Sabela MunozSantos, Mixture models as an

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
sabela.munozsanta@adelaide.edu.au
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