Badri Padhukasahasram

Multi-marker approaches are currently gaining a lot of interest in genome wide association studies and can enhance power to detect new associations under certain conditions. Gene and pathway based association tests are increasingly being viewed as useful complements to the more widely used single marker association analysis which have successfully uncovered numerous disease variants. A major drawback of single-marker based methods is that they do not consider pairwise and higher-order interactions between genetic variants. Here, we describe novel tests for multi-marker association analyses that are based on phenotype predictions obtained from machine learning algorithms. Instead of utilizing only a linear or logistic regression model, we propose the use of ensembles of diverse machine learning algorithms for constructing such association tests. As the true mathematical relationship between a phenotype and any group of genetic and clinical variables is unknown in advance and may be complex, such a strategy gives us a general and flexible framework to approximate this relationship across different sets of SNPs. We show how phenotype prediction obtained from ensemble learning algorithms can be used for constructing tests for the joint association of multiple variants. We first apply our method to simulated datasets to demonstrate its power and correctness. Then, we apply our method to previously studied asthma-related genes in two independent asthma cohorts to conduct association tests.

Meiotic recombination occurs in the form of two different mechanisms called crossing-over and gene-conversion and both processes have an important role in shaping genetic variation in populations. Although variation in crossing-over rates has been studied extensively using sperm-typing experiments, pedigree studies and population genetic approaches, our knowledge of variation in gene-conversion parameters (ie, rates and mean tract lengths) remains far from complete. To explore variability in population gene-conversion rates and its relationship to crossing-over rate variation patterns, we have developed and validated using coalescent simulations a comprehensive Bayesian full-likelihood method that can jointly infer crossing-over and gene-conversion rates as well as tract lengths from population genomic data under general variable rate models with recombination hotspots. Here, we apply this new method to SNP data from multiple human populations and attempt to characterize for the first time the fine-scale variation in gene-conversion parameters along the human genome. We find that the estimated ratio of gene-conversion to crossing-over rates varies considerably across genomic regions as well as between populations. However, there is a great degree of uncertainty associated with such estimates. We also find substantial evidence for variation in the mean conversion tract length. The estimated tract lengths did not show any negative relationship with the local heterozygosity levels in our analysis.European Journal of Human Genetics advance online publication, 27 February 2013; doi:10.1038/ejhg.2013.30.

I describe an analytical approximation for calculating the short-term probability of loss of a chromosome under the neutral Wright-Fisher model with recombination. I also present an upper and lower bound for this probability. Exact analytical calculation of this quantity is difficult and computationally expensive because the number of different ways in which a chromosome can be lost, grows very large in the presence of recombination. Simulations indicate that the probabilities obtained using my approximate formula are always comparable to the true expectations provided that the number of generations remains small. These results are useful in the context of an algorithm that we recently developed for simulating Wright-Fisher populations forward in time. C++ programs that can efficiently calculate these formulas are available on request.

We describe a novel method for jointly estimating crossing-over and gene-conversion rates from population genetic data using summary statistics. The performance of our method was tested on simulated data sets and compared with the composite-likelihood method of R. R. Hudson. For several realistic parameter values, the new method performed similarly to the composite-likelihood approach for estimating crossing-over rates and better when estimating gene-conversion rates. We used our method to analyze a human data set recently genotyped by Perlegen Sciences.