Marcos Deon Vilela de RESENDE[1]



§         ABSTRACT: The advantages of using spatial analysis in annual crop experiments are well documented. There is much less evidence for perennial crops. For the sequence of measurements in perennial crops, apparently, there are no published articles in spatial analysis to date. This paper aimed at the comparison of several models, including auto-regressive, ante-dependence and character process models, in modelling sequences of measurements in perennial plants. The use of smoothed models, including splines, to give parsimonious response models, was also investigated. To access model performance, residual maximum likelihood ratio tests (LRT) and Akaike Criterion Information (AIC), were used. We analysed a total of 22,320 observations from 2 trials of tea plant concerning 5 yield annual measures through different spatial and non-spatial models. The classes of methods used were: (1) univariate spatial models for individual annual measures on each trial; (2) longitudinal non-spatial models for the several measures on each trial; (3) longitudinal and spatial models simultaneously for repeated measures in each trial. The main results obtained were: for individual analysis, the best model out of 19 was the row-column analysis + a first-order spatial auto-regressive (AR1 x AR1) correlated error + independent term error, which provided efficiency (ratio between adjusted heritabilities associated with spatial and non spatial models) between 1.09 and 1.76 over block analysis, i.e., between 9% and 76% of improvement; the same model, however, with a second-order spatial auto-regressive (AR2 x AR2) correlated error, was not superior to (AR1 x AR1); the traits (sequence measurements in consecutive years) gave approximately the same behaviour in terms of results across models; the repeatability and the full unconstrained models were not adequate for the sequences of measures, which exhibited considerable variance heterogeneity between traits and high correlation between measures, revealing a need for new modelling. In general, the best approaches involved the modelling of treatment effects by ante-dependence (SAD) or auto-regressive models with heterogeneous variance (ARH). When the spatial effects are important, a combination of first order spatial auto-regressive approach for modelling errors and a multivariate (including simpler options such as SAD and ARH) approach for modelling treatments effects should be used.

§         KEYWORDS: Repeated Measure; environmental trends; mixed models; REML; BLUP; auto-regressive models; ante-dependence models.


[1] EMBRAPA FLORESTAS, Caixa Postal 319, CEP: 83411-000, Colombo, PR, Brasil. E-mail:

[2] Rothamsted Research Institute, AL5 2JQ, Harpenden, UK. E-mail: