University of Queensland
Friday 21 April, 2006

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 had two aims.  The first was 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 was to gather together and hopefully build a greater sense of community among local statisticians and mathematicians who work on applications in genetics.

Approximately 40 people attended the Workshop.  Most came from universities or research institutes in South East Queensland although there were about five from interstate. 

The workshop was sponsored by the ARC Centre of Excellence for the Mathematics and Statistics of Complex Systems (MASCOS).

Invited Speakers  

• Mark Blows (Zoology & Entomology, University of Queensland)
• Grant Hamilton (School of Mathematical Sciences, Queensland University of Technology)
• Liat Jones (ARC Centre for Bioinformatics, Univeristy of Queensland)
• Jonathan Keith (Mathematics, University of Queensland)
• Martin O'Hely (MASCOS, University of Queensland)
• Paul Slade (Statistics, University of Adelaide)
• Ian Wood (School of Mathematical Sciences, Queensland University of Technology)

Organizer   Martin O'Hely (MASCOS, University of Queensland)

Programme   

Abstracts 

• Mark Blows, speaking on joint work with Emma Hine (Zoology & Entomology, UQ) The dimensionality of the genetic variance-covariance matrix

• Grant Hamilton (School of Mathematical Sciences, QUT) Bayesian estimation of recent migration rates during a range expansion

• Liat Jones (ARC Centre for Bioinformatics, UQ) Statistical Analysis of Microarray Data

• Jonathan Keith (Maths, University of Queensland)  Segmenting Eukaryote Genomes with the Generalised Gibbs Sampler
  
  A surprising result that has emerged from the comparison of large eukaryotic genomes is that the proportion of such genomes under purifying selection is apparently much larger than the proportion coding for proteins. Although the task of delineating protein-coding elements is well advanced, the functional non-coding portion is much less well understood, and is only beginning to be delineated. In this talk I will present a new method for delineating the conserved fraction of eukaryote genomes based on Bayesian sequence segmentation of pair-wise whole-genome alignments. The method is applied to an alignment of the Drosophila melanogaster genome to the Drosophila simulans genome. Despite the fact that these species diverged only a few million years ago, the new method was able to identify well-resolved slowly and rapidly evolving fractions. The method is also able to identify most of the sequences within these fractions, unlike previous approaches. The results indicate that approximately 61.7% of the Drosophila melanogaster genome is in the slowly evolving fraction,  approximately 2.7% is in the rapidly  evolving fraction and approximately 18.3% is evolving at an intermediate rate (the remaining 17.3% is comprised of indels or is not aligned). Almost all (approximately 90%) of the aligned protein-coding sequence is in the slowly evolving fraction, suggesting that this fraction (which comprises the majority of the Drosophila genome) is functional. The rapidly evolving fraction is also enriched for protein coding sequence, suggesting that this fraction may also be functional.
  
  Software, data, and results will shortly be made available online at http://www.uq.edu.au/~uqjkeith/.
  
  
• Martin O'Hely (MASCOS, University of Queensland) The frequency of a segregating duplicate gene

• Paul Slade (University of Adelaide) Stochastic and computational modeling of gene genealogy: does natural selection mimic varying population size? 
  
  The Coalescent process is a well established tool of mathematical population genetics and provides a mathematical description of the genealogy of a sample of genes.  Various simplifying assumptions and mathematical devices are utilized to render a continuous-time stochastic death process that yields a Markov chain that is amenable to computational simulation.  In the presence of weak natural selection the coalescent analogue is a branching-coalescing random graph called the ancestral selection graph.  The main body of coalescent theory is restricted to consideration of a population of constant size over time.  I will present an overview of a recent extension to the ancestral selection graph that allows for exponential population size growth.  The resulting model informs us of how selection and population growth interact to influence genealogical timing properties.
  
  
• Ian Wood (School of Mathematical Sciences, QUT) Bayesian Hierarchical Models for Meta-Analysis 
  
  Meta-analysis provides a means of statistically combining the results of a number of studies. It can be applied to genetic association studies with the aim of producing clearer results than any of the individual studies. I am currently interested in meta-analysis of studies of the effects of genetic polymorphisms such as SNPs (single nucleotide polymorphisms) on quantitative phenotypic traits. These are of interest in breeding livestock and also in human genetic epidemiology.
  
  Here I discuss the use of a Bayesian hierarchical model to combine genetic association studies which contain significant heterogeneity. I use the example of a meta-analysis of the association between the TG5 Thyroglobulin SNP (C/T) in cattle and with levels of marbling in their beef. A random effects formulation is used with assumptions of normality at each level, with different variances used at the estimate, study and breed levels.
  
  We required that study results included were able to be represented as pair-wise contrasts with corresponding standard errors. The prior distributions on the variances were of a conjugate form (1/chi-squared), and were made informative by centering them on variances estimated from the data. Results obtained using WinBUGS showed a high probability of overall association between copies of the T allele and beef marbling.
  

Participants

(Email addresses can be constructed using the email given, the at sign, and the standard institutional domain name.  Where a subdomain is needed it is indicated in parentheses).