, and costs of parameter estimation increased dramatically. The estimation with 20K genotyped animals can take many days. Details in matching pedigree and genomic information influence estimated parameters. Estimation without the genomic information when GS is practiced leads to biases due to genomic-preselection. Truncating data to too few generations or to only genotyped animals leads to additional biases by excluding data on which the selection was practiced. Current studies indicate strong declines in heritability due to GS. Regular models for parameter estimation compute parameters only for the base population. Models that trace changes of parameters over time, such as random regression model on year of birth or a multiple trait model treating times slices as separate traits, are very expensive. A good compromise in parameter estimation under GS is to use slices of only 2–3 generations, with genotypes of young animals removed. When complete populations are genotyped, estimations with large number of genotyped animals are possible either with a SNP model or with GBLUP (inversion of genomic relationship matrix by APY algorithm). For simple models, Method R can provide estimates for any data size. An indirect indication of changing parameters over time is reduced predictivity or lower genetic trend despite increased data. Parameter estimation in GS would benefit from new, efficient tools.