Empirical comparison of time series models and tensor product penalised splines for modelling spatial dependence in plant breeding field trials - Gogel, Beverley; Welham, Sue; Cullis, Brian (Frontiers in Plant Science, 2023)
Plant breeding field trials have been widely analysed using linear mixed models in which low order autoregressive integrated moving average (ARIMA) time series models, and the subclass of separable lattice processes, are used to account for two-dimensional spatial dependence between the plot errors. A separable first order autoregressive model has been particularly useful in the analysis of plant breeding trials. Recently, tensor product penalised splines (TPS) have been proposed to model two-dimensional smooth variation in field trial data. This represents a non-stochastic smoothing approach which is in contrast to the autoregressive (AR) approach which models a stochastic covariance structure between the lattice of errors. This paper compares the AR and TPS methods empirically for a large set of early generation plant breeding trials. Here, the fitted models include information on genetic relatedness among the entries being evaluated. Judged by Akaike Information Criteria, the AR models were a better fit than the TPS model for more than 80% of trials. Where the TPS model provided a better fit it did so by only a small amount whereas the AR models made a substantial improvement across a range of trials. Using the best fitting model for a trial as the benchmark, the rate of mis-classification of entries for selection was greater for the TPS model than the AR models. This has important practical implications for breeder selection decisions.