| 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
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
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 cross-disciplinary collaborations. The second
is to gather together and hopefully build a greater sense of community
among local statisticians and mathematicians who work on applications
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 on-site. 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)
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 variance-covariance (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), factor-analytic 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 factor-analytic 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 two-dimensional 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 genome-wide scale, and form part of the high-throughput -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 well-modelled by a one-dimensional 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