Data analysis tools

In WP 3.1 the emphasis is on developing and adjusting existing deterministic crop models to make these applicable for use in QTL analysis. An inventory of crop growth models has been made and three crop models, ranging from simple to complex, have been developed or selected. The simplest model simulates growth of vegetative and generative biomass based on light use efficiency. Partitioning to the fruits (harvest index) is assumed to be constant. The second model resembles the simplest model, but includes a boxcar train method to simulate fruit development. The most complex model is INTKAM (> 50 parameters), which contains many submodels for e.g. light interception, photosynthesis, respiration, dry matter partitioning and fruit growth.

It is an important research question in this project, to determine which model will best serve our goals. A simple model with only view parameters that can all be determined for all genotypes, or a complex model with many parameters. Such a complex model is more flexible and ‘physiologically sound’. However, it contains many parameters which can not be determined for each genotype and hence have to be assumed equal for all genotypes. Furthermore, part of the parameters will hardly influence the model output. Based on sensitivity analysis the most relevant parameters in such a complex model have to be determined and will be measured on all genotypes.

In a preliminary greenhouse experiment some crop model parameters have been determined for 9 genotypes of the mapping population. These 9 genotypes were selected from the 150 genotypes in such a way that phenotypic and genotypic variability was still covered. A large genetic variation in leaf photosynthetic rate was determined (Fig. 1). The highest value was about 60% larger than the lowest value. This result is promising, and quite unexpected. Often it is believed that genotypic variation in leaf photosynthetic rates in rather small. This large genetic variation in leaf photosynthetic rates opens possibilities for breeding for substantial increases in pepper yield.

Figure 1: Genotypic variation in photosynthetic capacity for 9 genotypes from the mapping population. A start has been made with the selection of the most relevant crop growth model parameters and a model uncertainty and sensitivity analysis concerning yield. A probabilistic sensitivity analysis will be applied (Fig. 2).

Fig. 2. Schematic presentation of so-called probabilistic sensitivity analysis.

This is a better way to determine the importance of parameters in a model than the often used percentual change approach in which a parameter value is varied by plus or minus 10% and compare this with the percentual change in output. In a probabilistic sensitivity analysis, probability distributions for the model parameters are determined, and a large number (e.g. 1000) of parameter combinations (for each parameter a random drawing from its distribution) are created. The model is running for each of these 1000 parameter combinations and a statistical analysis between input and output will reveal the importance of each parameter in the output. Preliminary results showed that some photosynthesis parameters are very important, whereas e.g. the leaf scattering coefficient or the stomatal response to humidity and temperature plays only a minor role.

One omission in this advanced sensitivity analysis, but also in the more common percentual change approach, is the fact that correlations between parameters are not yet taken into account. We will try to take this into account in our final analysis when possible.

WP 3.2 is dedicated to the development of QTL mapping methodology for the identification of crop growth parameters. Attention should be given to the modeling of phenotypic traits over time, and more specifically to the changes (increase/decrease and acceleration/deceleration) that these traits show. Furthermore, growth traits/ the growth of traits should not be studied for individual traits, but for all traits simultaneously. The mapping of QTL for longitudinal traits may be done by a two step approach comprising the fitting of a suitable growth curve (e.g., logistic, exponential, Gompertz) and subsequently treating the curve parameter estimates as trait records (e.g., Malosetti et al. (2006) TAG113:288-300). However, here we aim to integrate these two steps into one flexible method that for example takes into account the uncertainty in parameter estimates.

Figure1: Logistic growth curve with three possible perturbations, i.e., earliness, maximum yield and growth rate.