Variance and Covariance Heterogeneity of Weight of Young Simmental Bulls Expressed over Time

Cilj ovog rada bio je procjena komponenti varijance i kovarijance težine mladih simentalskih bikova u različitoj dobi uz uvažavanje heterogenosti varijance i kovarijance upotrebom funkcije kovarijance. Analizirane su težine 779 bičića u dobi od 6, 9 i 12 mjeseci, rođenih između 1974 i 1995 godine. Zajedno sa jedinkama iz rodoslovlja, u analizu je bilo uključeno ukupno 2215 životinja. Aditivne genetske i okolišne varijance i kovarijance procijenjene su REML metodom koristeći multivarijatni ‘animal’ model, u kojem je interakcija sezona x godina bila definirana kao fiksni utjecaj. Varijance i kovarijance protumačene su i pomoću funkcije kovarijance. Procjene heritabiliteta su bile 0.08, 0.21 i 0.23 za težinu u dobi od 6, 9 i 12 mjeseci. Krivolinijska promjena aditivnih genetskih i okolišnih varijanci i kovarijanci u vremenu koja je objašnjena kvadratnom prostornom funkcijom. Između različitih dobi aditivne genetske korelacije bile su veće nego okolišne, što jasno pokazuje da će životinja većeg kapaciteta za rast imati veći prirast u cijelom tom razdoblju. Utvrđena heterogenost varijanci i kovarijanci navodi na zaključak da multivarijantni model i funkcija kovarijance bolje objašnjavaju varijabilnost podataka tijekom vremena pa je i procjena genetskih parametara točnija.Genetic and environmental variances and covariances and associated genetic parameters were estimated for weight of young Simmental bulls expressed over time. Heterogeneity over time was analyzed using covariance functions. Data utilized in the study consisted of weight records of 779 young bulls measured at the age of 6, 9 and 12 months. Accounting for the pedigree there were 2215 animals. Variances and covariances were estimated by REML from a multivariate animal model with interaction season x year defined as a fixed effect. Variances and covariances were also explained using covariance functions. Heritability estimates were 0.08, 0.21 and 0.23 for the ages of 6, 9 and 12 months, respectively. Curvilinear changes in additive genetic and environmental variances and covariances were detected and they are explained by quadratic functions. Between any two age points, additive genetic correlations are larger then environmental correlations. This explains that the animal with high capacity of growth shows its potential during the whole growth period. Detected variance and covariance heterogeneity leads to conclusion that a multivariate model or a covariance function must be used to explain variability of trajectory variables in order to correctly estimate genetic parameters