Lambda-Fleming-Viot type models and their diverse applications
Lead Research Organisation:
University of Oxford
Department Name: Statistics
Abstract
In their seminal work, Fleming and Viot introduced a measure-valued analogue of the famous Wright-Fisher diffusion. Today, both the generalization to events of non-infinitesimal impact, the Lambda-Fleming-Viot process and the generalization to continuous space, the spatial Lambda-Fleming-Viot process (SLFV) inherited their names. As such, the class of Fleming-Viot type models has received much attention of the probability research community in recent years owing to both their rich mathematical properties as well as their manifold applications in biology. This project has and will contribute to a better understanding of this class of models along three different research directions:
1. Capturing ecological effects such as the interaction between species or competition for a fluctuating abundance of resources requires a varying population size. However, many classical genetics models including the Lambda-Fleming-Viot process have not been studied yet with intrinsically varying population size, i.e., a reproduction mechanism which changes both the genetic decomposition and the population size at the same time. Together with Julian Kern (WIAS, Berlin) we have completed a paper draft on this intermediate step, which we hope to submit soon.
2. Spatial separation is often not easily bridged by a species due to geographic, environmental, or energetic constrains. Naturally, in the presence of neutral mutation differences in relatedness arise at different locations in space, which is known as isolation by distance. Together with Raphael Forien (INRAE, Avignon), we have extended a novel technique which allows to interpret central limit theorems as isolation by distance patterns reflecting the asymptotic spatial behavior of ancestral lineages. This research direction has yielded the preprint https://arxiv.org/abs/2211.16286 and a follow-up paper is in progress.
3. A slight modification of the SLFV, in which infected and healthy individuals interact instead of genetic types, can be used to model an epidemiology in a spatial continuum. Together with Apolline Louvet (University of Bath), we have started to analyze the mathematical properties of this model, whereas with David Helekal (Warwick, soon Harvard) we plan to use this model to infer spatial oversampling in tuberculosis data. At least one of the projects should lead to publishable results.
This project spans the EPSRC Applied Probability and Statistics, Mathematical Analysis and Mathematical Biology research areas. It aligns well with the EPSRC aims, as it tries to achieve novel applications of mathematics to biological phenomena along three different research directions.
1. Capturing ecological effects such as the interaction between species or competition for a fluctuating abundance of resources requires a varying population size. However, many classical genetics models including the Lambda-Fleming-Viot process have not been studied yet with intrinsically varying population size, i.e., a reproduction mechanism which changes both the genetic decomposition and the population size at the same time. Together with Julian Kern (WIAS, Berlin) we have completed a paper draft on this intermediate step, which we hope to submit soon.
2. Spatial separation is often not easily bridged by a species due to geographic, environmental, or energetic constrains. Naturally, in the presence of neutral mutation differences in relatedness arise at different locations in space, which is known as isolation by distance. Together with Raphael Forien (INRAE, Avignon), we have extended a novel technique which allows to interpret central limit theorems as isolation by distance patterns reflecting the asymptotic spatial behavior of ancestral lineages. This research direction has yielded the preprint https://arxiv.org/abs/2211.16286 and a follow-up paper is in progress.
3. A slight modification of the SLFV, in which infected and healthy individuals interact instead of genetic types, can be used to model an epidemiology in a spatial continuum. Together with Apolline Louvet (University of Bath), we have started to analyze the mathematical properties of this model, whereas with David Helekal (Warwick, soon Harvard) we plan to use this model to infer spatial oversampling in tuberculosis data. At least one of the projects should lead to publishable results.
This project spans the EPSRC Applied Probability and Statistics, Mathematical Analysis and Mathematical Biology research areas. It aligns well with the EPSRC aims, as it tries to achieve novel applications of mathematics to biological phenomena along three different research directions.
Organisations
People |
ORCID iD |
| Alison Etheridge (Primary Supervisor) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/V520202/1 | 01/10/2020 | 31/10/2025 | |||
| 2444521 | Studentship | EP/V520202/1 | 01/10/2020 | 30/09/2024 |
| Description | Individuals of a certain species carry, on average, less similar genetic information, if they are further separated in space, a phenomenon which is called 'isolation by distance'. We rigorously prove and quantify that isolation by distance is less drastic under long-range reproduction, i.e., if offspring are dispersed over a large spatial area during reproduction events. This situation is, e.g., found in plant species, where pollen or seeds occasionally travel a far greater distance, if caried away by a storm. This result might be used to infer long-range reproduction from genetic data. The mathematical technique might be helpful in a larger context, e.g., to infer historic spatial population sizes after generalizing the respective findings. |
| Exploitation Route | The outcomes might be used for inference of long-range reproduction parameters from genetic data. We analyze isolation by distance patterns by considering the probability of identity for individuals to be of the same type, e.g., the same genetic type at a specific locus. This low-complexity genetic statistics makes it seem feasible to conduct inference. Mathematically, the preprint illustrates that the toolset can be used to understand complex influences on the evolution of a population. In particular, we would like to extend this to a model with varying population size, so that in turn, it becomes possible to infer historic spatial population sizes from genetic data. |
| Sectors | Environment,Other |
| URL | https://arxiv.org/abs/2211.16286 |