Experimental designs and spatial and/or temporal models in agricultural, livestock and forestry production systems

Abstract

One of the main objectives of agronomic experimentation is to obtain reliable data to establish comparisons between treatments and test working hypotheses. To meet this objective, it is essential to have well-designed and planned experiments, as well as a data analysis strategy that takes into account the design factors and additional relevant information, mainly in large field scale trials evaluated for several years which generate correlations in space and/or time. The purpose of this research was to evaluate the efficiency of experimental designs with different degrees of complexity and the adjustment of spatial, temporal and spatio-temporal models in experiments with different crops, seeking to avoid biases in the variance estimates, and an adequate control of the empirical type 1 error rate. The most relevant results of this work show that with high experimental field heterogeneity and large experiment size, the choice of the experimental design becomes essential to obtain accurate and precise treatment effect estimates. Once the appropriate experimental design has been chosen, spatial modeling of the correlation between experimental units further improves the design performance. These improvements can be accompanied by unbiased standard errors and a correct control of the type 1 empirical error rate if the model used to estimate the spatial correlation of the response variable is adequate. Additionally, with high number of replicates, reliable results can be obtained beyond the preferred spatial model. On the other hand, when intra-plot spatial correlations are included, the advantage of spatial modeling is not as clear. In the case of forest tillage experiments, the inclusion of spatial correlation between trees in the same plot increased the precision of comparisons between treatment means, achieving reductions in the standard error of the mean difference of up to 40 %. However, in trials conducted on permanent grasslands with large plot sizes, the advantages were not clear. These differences between trials may be due to the scale at which these spatial correlations are manifested, the number of subsamples per plot and the effect of treatments on the spatial distribution of the variables of interest.