Research

My PhD project is titled "Collective behaviour under non-reciprocal pairwise interactions", supervised by Dr. Richard James and Prof. Tim Rogers. Preliminary experimental work and mathematical modelling suggest that sexual conflict can give rise to non-reciprocal interactions and anomalously fast diffusion of pairs of Trinidadian Guppies (Poecilia reticulata). In the long-term, their behaviour also results in key ecological and evolutionary processes such as population dispersal and invasion of alien species. To combine the biology of pairwise interactions through to population level consequences will require mathematical models of processes at different time, spatial and social scales. In biological terms, such problems lie at the intersection of movement ecology and collective behaviour. Using mathematical techniques from agent-based modelling, mean-field and coarse-grained approximations and continuous time PDE modelling, the aim of the project is to develop a general framework, or suite of mathematical models, to interpolate between and extrapolate from one social, spatial and temporal scale to the next, modelling the effect on non-reciprocal social forces in Trinidadian Guppies on large-scale population structure and the ecological and evolutionary consequences of their behaviour.

As part of my PhD project, I have also had the privilege of spending two weeks working at the University of Exeter with my external supervisors Dr. Safi Darden and Prof. Darren Croft, designing and carrying out experiments with Trinidadian Guppy Fish. The experiments aimed to investigate the role of sexual conflict in animal movement, and how significant a factor it is in driving it. Guppies were housed in tanks at different sex ratios and monitored for 24 hour periods. Within each tank, there was a waterfall leading to a separate area of the tank, requiring the guppies to make an active decision to leave their existing environment, we could then gain insight into which sex was more likely to jump at different ratios. Analysis of the data is ongoing, but the results from the experiments will eventually inform the mathematical modelling I develop, meaning it will be grounded in real-word observations and behaviours.

During my undergraduate degree, I had the opportunity to complete two research internships. The first of which, funded by EPSRC, was an in depth study of the Cucker-Smale and Cucker-Dong models of collective animal motion. I subsequently completed both my third year and Master's projects on the topic, both of which were supervised by Dr. Galane J. Luo. In the latter, I devised a new, agent-based model of collective motion, specifically designed to recreate the murmuration phenomena commonly observed in large flocks of starlings. The model was simulated numerically for a wide range of parameter values and the rich behaviours resulting from these simulations were investigated in detail. I was also part of a British Academy funded project which set out to develop a novel, agent-based model of human opinion dynamics. Agents in the model update their opinions based on interactions with others, providing the pair exceeds a certain "affinity threshold". The concept of memory was also introduced, creating a non-Markovian process of opinion updating. The model successfully recreates many socio-psychological phenomena, such as extremism, segregation and oscillatory opinions, more details can be found in our publication in the Journal of Mathematical Sociology.