Mathematical modelling in the science and technology of plant breeding
The livelihood of humanity depends crucially on the growing and harvesting of crops, the processing of crops to produce the various foods that are eaten and the distribution of the resulting products and produce to the various consumers. The underlying biological foundation on which the success of this complex industrial hierarchy of activity rests is the success of the ongoing process of plant breeding. Not only must plants be bred to ensure that the planned end-products, such as bread, cakes, pasta and noodles, are of acceptable quality, they must, in order to minimize crop failure and thereby ensure food security and supply, also be insect and/or disease resistant. The success of such endeavours rests on the quality of the underlying science, which has become highly sophisticated in recent years. Its utilization, in terms of the modern understanding of the genetics of plant growth and the increasing sophistication of experimentation and instrumentation, has greatly improved the speed and quality of plant breeding. The associated implementation of these new plant breeding protocols is generating a need for improved quantification through the utilization of mathematical modelling. In order to illustrate the diverse range of mathematics required to support such quantification, this paper discusses some illustrative aspects connected with the recent modelling of the flow and deformation of wheat-flour dough, information recovery from spectroscopic data (e.g. such as the determination of the protein content in wheat), antiviral resistance in plants and pattern formation in plants. Various aspects of the mathematics involved are highlighted from a mathematical modelling perspective, with a key secondary goal, using the discussion about these examples, of illustrating how applications impact on mathematics with the resulting mathematical developments in turn contributing to the solution of other applications with the process starting all over again.