Joint modelling of competition and spatial variability in forest field trials



Publication Details

Resende, M. Deon Vilel., Stringer, J., Cullis, B. & Thompson, R. (2005). Joint modelling of competition and spatial variability in forest field trials. Brazilian Journal of Mathematics and Statistics, 23 (2), 7-22.


Analysis of plant field experiments should be based on realistic approaches taking into account the biological process associated with the evaluated trait as well as the environmental influences. There are at least three underlying assumptions in the classical block model of analysis. Firstly, that the environment associated with plots in a block is constant (or nearly so). Secondly, that the response on a plot due to a particular treatment does not directly affect the response on a neighbouring plot. Thirdly, the residual errors are independent. The first assumption is concerned with environmental effects and is often called spatial trend, whilst the second assumption is concerned with treatment effect and is referred to as interference. The third assumption is concerned with spatial correlation. Adjustments for these three effects are likely to improve the analysis and reduce bias. This paper aims at accounting simultaneously for trend, interference and correlation in field trials of forest trees. The objectives are the comparison and extension of alternative models, the quantification of competition levels in these species and the inference about the need for more complex models in routine data analysis in these crops. Several models including traditional block, spatial (autoregressive row and column effects), phenotypic competition, phenotypic competition + spatial, genotypic competition + spatial models were applied on two data sets, one concerned with a Eucalyptus species and the other referring to Pinus. Results showed that the genotypic competition + spatial model, including the genetic competition effect and a balance between residual competition effects and environmental trend considers explicitly the genetic competition and allows for the covariance between variety and competition effects. It encompasses the whole correlation pattern and tends to be more precise than a phenotypic competition model. Results revealed the inconsistency and inadequateness of the covariate approach for modelling competition and trend simultaneously, which is a well known result for modelling competition effects alone. Adjusted REML methods provide precise fitting of phenotypic competition models and improve the estimation of the variance and competition parameters. Phenotypic competition addresses largely the same source of variation as the autoregressive parameters. General models with genotypic competition + spatial terms are often a usual first model to fit as this will indicate if a more limited model is appropriate.

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