Mathematical Modelling of Grazing in Drylands

Drylands are areas where the rainfall is so low that it limits vegetation growth. If we exclude deserts, drylands represent about 40% of the Earth land surface. These regions are threatened by desertification i.e. degradation of the land into a state of non-productivity. It is driven by climatic factors as well as human activities. Alongside deforestation and poor agricultural practice, animal husbandry is identified as one of the causes of land degradation. However, there is some controversy around the impact of grazing in arid regions. Livestock have been alternately charged and absolved of being a leading cause of desertification, with some actors even prescribing grazing as a solution to the problem. The general consensus is that overgrazing is a driver of land degradation but the dynamics of grazing systems are still not well understood. Half of the world's livestock is concentrated in arid regions and about 70% of the rural West and East African drylands population rely fully or partially on livestock for survival. Furthermore, "demand for African livestock and livestock products is expected to grow rapidly". Trying to satisfy this increasing demand without adequate policing can lead to irreversible long-term ecological and hence socio-economical prejudice. It is therefore essential to to try to elucidate the processes involved in grazing systems and design optimal grazing strategies. One source of uncertainty when trying to predict the effects of grazers on a system lies in the plants' response to grazing. There is evidence that plants can respond to biomass removal with a modified growth rate. The nature and extent of this response, known as compensatory growth, can determine the tolerance of a vegetated system to grazing. The project aims at informing decisions about the optimal number of grazers a system can sustain, through mathematical modelling. We can refer to this goal as a management approach. In this project we incorporate 3 different plant response scenarios -namely constant growth rate, linearly increasing growth rate and linearly decreasing growth rate- into a preexisting mathematical model for grazing in arid ecosystems. We study the outcome through stability analysis and discuss the ecological interpretation for each of these scenarios.

MAC-MIGS develops computational modelling and its application to a range of economic sectors, including high-value manufacturing, energy, finance and healthcare. These fields contribute over £500 billion to the UK economy. The CDT involves collaborations with more than a dozen companies and organisations, including large corporations (AkzoNobel, IBM, Dassault, P&G, Aberdeen Standard Investments, Intel), mid-size firms, particularly in the engineering and power sectors (NM Group, which provides monitoring services to power grid operators in 30 countries, Artemis Intelligent Power, the world leader in digital displacement hydraulics, Leonardo, a provider of defense, security and aerospace services, and Oliver Wymans, a management consultancy firm) and startups such as Brainnwave, which develops data-modelling solutions, and Opengosim which designs state-of-the-art and massively parallel software for subsurface reservoir simulation. Government and other agencies involved will include the British Geological Survey, Forestry Commission, James Hutton Institute, and Scottish National Heritage. Engagement will be via internships, short projects and PhD projects. BIS has stated that "Organisations using computer generated modelling and simulations and Big Data analytics create better products, get greater insights, and gain competitive advantage over traditional development processes". Our partners share this vision and are keen to develop deeper collaborations with us over the duration of the CDT.

Our CDT will achieve the following:

- Produce 76 highly skilled mathematical scientists and professionals, ready to take up positions in academia or in companies such as our partners. The students will have exposure to projects, modelling camps and high-level international collaborations.

- Deliver economic and societal benefits through student research projects developed in close collaboration with our partners in industry, business and government and other agencies.

- Create pathways for impact on computer science, chemistry, physics and engineering by involving interdisciplinary partners from Heriot-Watt and Edinburgh Universities in the supervision and training of our students.

- Organise a large number of lectures and seminars which will be open to staff and students of the two universities. Such lectures will inform the wide university communities about the state-of-the-art in computational and mathematical modelling.

- Work with other CDTs both in Edinburgh and beyond to organise a series of workshops for undergraduates, intended to foster an increased uptake of PhD studentship places in technical areas by female students and those from ethnic minorities, with potential impact on the broader UK CDT landscape.

- Organise industrial sandpits and modelling camps which offer the possibility for our partners to present a challenge arising in their work, and to explore innovative ways to tackle that challenge, fully involving the CDT students. This will kick-start a change in the corporate mindset by exposing the relevant staff to new approaches.

- Develop a new course, "Entrepreneurship for Doctoral Students in the Mathematical Sciences" in conjunction with Converge Challenge (Scotland's largest entrepreneurial training programme) and UoE's School of Business. This and other support measures will develop an innovation culture and facilitate the translation of our students' ideas into commercial activities.