## General

In a harvest not every grain has the same weight. Some are lighter, some are heavier. In case of source limitation, often a bimodal frequency distribution function is seen with a peak to the left for unfilled grains (also called unfilled spikelets). I developed a mathematical model that predicts the frequency distribution. The model simulates a larger peak for the unfilled grains when source limitation and/or sterility occurs. A paper for this model is in preparation. An Excell implementation of the grain weight distribution model can be downloaded from this website.

## Specifications

Frequency distribution of grain weights

Yield of grains within a specific weight range (e.g. only grains heavier than 15mg)

## Software requirements

MS Excell

N/A

## Examples

Grain weight distribution modelling is completely new. This is a first effort to develop a model and there has been limited experimental research. However, we foresee the tollowing applications:

- Economics, for example defining quality thresholds and calculate how much “economic” yield remains after selecting only those grains in a particular weight range (the shaded area in Fig 1). With a mathematical model, calculating this “economic” yield becomes a simple matter of calculating the integral of the area in this range. Note that just as easily the “economic” yield can be calculated with a lower threshold only.
- Grain quality research. Logically we expect correlations to exist between grain weight categories and other quality characteristics. Because for the lighter grains, the bio-chemical maturation process may not yet be completed, so their chemical composition will be different. Likewise there may be reason to expect lower quality for the heaviest grains. We expect that a plant would first allocate the essential minerals, enzymes and fats to a seed to allow this seed to germinate successfully and we expect that this is achieved at peak grain weight. Beyond that, extra weight will be mostly extra energy provision (starch) that allows the seeds to germinate even better but not necessarily benefits consumption quality. It is therefore logical to expect correlations between grain weight categories and grain quality characteristics. Yet such correlations have not been investigated before. New instruments for grain weight separation will allow for doing so. A grain weight distribution model would allow to scale up from quantification of correlations to quantification of “economic” yield. Or develop product diversification based on weight and quality characteristics.
- Physiological / agronomic research. How do different forms of environmental stress, at different stages during crop growth, affect the shape of the distribution function? And in turn how does this affect quality and “economic” yield? For example Fabre et al 2005 found salinity affected the peak weight. A model would allow to simulate how reductions in peak weight by itself or in interaction with other effects of salinity such as reduction in spikelet number and total yield, would affect “economic” yield or quality as discussed above.
- Ideotyping (= right word in this case?): with a grain weight distribution model that can mathematically reproduce shapes such as in figure 1, it is possible to change shape parameters such as peak grain weight, standard deviation around the right peak, minimum and maximum spikelet weight and investigate how this can affect “economic” yield. Subsequently, it can be investigated if genetic variation in such shape parameters can be exploited to increase “economic” yields.