By Ed Donlon

The UK Graduate Modelling Camp (www.maths.ox.ac.uk/r/infommgradcamp) took place from 15-17 July 2020 under slightly unusual circumstances, as the COVID-19 pandemic necessitated online-only attendance, rather than the usual

in-person experience. Nevertheless, the camp was undoubtedly a huge success, thanks in no small part to the fantastic work put in by the organising committee. The aim of this annual event is for attending PhD students to gain hands-on mathematical modelling experience, working together on problems that have been inspired by real-world applications arising in industry or science. Following opening presentations from the attending project mentors, students then rank the projects in order of preference and are subsequently formed into teams. The main modelling work then begins under the supervision of the project men- tor, with intermediate progress presentations on the second day and final group presentations to finish the camp.

I had forgone the opportunity to participate in any summer schools or modelling camps during my first summer as a PhD student in 2019, as I decided to complete an industrial internship in Germany instead. Therefore I was extremely eager to attend the 2020 modelling camp. This camp traditionally serves as a warm-up to a subsequent European Study Group with Industry, which in this case was ESGI 162 hosted by the University of Leeds.

This year’s camp featured many interesting and wide-ranging problems, such as investigating how a plant root generates curvature to exploring optimal ship berthing strategies to reduce tugboat fuel consumption. Having read scientific and wider media coverage of the global plight of bee populations, the problem that really intrigued me was the project presented by Ashleigh Hutchinson from the University of the Witwatersrand, South Africa, which involved investigating the impact that climate change has on bee-blossom interactions.

Mismatch of Bee Behaviour and Flowering Dates

Bees and other pollinators are critical for maintaining the stability of the global ecosystem. In fact, a 1976 United States Department Of Agriculture report claimed that every third bite of food in the human diet relies upon insect pollinators. While later commentators have suggested that this claim may have been a slight exaggeration, it nevertheless indicates the importance of bees to global agriculture. However, their numbers are declining and one of the contributing factors towards this is the impact of climate change on the phenology of their food supply, namely blossoming flowers.

There exists a mutually beneficial relationship between bees and flowers: bees consume pollen and nectar from blossoming flowers, and in return plants require bees for fertilization and propagation, allowing for new plants to develop. Many other organisms then also rely on these flowers as a food source. In order to optimise the amount of food that will be available to the colony, bees have developed an internal calendar that attempts to time the end of their circannual hibernation period with the beginning of the blossoming season. They use external stimuli, such as changes in mean day length and temperature, to determine the appropriate end of their dormancy period. Unfortunately, climate change has increased mean global temperatures and the frequency of extreme weather events, amongst numerous other negative effects, and thus has disturbed many temporal phenomena in the natural world. Due to this, bees have begun to emerge from their torpid state and leave their hives in search of food before flora have begun to bloom in spring, thus upsetting the delicate balance between the two populations (see Figure 1).

Bees live in eusocial colonies, exhibiting an organised social hierarchy with interactions between the various population subgroups. To simplify matters, our work considered only two of these subgroups: hive bees and worker/forager bees. Worker bees are primarily responsible for food collection and bring pollen back to the hive. This is then converted into honey, which is stored in the hive and feeds the larvae in the brood. During the winter hibernation period, the workers bees die out and leaving the fertilised hive bees to survive the winter and perpetuate the species the following spring. Depending on available food supplies and other factors, hive bees can be recruited into worker bees.

The aim of our work was to develop a discrete dynamical system to describe the complex dynamics within bee populations, their interactions with blossoms, and the resulting change in behaviour due to global warming. Research has shown that different species are adapting their annual behaviour to climate change, but that not all species are adapting at the same speed or in the same ways. This discrepancy could significantly damage the way that the global ecosystem functions. It is hoped that accurately quantifying and modelling this relationship could provide direction for more targeted data collection and guide future research in this area.

Personal Takeaways

I thoroughly enjoyed the camp and will definitely look to take part in similar events in future. All credit must go to Professor Chris Breward and Sarah Howle from the Mathematical Institute at the University of Oxford for expertly organising the event, and to the project mentors for their helpful guidance. I had been a little unsure what to expect on the first day and was rather surprised to be introduced as the long distance participant! Of course, other international students from further away places did attend, but it turned out that I was the only the only one registered from a non-British university.

As the event was held online, we of course missed out on the opportunity for in-person social interactions and the usual networking that takes place during lunches and coffee breaks. However, I still found that our group worked very well together. The small group sizes definitely helped, as each team had on average 6 students, which gave everybody ample opportunity to contribute. My team members Alex, Anna, Constantin, Tosin and Yoana each made valuable contributions to the project and everybody brought different approaches and skills to the table, which made for some really engaging discussions about our problem. The remote collaboration tools that were suggested for us to use were a big help and made online working easier. Some of these I was already familiar with, such as Microsoft Teams and Overleaf, while others like WhiteboardFox were new to me but definitely helped our team to share ideas.

What really impressed me from watching the final project presentations was the many branches of mathematics that each group used, such as continuum mechanics, dynamical systems, numerical simulations, and data analysis. The standard of each group’s work was extremely high, and our group were delighted to end up finishing in second place in the competition. I hope that I will have further opportunities to work with my team members in future.

Ed Donlon is a PhD student in Applied Mathematics at Technological University Dublin, Ireland. An amended version of this article also appeared in the October 2020 edition of Mathematics Today, published by the IMA (Institute of Mathematics & its Applications).