Multivariate spatial statistical analysis of multiple experiments and longitudinal data.

Abstract

This document reports the work undertaken by Dr. Marcos Deon Vilela de Resende whilst a Fellow of the Rothamsted Research institute as a Post Doctoral Scientist in the biomathematics Unit, under the guidance or Dr. Robin Thompson and with financial support of the referred institute, located in London, England. The research project entitled “Spatial Analysis in Perennial Crops“ concerned with adapting and extending statistical models for efficient analysis of field experiments. The analytical procedures described are based on the REML method for variance components mixed models. The REML method was invented and improved by Dr. Robin Thompson and co-authors and nowadays is the standard procedure for statistical analysis in a great range of applications. ln agricultural field trials the REML method replaced the traditional method of analysis of variance (ANOVA), providing more accurate estimates and predictions. Chapter 1 considers the spatial statistical analysis of longitudinal data or repeated measures. Practical experiments with several perennial plants generate annually a large amount of data on repeated measures. Improved methods for analysis of such kind of data were developed which will lead to higher efficiency of scientific research in this field. Chapter 2 considers the analysis of multi-environment trials the factor analytic multiplicative mixed models (FAMM) which present several advantages over the traditional additive main effects and multiplicative interaction analysis (AMMII). The FAMM models allow for variance heterogeneity, correlated errors within trials and unbalancing. In addition, provide BLUP of treatments effects, easy choice of the number of multiplicative terms needed and estimates of the full correlation structure among environments. Chapter 3 deals with competition among plants and its influences on statistical inference from field trials. Several alternative modelling approaches were evaluated for joint consideration of competition and environmental trend or spatial effects. Improved models were found for routine of data analysis in annual and perennial plants. Several plant species are of great economic and social importance in Brazil. Scientific experiments with these plants are designed with the objectives of providing new technologies which will contribute for the enhancement of production and productivity of the crops. These enhancements will contribute for the economic and social development of the country as well as for the environmental conservation as a result of a reduced pressure over the natural resources. The plant breeding programmes in the country produce annually a huge amount of field data which need to be statistically analysed in an efficient way. In this context, optimal statistical methodology is essential in transforming data in useful scientific information for the rural development. in this sense, the research reported here will bring great impact. Vitor Afonso Hoeflich - Chefe Geral da Embrapa Florestas.