Math Biology

Applied mathematicians are omnivores, any interesting phenomena we observe we develop tools to describe and understand it using the language of mathematics. The biological world provides many lifetimes (and beyond) of interesting phenomena and so it is no surprise that mathematical biology is an active, diverse and important research field; my interests span a number of fields. I am interested in the interaction between fluid motion and microbial or animal behaviour. This includes the behaviour of gyrotatic organisms in the presence of complex fluid motions and understanding how the presence of underlying fluid motion can aid our understanding of how animals exhibit collective motion, bird flocks for example. More recently, I have become involved in a number of projects attempting to understand the spread of tree disease in UK forests. This is particularly motivating as at present a series of silent pandemics in tree and plant species pose a massive threat to humanity and our current way of life. Mathematical modelling may provide some insights into how to plan, react and inform policymakers. Finally, I am interested in understanding the spread of farming in the Neolithic epoch using mathematical modelling. Contributions I believe are important to the field are highlighted below.

Research Highlights


Early warning signals in tree disease Native trees are under constant threat from alien pests and diseases, as exemplified by recent outbreaks affecting ash and sweet chestnut trees. Such outbreaks have massive social and economic impacts and motivate the need to sustain their existence through suitable planning and management. Climate change exacerbates this threat by promoting the migration, survival and growth of alien pathogens. Indeed, the Department for Environmental, Food and Rural Affairs (Defra) has highlighted the importance of modelling in developing robust plans and management policies for minimising the impacts of these threats.
In a recent paper we used the framework of early-warning indicators for impending regime shifts, widely applied to dynamical systems, to study the transition between the confinement of forest disease to a catastrophic outbreak. Our study demonstrates early-warning indicators can prediction of forest disease epidemics, and may also be useful to identify a suitable planting density to slow down disease spread.


Stem cell colonies Stem cells are at the forefront of modern biological research. Indeed, human embryonic stem cells (hESCs), pluripotent cells, have the capacity to differentiate and give rise to all tissues of the body. Thus it is hoped that stem cell based therapies may be used in the future to treat life-changing illnesses and intensive efforts. In lab-grown stem cell colonies maintaining undifferentiated cells is critical for developing applications in regenerative medicine, drug testing and also studying fundamental biology. At present, the selection of the best quality cells and colonies is typically performed by eye, relying on expertise to identifying key morphological features such as a colony with a tightly packed appearance and a well-defined edge. In a recent study, we developed a methodology using image analysis and computational modelling to quantify such properties. The findings of this study are important to help understand the biological processes that lead to the establishment of quality of hESC colonies, and establish a colony characteristics database to guide future studies.


Anticipation in Flocks Collective animal motion produces some of the most spectacular displays the natural world has to offer. From the rotating of ant colonies, to starling murmurations, to wildebeest stampeded across the African savannah, all have captured human imagination and interest. Mathematicians have developed several approaches which try to explain how such behaviour can be modelled and then understood. One of the most widely applied models to understand the emergence of 'flocking' behaviour is the Vicsek model. In this agent-based approach, each organism is modelled as a point object, and flocking arises due to local alignment rules. Numerous examples have shown flocking is robust to noise which is delta correlated in both time and space. However, a study by Khurana & Ouellette showed that spatiotemporally correlated noise strongly affected the ability for Vicsek flocks to form. Cleary schools of fish and flocks of birds form in turbulent environments and so it is important to revisit the alignment mechanism proposed in the original Vicsek model. In a paper published in 2016, I showed that a combination of alignment with local neighbours and an anticipation of their motion provides a mechanism for flocks to persist in the presence of vortical fluid motion. Whilst the primary motivation is to help understand the complex interactions present in animal groups there may also be applications in the design of flocking autonomous drones and artificial microswimmers.


Neolithic Riverways The transition to the Neolithic was a crucial period in the development of Eurasian societies, defining to a large extent their subsequent evolution. The introduction of agro-pastoral farming, which originated in the Near East ~12,000 years ago and then spread throughout Europe, is considered a defining feature of this transition. In a series of papers, we developed a mathematical and statistical framework to understand the role of waterways in aiding the spread of farming into western Europe. Our results confirmed several of the conclusions of earlier studies: i ) an accelerated spread of the Neolithic along the western Mediterranean coast, ii)m evidence for a modest acceleration of the Neolithic dispersal in the eastern Mediterranean, iii) an enhanced spread in the Danube–Rhine corridor. Such findings help understand the global picture of the emergence of farming across Europe.

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