----------------------------------------------------------------------
      Incorporating genetic information into spatially-explicit,
        state-space models of the British grey seal population
______________________________________________________________________
----------------------------------------------------------------------

This NERC/EPSRC Environmental Mathematics & Statistics studentship will
extend a framework we have begun to develop for modelling the dynamics of
wildlife populations (Buckland et al., 2000, in prep.; Trenkel et al.,
2000) to incorporate observational data on the genetic structure of such
populations. In this framework, the true but unknown state of the
population is modelled as a state process, and this is linked to survey
data by an observation process. All sources of uncertainty in the inputs,
including uncertainty about model specification, can be readily
incorporated. Recent advances in computer-intensive statistical inference
(such as Markov chain Monte Carlo analysis and sequential importance
sampling) have made it possible to estimate the parameters of these
models, and to quantify the uncertainties associated with these estimates
and the models' predictions.

The student will apply this state-space approach to the 40 year
time-series of data on the numbers of pups born at individual grey seal
(Halichoerus grypus) colonies in the UK, which has been collected by the
NERC Sea Mammal Research Unit (SMRU) since the early 1960s, and an
extensive database on genetic variation within some of these colonies,
which has been compiled by Cambridge University in collaboration with
SMRU.

The UK holds more than 90% of the European population, and nearly 50% of
the world population, of the grey seal, which was the first mammal to be
protected by legislation in the UK. It is listed as a species of Community
Interest in the EU Species and Habitats Directive, and a number of
potential Special Areas of Conservation have been identified in the
UK. Grey seal numbers increased steadily throughout the 20th century and
are still increasing, but almost all of the increase in recent years has
occurred at a few colonies: many have hardly changed in size since the
mid-1990s. In addition, completely new colonies continue to form and some
vacant sites have now been recolonised.

The continuing increase in the size of the British grey seal population
has generated growing concern from fishermen about the impact of seal
predation on depleted fish stocks, and from conservation agencies about
the effects of breeding seals on sensitive terrestrial habitats. It is
therefore important to be able to predict the future size and spread of
the population. However, existing models for the population's dynamics
(Hiby et al., in press) do not account for differences between individual
colonies and assume continuing exponential growth.

The student will extend the model framework in Buckland et al. to include
a genetic process model, and a genetic observation process that models the
way genetic samples are collected and analysed. This will build on the
approach developed by Gaggiotti et al. (2002).

As with most spatially-explicit models, the most difficult problem we have
experienced to date is the validation and parameterisation of realistic
models of movement between population units. We believe that much of the
model and estimation uncertainty can be removed by combining the time
series of abundance estimates with information on migration and
colonisation rates obtained from the mark-recapture and genetics studies
we have already conducted. In particular, the genetic data can provide
information on the likely origin of the founders of new colonies, and the
mark-recapture data can provide information on migration rates. These
parameters can only be inferred from the abundance data. However, genetic
samples have not been collected from all of the colonies which could act
as a source of colonists, nor from some of the most recently founded
colonies. Samples from these sites (in the Orkney islands and along the
east coast of Scotland and England) will be collected by the student in
October and November 2002, and analysed in Cambridge.

We feel that this studentship is most appropriate for a mathematics or
statistics graduate who wants to work in the environmental sciences, or
biology students who can demonstrate the necessary mathematical skills
that will be needed for this project. The student will be based in the
newly-established Centre for Research into Ecological and Environmental
Modelling (CREEM) at St Andrews. From August 2002 this will be housed in
accommodation which has been extensively refurbished to provide an ideal
environment in which numerate biologists and biologically-inclined
mathematicians and statisticians can work together. Centre staff will have
access to a Beowolf supercomputer cluster for computer-intensive work. The
student will, if necessary, receive additional training by participating
in some modules from the NERC-approved MRes "Environmental Biology
Conversion for Mathematical, Physical and Molecular Sciences". This
provides training in mathematical and statistical modelling, as well as
relevant aspects of environmental biology. Additional training in
molecular and population genetic techniques will be provided in Cambridge.

References
Buckland ST, Newman KB, Thomas L, Koesters N (in prep) State-space models
for the dynamics of wild animal populations. (pdf file available on
request)
Gaggiotti OE, Jones F, Harwood J, Amos W, Nichols RA (2002) Patterns of
colonisation in a grey seal metapopulation. Nature
(Lond.) 416: 424-427. (pdf file available on request)
Buckland ST, Goudie IBJ, Borchers DL 2000. Wildlife population
assessment: past developments and future directions. Biometrics 65: 1-12.
Trenkel VM, Elston DA, Buckland ST 2000. Calibrating population dynamics
models to count and cull data using sequential importance
sampling. J.A.S.A. 95: 363-374.

Supervisors
Professor Steve Buckland and Professor John Harwood, Centre for Research
into Ecological and Environmental Modelling, University of St Andrews
Dr Bill Amos, Department of Zoology, University of Cambridge

Further information is available from John Harwood ([log in to unmask])

_________________________________________________________________________
Stephen T. Buckland
School of Mathematics and Statistics
North Haugh, St Andrews KY16 9SS, Scotland
Tel. 01334-463787 (+44-1334-463787)
Fax 01334-463714 (+44-1334-463714)
e-mail [log in to unmask]
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Professor of Statistics http://www-maths.mcs.st-and.ac.uk/
Director, CREEM http://www.creem.st-and.ac.uk/
RUWPA http://www.ruwpa.st-and.ac.uk/
CCS http://www.ccs.st-and.ac.uk/
_________________________________________________________________________