Recent spatiotemporal field data indicates periodic wave activity in a
range of cyclic populations. We propose a detailed study of such
waves, building on previous collaborative work of the two supervisors.
This previous work showed that landscape obstacles generate periodic
waves in cyclic populations. Using a phenomenological modelling
approach, we investigated issues such as the dependence of wave
properties depend on obstacle size and shape, and the interaction of
waves generated by different obstacles. We now propose a more
mechanistic study of periodic wave generation.
Stage 1: General modelling.
Stage 2: Application field voles in Kielder.
We will begin by including the specifics of a
predator-prey/pathogen-host interaction, in a
neutral landscape. A key part of this phase of the project is to
explore the potential
consequences of the growing evidence that the dispersal rate of small
mammals varies inversely with density over average to high densities;
at high densities, voles almost stop moving.
Such density-dependent dispersal has been well studied for simple population
dynamics (including work by JAS) but has not been considered
previously in the context of population cycles. There is now
strong enough empirical evidence for the vole population in Kielder to
enable such a study.
We will then incorporate into the model the specifics of the Kielder
landscape. Here we will use the very detailed
data available from a GIS study lead by Chris
Thomas (Durham) with whom we have an established collaboration.
Parameter estimation for the model will be based on a mixture of
general data on vole behaviour available in the literature, and
specific demographic data from Kielder. The latter includes, for
example, recent results on weasel dispersal obtained by XL via radio
tagging in Kielder, and extensive vole capture-recapture data collected over 7
years. Statistical advice on parameter estimation will be provided
by Prof Gavin Gibson (Heriot-Watt). Field data against which the model
can be tested is now available at a wide range of spatial scales. A key
component of this part of the project is the hands-on involvement of
the student in data collection in Kielder. As well as giving training
in ecological field work, this will ensure that the student is fully
conversant with the Kielder habitat and field vole ecology, so that the
modelling is a genuine representation of ecological reality.
Stage 3: Other applications.
Training:
Track record:
XL leads a group of population ecologists presently
including 2 PDRAs, one (NERC funded) technician, and 7 postgraduate
students. He has previously supervised 7 successful PhD and 2 MSc by
Research students, all of whom have gained employment in universities
or research institutions. XL also chairs the Aberdeen Population
Ecology Research Unit (APERU), a collaborative group of statisticians
and population ecologists from five of the Aberdeen Research
Consortium partners (CEH, MLURI, FRS, BIOSS and AU) and aims to
develop and enhance expertise in modelling data ranging from molecular
descriptions of individuals to estimates of population size of
organisms ranging from microbes to large vertebrates. He has
published over 55 papers (26 since 1999) so far cited >541 times.
Suitability for EMS scheme:
We will compare and contrast periodic waves generated by
obstacles in populations which cycle because of predator-prey,
host-parasite and host-parasitoid interactions. Our aim is to
determine the extent to which such mechanisms could be distinguished
on the basis of spatiotemporal field data. This will involve a
systematic programme of computer simulation of representative models,
which will be both discrete and continuous in space. In addition, some
mathematical analysis of continuous-space models will be possible (via
reduction to normal forms), providing a balanced training in the study
of mathematical models. Our expectation is that periodic waves will
arise in all cases but with significant differences in wave
properties. In particular, our previous phenomenological work suggests
that some ecological mechanisms for cycling will tend to generate
waves which develop instabilities and evolve to spatiotemporal chaos,
while others robustly generate stable waves.
XL is coordinating an
on-going spatiotemporal field study of field voles (Microtus agrestis)
in Kielder forest, on the Scotland-England border. Statistical
analysis has shown that the data imply periodic travelling waves in
vole density, moving in a particular direction at about 15-20 km per
year. This will be the major case study in this project . We will
develop detailed mathematical models for the vole population, assuming
that cycles are driven either by predation by weasels, or by zoonotic
vole pathogens with contrasting transmission dynamics. We will
contrast cowpox, an orthopox virus with short (4 weeks) infectivity
but influencing both survival and reproduction and whose transmission
dynamics appears intermediate between frequency, and vole
tuberculosis (a chronic disease related to bovine TB with long
infectivity). Data on prevalence and disease dynamics is accumulating
with current NERC funding.
We will also consider applications of
our modelling work to a range of other ecological systems in which
field data indicate periodic travelling waves. These include a
spatially extensive data set on cyclic outbreaks and wave like
patterns of fossorial water voles in Franche Comt and Jura in
France, which causes substantial damage to farming and secondary
poisoning of predators following eradication attempts. Data on cycles
of larch budmoth cycles from Switzerland for which there is strong
evidence of a parasitoid-host relationship will also be considered
This studentship is suitable for individuals with either a
primary background in mathematics, or with a mainly ecological
background but some mathematical expertise. The training programme
will inevitably depend on the particular background of the selected
student. The central component of the training will be direct
instruction in mathematical modelling and model solution by JAS, and
in ecological theory and field work by XL. On top of this, general
exposure to a wide range of relevant science will come from
interactions with the research groups at Heriot-Watt and Aberdeen.
Heriot-Watt has a strong mathematical biology group with three faculty
members, one of whom (Andrew White) currently holds a NERC fellowship
under the EMS scheme. There are active collaborations with ecology
groups at Aberdeen, Stirling, Oxford and Durham. The population
ecology group in Aberdeen includes empiricists studying population
dynamics, behavioural and conservation issues using molecular markers,
field studies and modelling as well as statisticians. There are active
collaborations with CEH Banchory, Heriot Watt, Liverpool, Oslo and
Troms and CNRS Paris.
Together, the two groups will provide an excellent training
environment for the student.
We request specific funding to enable the student to attend the short
course on Advanced Ecology at Silwood Park, which will be an
invaluable training resource. In addition, specific training via taught
courses is available in both departments.
JAS is head of the mathematical biology group at Heriot-Watt.
His primary research background is in the application of mathematics
to medicine, but in the last few years he has also worked actively in
ecological applications, most recently in collaboration with XL.
At Heriot-Watt and in his previous post at University of Warwick, he
has supervised 6 PhD students, all of whom have followed scientific
careers (5 in academia, one at CEH).
He has published over 90 scientific papers and was recently awarded
the Sir Edward Whittaker Memorial Prize by the Edinburgh Mathematics
Society.
This project depends fundamentally on the student doing hands-on
field work in addition to theoretical modelling. As such it is
unsuitable for funding by either EPSRC or NERC, but fits naturally
into the joint scheme.