Empirical comparison of time series models and tensor product penalised splines for modelling spatial dependence in plant breeding field trials

Publication Name

Frontiers in Plant Science


Plant breeding field trials are typically arranged as a row by column rectangular lattice. They 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 shown to be 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. This provides a more relevant framework for comparison than the assumption of independent genetic effects. Judged by Akaike Information Criteria (AIC), the AR models were a better fit than the TPS model for more than 80% of trials. In the cases 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. When the AR and TPS models differ, there can be marked differences in the ranking of genotypes between the two methods of analysis based on their predicted genetic effects. 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.

Open Access Status

This publication may be available as open access



Article Number


Funding Number


Funding Sponsor




Link to publisher version (DOI)