Statistical methods in variety testing

As part of accompanying Rosemary to her conferences, I have just spent four days at the Thirteenth Working Seminar on Statistical Methods in Variety Testing, at COBORU at Sŀupia Wielka, Poland.

COBORU is an acronym for a Polish phrase which translates as Research Centre for Cultivar Testing. The acronym is a little misleading: the C is soft, since it stands for “Centralny”. The institute has a legal duty to test varieties of crop seeds from plant breeders and recommend the best ones to farmers. The region is agricultural land, dead flat (much flatter than, say, the English fens) and with hardly any farm animals to be seen. Our hotel was almost next door to the factory that processes sugarbeet, and maize and vegetables are also common in the fields, with the occasional field of sunflowers.

I had expected to spend my time getting on with work while Rosemary was at the talks, but in fact I found a lot of the talks rather interesting. Not in a mathematical way, partly due to my lack of knowledge. I don’t know the difference between fixed and random effects, and my eyes glaze over at the sight of the equation defining a linear model which runs over two lines and has terms with four subscripts. But there were some interesting general principles addressed.

I know that, if you get a group of statisticians together, they will grumble about the fact that scientists don’t consult them before doing an experiment, but just bring along the data to be analysed; some thought about design could make the results much more informative. But there were a few more specific things discussed by some of the speakers.

For example, who is the testing for? It is a legal requirement, sure, but ultimately it is for the farmers. Recommendations are made by region, but farms even within a region can differ significantly in soil, drainage, etc. Can the statistical models be strengthened to give tailored information to farmers? Of course, there is another problem. The big uncertainty for farmers is next year’s weather; this could easily affect which variety will perform best, So, like the meteorological office, the variety testing can only offer probabilistic forecasts, and it is up to the farmers to interpret this.

A smaller problem of the same sort concerns varieties likely to perform best under conditions of climate change. For example, nitrogen uptake by wheat gives an estimate of the protein content of the grain; but breadmaking needs specific proteins which require much more elaborate tests.

Several talks involved what might be called “statistical archaeology”. There is a large quantity of data available, since the tests have been running for a long time. Sometimes, the experiments were not well designed according to statistical principles. If it could be shown that this mis-design causes a loss of precision in the results, and consequently the risk of recommending inferior varieties, this would be evidence to persuade scientists to seek statistical advice before setting up the experiment. Some ot the data permitted this to be done, given some reasonable assumptions, and results show that the statisticians were right.

Another case in point was driven by a change in the regulations about the information required. New statistical protocols are required, but it is important that the new results should be comparable with the old. So it was neceessary to re-analyse the old data according to the new methods, and check that the results were consistent with what was obtained before.

There was a day off for an expedition to Poznań. The morning was spent at the Institute of Plant Genomics, part of the Polish Academy of Sciences, where we were shown some of the equipment and one of the greenhouses (not much to see because of the time of year). We were shown two pots each containing a plant of genetically modified ryegrass, hopefully able to better cope with extreme climate, along with two pots containing normal ryegrass. It was not possible to see a difference with the eye. Later, the Director of the Institute recognised Rosemary and reminded her that they had interacted at Rothamsted more than forty years ago.

In the afternoon, the intention had been to take us to the coding museum. Before the Second World War, the cryptanalyst Marian Rejewski and his colleagues in Poznań had obtained a commercial Enigma machine and had figured out what would be required to break the code produced by the more elaborate military machine. They were later able to get to Bletchley Park with their expertise and their Enigma, both of which were very helpful to Alan Turing and the other British codebreakers. Without this, no doubt things would bave been rather different.

Unfortuntely the museum was closed for refurbishment, so we were taken to a different museum, where we were told the history and manufacturing method for special Poznań filled croissants inspired by St Martin and a speciality of the city. At the conclusion of the session we got to eat half a croissant each and to watch the two goats on the City Hall who come out and head-butt each other fifteen times at 15:00.

Later, Marcin Przystalski (one of the meeting organisers), seeing my interest in matters cryptographic, sent me a paper in English written by Rejewski in 1980 and published in Zastosowania Matematyki describing the mathematics behind breaking the Enigma code, which Marcin described as “solving simultaneous equations in permutations”.

The remainder of the trip was free time to explore around the Old Market Square. We found nearby, outside a church, a wonderful photographic exhibition of the people of Nagaland, on the border of India and Myanmar, who had been headhunters until just fifty years ago. A Polish photographer had visited for their Hornbill Festival and taken some really remarkable pictures of the people, their crafts and customs.

The food, both breakfast and dinner in the hotel and lunch in the Institute, was really good; the only problem was that there was far too much of it. The conference dinner (unusually, held on the evening after the conference) had four courses; the seecond course alone had four different kinds of cooked meat along with several plates of vegetables and salads. The final course, after we thought everything was over, consisted of meat, cheese and salad, with unlimited bread in case we were still hungry.