Mathematical modeling of scatter-hoarding
PhD (submission 2018)
Supervisors: Alex James, Mike Plank, Hazel Chapman
Carapa oreophila is one of the most important plant species that can be found at the Nigerian Montane Forest, Mambilla Plateau, Nigeria. Recently, an empirical study unveils that due to the large size of Carapa seed, it can only be dispersed by a large rodent, the African pouched rat. When a rodent carries a seed, it will either eat it if it is hungry (i.e. predation) or cache it for the future use. Sometimes, the rodents may not remember all the seeds they cached and this may lead to the successful germination of Carapa plant (i.e. mutualism). This research will investigate the coexistence of both Carapa trees and the rodents using the stochastic simulation algorithms (Gillespie algorithm) and their deterministic analogues, the Lotka-Volterra models. The caching activities and the behavioral movement of the rodents when encounter the seeds in the forest will be analyzed through the stochastic spatial models and partial differential equations for the sustenance of the ecosystem at the forest.
Spatial moment models of collective cell behaviour
Supervisors: Alex James, Mike Plank, Mat Simpson
The ability of cells to invade to local sites or distant parts of the body is fundamental for a number of physiological processes, for example embryonic development and wound healing. We are using random walk theory to develop a model that describes how invading cells behave at the individual-level. We also consider how spatial moment dynamics can be used to relate these microscopic events to the emergent behaviour of the whole cell population. Running experiments with live invading cells will allow us to refine our model so that it is an accurate representation of a real invasion process. In the long-run this model could be used to test the efficacy of therapeutic strategies for manipulating invasion.
Binny, R. N., Plank, M. J., & James, A. (2015). Spatial moment dynamics for collective cell movement incorporating a neighbour-dependent directional bias. Journal of The Royal Society Interface, 12(106), 20150228. http://rsif.royalsocietypublishing.org/content/12/106/20150228
Synopsis: The ability of cells to migrate as a collective, either to local sites or distant parts of the body, is fundamental for tissue repair, development and cancer. Interactions occurring at the level of individual cells may give rise to spatial structure, such as clustering, which can in turn have a significant impact on the emergent dynamics of a cell population. We develop a mathematical model for collective cell movement to explore how individual-level behaviour scales up to the level of a moving population. Our model allows an individual's direction of movement to be affected by interactions with other cells in its neighbourhood, providing insights into how directional bias generates spatial structure.
This project is partially funded by the Marsden Fund (royalsociety.org.nz).
Modelling orange roughy population dynamics
Supervisors: Elena Moltchenova, Alex James, Sharyn Goldstien
The Ministry of Primary Industries (MPI) is responsible for fisheries management in New Zealand. In order to make sound management decisions they require a range of mathematical and statistical modelling techniques. The available data for modelling is often catch and effort data which may not be representative of the true population dynamics so it is important to quantify the uncertainty which is inherent in the data and modelling process. Orange roughy is a long-lived deep-sea fish which matures late and has low fecundity. The orange roughy life cycle was not taken into account in early modelling which contributed to overestimates of population biomass and subsequent overfishing in many orange roughy fisheries. My project involves modelling orange roughy biomass based on twenty years of catch and effort data to gain insight into the effect of fishing on population dynamics.
Computational modelling of neurovascular coupling pathways with the effects of oxygen
dependency of the sodium-potassium exchange pumps (Na+/K+ -ATPase) in the neuronal membrane.
PhD student (2013-2016)
Supervisors: Prof. Tim David and Dr. Michael Plank
Neurovascular coupling is the mechanism by which neural stimulation affects the vascular constriction or dilation and hence blood flow in the brain. This mechanism facilitates the almost instantaneous supply of nutrients (oxygen and glucose) to the region of the brain in need. A disrupted neurovascular coupling is noticed in pathological conditions such as hypertension, Alzheimer disease and ischemic stroke. My project aim is to computationally model the neurovascular coupling mechanism pathways from a neuronal input to the mechanical vessel response with the effects of oxygen dependency of the neuronal membrane for energy (ATP) production. The model framework may help to understand the exact set of neurovascular coupling pathways and thereby an understanding of the various associated pathological conditions.
This project is partially funded by College of Engineering.
Predicting Range Limits of Multiple Competing Species along Environmental Gradients
PhD student (2013 - 2016)
Supervisors: Rua Murray, Michael Plank and William Godsoe
My project aims at developing a mathematical model for multiple competing species to study the interplay of competitive interactions and range limits (i.e. the boundaries of locations in which a species is found) along environmental gradients. We use ideas from ordinary and partial differential equations, as well as bifurcation theory in modelling the spatial distributions of species. We hope to utilise this model in order to predict the invasive species spread over heterogeneous environments, which is one of the serious problems in New Zealand.
