RESUMO
In plant and animal breeding, sometimes observations are not independently distributed. There may exist a correlated relationship between the observations. In the presence of highly correlated observations, the classical premise of independence between observations is violated. Plant and animal breeders are particularly interested to study the genetic components for different important traits. In general, for estimating heritability, a random component in the model must adhere to specific assumptions, such as random components, including errors, having a normal distribution, and being identically independently distributed. However, in many real-world situations, all of the assumptions are not fulfilled. In this study, correlated error structures are considered errors that are associated to estimate heritability for the full-sib model. The number of immediately preceding observations in an autoregressive series that are used to predict the value at the current observation is defined as the order of the autoregressive models. First-order and second-order autoregressive models i.e., AR(1) and AR(2) error structures, have been considered. In the case of the full-sib model, theoretical derivation of Expected Mean sum square (EMS) considering AR(1) structure has been obtained. A numerical explanation is provided for the derived EMS considering AR(1) structure. The predicted mean squares error (MSE) is obtained after including the AR(1) error structures in the model, and heritability is estimated using the resulting equations. It is noticed that correlated errors have a major influence on heritability estimation. Different correlation patterns, such as AR(1) and AR(2), can be inferred to change heritability estimates and MSE values. To attain better results, several combinations are offered for various scenarios.
