Maths, modelling and quantitative biology

The diverse group of modellers and mathematical biologists in EPI has now reached critical mass with some 15 in-house researchers and students. They direct a range of concepts and tools to questions in systems biology, at scales of organ, individual and community, and in applications as diverse as plant-plant sensing, multi-trophic interactions, ‘industrial’ genotypes and GM coexistence policy.

Modelling and various mathematical approaches now permeate much of the science and some of the applications in EPI. A common and defining feature of the work is the exploration of 'the individual' in 'the system', in which the interactions among individual organisms, organs or cells give rise to emergent properties not predictable from the characteristics of the individuals themselves. Biologists, modellers and software developers combine their skills to address central and essential challenges in modern biology. The examples below are of current work (main funders in parenthesis).

Root hair expansion (colours) shown on living rootQuantitative motion analysis PlantVis is a flexible tool for analysing movement in living organs, used for example to estimate the rate of extension of root cells, root hairs and roots from time lapse, confocal, scanning microscopy (BBSRC, Scottish Government). The method has potential for exploring gene expression and quantifying rooting traits in advanced genotypes. Developed in collaboration with the University of Dundee. The web page for this project gives more information. Contact: Tracy Valentine, Glyn Bengough

3-D imaging of living plants Mathematical approaches to analyse 3-dimensional images of roots and other in situ plant material by optical projection tomography microscopy – for elucidating local mechanisms responsible for whole-plant architecture (Scottish Government). With SIMBIOS at the University of Abertay Dundee. Contact: Lionel Dupuy

Image of modelled root system expanding in timePlant architecture Simplified, and computationally efficient, plant architectural models for exploring the acquisition of resources, plant to plant competition and ultimately resource-driven population dynamics (Scottish Government). Applications in quantifying plant phenotypes and designing future crop ideotypes (for example, designed to grow on less nitrogen or water). Contact: Lionel Dupuy

Photograph of root and root hairs - by Paul HallettCatastrophic root failure A descriptive model of the mechanical conditions that cause roots to undergo progressive, and finally catastrophic, failure, takes into account the mechanical behaviour of roots, the soil and the root-soil interface. Used in predicting slope failure, green engineering solutions and blueprints for ‘industrial’ plant varieties (Scottish Government). With the Geotechnical Engineering group at the University of Dundee. Contact: Paul Hallett

Aphids, viruses, endosymbionts and parasitoids  Pest aphids, their ability to harbour and transmit viruses in crops, their endosymbiont bacteria and the parasisitoids that feed on them, form a complex multi-trophic system that is here examined by differential equation and individual based models (CASE PhD studentship). Potential applications in integrated pest management. With University of Dundee Department of Mathematics (Mark Chaplain, student Ananthi Anandanadesan). Contacts: Steve Hubbard, Alison Karley

Map of modelled field showing transgenic volunteer plants (blue), non-transgenic (green) and hybrids (red)Gene flow and introgression An individual-based, spatially explicit, model of plant growth, competition, seed dispersal and cross pollination, allows exploration of the links between plant traits and emergent community properties in domains equivalent to 1 hectare in area. Used as a research tool for investigating local evolution (Scottish Government); and as a basis of informed decisions on GM management and policy (Defra, EU FP6 SIGMEA). Recent further applications with the Josef Stefan Institute, Slovenia and the University of Manitoba, Canada. The web page for this project gives more information. Contacts: Graham Begg, Geoff Squire

Plant trait distribution derived from outcome of individual based competition modelOptimising crop yield and food webs Individual-based, trophic model, linking plant and invertebrate functional groups, arable food webs and field management, is used to guide informed decisions on optimal field management for yield and biodiversity (BBSRC/Scottish Government Sustainable Arable LINK). Ideal for advanced teaching and demonstration. With Rothamsted Research (David Bohan, Geoffrey Carron Lormier) and Syngenta (Alan Raybould). Contact: Cathy Hawes, Richard Dye, Geoff Squire

Mining ecological data Machine learning software (for example, regression trees), applied to large ecological datasets, is exposing unrealised patterns (EU FP6 SIGMEA), for example in the association of oilseed rape as a (GM) weed with soil, location in the UK and other weed species. Uses in biosafety, biovigilence and ecological monitoring. Long term collaboration with the Josef Stefan Institute, Slovenia (Marko Debeljak). Contacts: Mark Young, Geoff Squire

(Added 3 April 2009)