Modelling dispersal of bio-control agents of Tradescantia fluminensis
Summer student (2013-2014)
Supervisor: Alex James
My project was to create a model for the prey density of T. fluminensis in a bio-control scenario, in particular allowing for the effect of prey depletion on population dynamics. We used simple random walks as a model of the movement of the bio-control agents predating T. fluminensis, and interaction rates were derived by considering these movements. Stochastic simulations were compared to both the classical Lotka-Volterra predator-prey model and the new model which takes prey depletion into account. This model can be used to more accurately predict the success of future bio-control activities.
The work was partially funded by AgResearch (agresearch.co.nz).
Biology and ecology of Etelis coruscans and Pristipomoides filamentosus at seamounts: Case study at Tonga deepwater bottomfish fishery
PhD (submission March 2015)
Supervisors: Sharyn Goldstien, Alex James and Ashley Williams (SPC)
There are concerns about the depletion of deepwater bottomfish stocks in the Pacific region and the assessments of the fisheries have been limited by lack of adequate biological and ecological data. The main objective of my study is to develop science-based management measures to ensure sustainable utilisation of the Tonga deepwater bottomfish fishery and the conservation of seamount communities. Biology and spatial ecology of Etelis coruscans (ruby snapper) and Pristipomoides filamentosus are being studied to determine the life history parameters such as age, maximum length (L8), growth rate (K), natural mortality (M), fishing mortality (F), total mortality (Z), fecundity, spawning season and size at maturity. These parameters are vital for stock assessment and management of deepwater bottomfish. In addition, the spatial distribution of Etelis coruscans and connectivity between seamounts are also studied. The outcomes of this study will strengthen the management and conservation of the Tonga deepwater bottomfish fishery. It can also be applied to the management of deepwater bottomfish fisheries in other pacific countries. My study is co-funded by the New Zealand Government, University of Canterbury and the Secretariat of the Pacific Community.
Modelling sepsis in the ICU
PhD (submission June 2014)
Supervisors: Geoff Chase, Alex James
Funded by Mechanical Engineering.
Modelling mat thickness of Tradescantia fluminensis
Supervisors: Alex James, Mike Plank, Shona Lamoureaux
This project is partially funded by AgResearch (agresearch.co.nz).
PhD (submission March 2014)
The Evolutionary Dynamics of Bacterial Addiction Complexes.
Supervisors: Jack Heinemann, Alex James, Anthony Poole.
I use mathematical models to understand the evolution and population dynamics of bacterial replicons (e.g. chromosomes and plasmids) and the genes they encode. My doctoral research is concerned with understanding how bacterial addiction complexes influence the horizontal transmission of plasmids.
This work was partially funded by a University of Canterbury Doctoral Scholarship.
Modelling Cell Invasion
Summer student (2013-2014)
Supervisor: Mike Plank
In my project I used several different models to investigate the movement of cells, and in particular, cell movement when the cells have some preferred direction (a real life example is white blood cells moving towards an infection). In one model, the cells could move in only four directions - up, down, left, and right. In another model, the cells could move in any direction, and the third model was based on a partial differential equation (PDE), and reflected net population movement over time. I compared results from all three models and found that although the solution to the PDE matched results from the first model reasonably well, the solution did not match results from the second model. Results from each of these models could also be compared with experimental data.
This project was partially funded by the Marsden Fund (royalsociety.org.nz).
Calcium Oscillations in Smooth Muscle Cells
Honours student (2014)
Supervisor: Mike Plank
The walls of arteries are composed of smooth muscle cells, which can generate rhythmic contractions and dilations. This behaviour is known as vasomotion and can be in response to increases in extracellular potassium concentration and oscillations of intracellular calcium concentration and membrane potential. In my project I consider a simple model of a the calcium, membrane potential and potassium dynamics of a single cell. I then consider two adjacent coupled cells and investigate the resulting dynamics.
Building ecological networks using phylogenetic trees
Summer student (2013-2014)
Supervisors: Alex James, Mike Steel
I spent the summer studying models of ecological networks. Ecological networks are vital to our understanding of ecosystems and with this understanding we can protect ecosystems from external influences such as climate change. Recent studies have indicated that the inclusion of species' genetic/evolutionary history are important in the formation of networks. I have incorporated the Yule-Harding phylogenetic tree model into the generation of a model network. Using data of real networks and with a variety of network metrics, I am comparing this phylogenetic network models against random network models. Further research may lead to the phylogenetic model being used not only to inform conservationists on ecosystem protection, but could also to assist evolutionary biologists to use network interactions to better understand evolutionary processes.
Thank you to the Allan Wilson Centre (allanwilsoncentre.ac.nz) for funding the project.
Estimating possum foraging habits from leaf browse data
Summer student (2013-2014)
Supervisors: Alex James, Pen Holland
Possums eat a vast amount of leaves in New Zealand forests, however we are unsure of the tactic they use while browsing. We investigated different browsing tactics with a stochastic model. We compared our results to leaf litter data collected in the Tararua ranges of New Zealandt's north island with the aim of determining which tactic is the most likely. It is found that repeatedly the same leaf or nearby leaves provides the best match with the data but all five methods would benefit from improvements to the model, such as adding leaf growth and leaf fall.
The project was partially funded by Landcare Research (landcareresearch.co.nz).