AUSTRALIAN RESEARCH COUNCIL Centre of Excellence for Mathematics and Statistics of Complex Systems University of Queensland site 

MASCOS Workshop on Mathematics and Statistics in Genetics
Description
The study of the genetics of populations and the
mathematics and statistics used to describe the underlying processes
have had a long association, to the extent that the names of many early
practitioners are as recognized in biology as in the mathematical
sciences (G. H. Hardy and R. A. Fisher, to name two).
Furthermore, a surprisingly large proportion of workers in mathematical
population genetics have either been based in or started their careers
in Australia. This workshop has two aims. The first is to showcase to
researchers at the more biological end of the spectrum what skills are
available within the mathematics and statistics community and
thus to encourage crossdisciplinary collaborations. The second
is to gather together and hopefully build a greater sense of community
among local statisticians and mathematicians who work on applications
in
genetics. The workshop is sponsored by the ARC Centre of Excellence for
the Mathematics and Statistics of Complex Systems (MASCOS). Venue Riverview Room, Emmanuel College, St Lucia Campus, University of Queensland. Parking (free for Workshop participants) is available onsite. Please note that the Riverview Room is just upstairs from Seminar Rooms 1 & 2 indicated in purple on the map, we recommend parking in the Riverbank carpark. Programme (subject to modification)
Speakers
Since the introduction of
Fisher's geometric model, the number of genetically independent
traits underlying a set of functionally related phenotypic traits
has been recognized as an important factor influencing the response to
selection. Determining the dimensionality of genetic
variancecovariance
(G) matrices provides an important perspective on the genetic basis of
a multivariate suite of traits that is not available when univariate
genetic variances and bivariate genetic correlations are interpreted
in isolation. We show how the effective dimensionality of G can be
established using three alternative methods; the determination of the
dimensionality of the effect space from a multivariate general linear
model (Amemiya 1985), factoranalytic modeling, and bootstrapping. A
simulation study indicated that while the performance of Amemiya's
method was more sensitive to power constraints, it performed as well
or better than factoranalytic modeling in correctly identifying the
original genetic dimensions at moderate to high levels of heritability.
The bootstrap approach, which is the only method to have been adopted
in the genetic and ecological literature, consistently overestimated
the number of dimensions in all cases, and performed less well
than Amemiya's method at subspace recovery. Applied to data from
transcriptional profiling experiments conducted within quantitative
genetic experimental designs, these approaches have the potential to
determine the number and nature of genetically independent sets of
regulated genes.
Using molecular genetic
data to make demographic inferences continues to be a challenging
problem. Recent maximum likelihood and Bayesian approaches have
shown that it is possible to make full use of the data. However,
simplified demographic models have generally been used due to the
difficulty in computing the likelihood for complex models.
Approximate Bayesian Computation (ABC) presents as a promising alternative in cases where likelihoods are intractable but simulation is relatively easy. Beaumont et al. (2002) recognised that a rejection sampling approach could be improved by the introduction of a regression. We have taken extended this approach into the spatial domain, by estimating the parameters of a range expansion under a twodimensional stepping stone model of range expansion. I will present two case studies illustrating the method.
Microarrays allow the
measurement of gene expressions for a biological sample (tissue) on a
genomewide scale, and form part of the highthroughput omics
methodology which is changing the face of biological research
(genomics, proteomics and metabonomics). They are now standard tools in
biology, with an ultimate goal for their use in clinical medicine for
diagnosis and prognosis, in particular in cancer towards guiding
therapeutic management.
Yet the data produced pose a real challenge for statistical analysis, where the numbers of genes can be in the tens of thousands, but the numbers of samples are in the tens, or hundreds in the largest studies. Traditional statistical approaches no longer apply, and need to be modified to carry out the analyses required, in order to draw sound conclusions from these experiments. In this talk I will briefly introduce the principles of the microarray experiment and mention some of the common approaches in data analysis, assuming the data have been cleaned and preprocessed. These include cluster analysis (clustering either the genes or tissues) and supervised classification to find subsets of "marker genes". The remainder and main part of the talk will focus on our work in detecting differentially expressed genes in a given number of classes, a problem still under debate in the literature and often the major goal for a microarray study.
Suppose a duplicate copy
of a gene appears at a locus which is loosely linked to the "normal"
position of the gene in the genome of some organism. Questions
which come to mind include: what is the chance that the function of
this gene will eventually be relocated to the new locus? how long would
this take? and how would the population genetics of the organism look
while this is happening? I present a stochastic model of the
situation, show that its overall behaviour is wellmodelled by a
onedimensional diffusion, and thereby infer answers to these
questions. In particular I show that there is a marked tendency
for the population to harbour equal frequencies of the gene at the two
loci.
Organizer Martin O'Hely (ohely at maths.uq.edu.au) Registration Although there is no registration fee, it is requested that you contact the organizer before 12 April so we know how many people will be coming. Lunch and refreshments will be provided.
Last
modified 19 April 2006
