Mixture models as an exploratory tool for the analysis of internal nitrogen use efficiency Munoz-Santa, I.; Marschner, P.; Haefele S.M.; Kravchuk, O. The University of Adelaide 1. Why analysing internal nitrogen use efficiency (IEN )? 5. Case study: nitrogen use efficiency in non-irrigated rice systems in Thailand IEN expresses the ability of plant to utilise nitrogen to produce grain and is the ratio of grain yield (GY ) and nitrogen uptake (N U ). A better understanding of this index will lead to efficient agronomic practices and improved yield. 5.1 Data collection 5.2 Results Three groups were identified in the (GY , N U ) data of the case study (Fig. 2). These groups appeared to be defined by the soil water status at post-flowering and the application of N in soil. Fig. 1: Typical scatter of grain yield and nitrogen uptake. Data source: Naklang et al. (2006) GY and N U are cumulative random variables collected in controlled field trials and measured at plot level. At harvest, the typical (GY , N U ) scatter for a particular cultivar grown under a range of conditions exhibits an increasing monotone linear-plateau shape (Fig. 1). 2. Univariate models for IEN vs bivariate models for (N U, GY ) At present, IEN data are predominantly analysed by univariate linear models. However, these models: • Lose information on the N U and GY traits, which complicates the interpretation of the effects of agronomic practices or environmental conditions on the N U utilisation for GY • May produce misleading results as the IEN data (see Marsaglia 2006) may violate the assumptions of normality and homogeneity of error variances required by these models Alternatively, we propose to use bivariate models on (GY , N U ) which maintain the information of N U and GY and avoid dealing with the abnormalities issues of IEN Fig. 3: Mixture groups for the grain yield and nitrogen uptake data of the case study together with the N fertiliser status (left) and the water status of the soil at post-flowering (right) 6. Conclusions 1. The usefulness of bivariate mixture models to identify potential environmental factors affecting (GY , N U ) has been demonstrated in our case study 2. In designed field trials, the independence assumption required for the application of mixture models may not be fulfilled and thus, the technique is proposed for exploratory purposes only 3. Collecting data from designed field surveys is a more appropriate sampling method for the application of mixture models 3. What if we want to identify environmental conditions affecting (GY , N U )? In the field, there are a myriad of non-controlled environmental conditions which can affect the utilisation of N U for GY . Non-controlled conditions may lead to different N utilisation patterns for GY and thus, to the presence of groups in the (GY , N U ) field data. These groups may not necessarily coincide with treatments groups. References Marsaglia, G. (2006). Ratios of normal variables. Journal of Statistical Software 16, 1-10. Naklang, K., Harnpichitvitaya, D., Amarante, S.T., Wade, L.J. & Haefele, S.M. (2006). Internal efficiency, nutrient uptake, and the relation to field water resources in rainfed lowland rice of northeast Thailand. Plant and Soil 286, 193-208. 4. Bivariate mixture models as an exploratory tool to identify environmental conditions Mixture models of bivariate Gaussian distributions are proposed to identify potential groups in (GY , N U ) field data when sampling across a range of environmental conditions. The inspection of the groups can reveal important environmental drivers and shed additional insight to treatment-based analyses. Acknowledgment Faculty of Science at the University of Adelaide for the scholarship for Masters in Biometry for the first author [email protected] LATEX Tik Zposter