Approximate likelihood methods for estimating local recombination rates

There is currently great interest in understanding the way in which recombination rates vary, over short scales, across the human genome. Aside from inherent interest, an understanding of this local variation is essential for the sensible design and analysis of many studies aimed at elucidating the genetic basis of common diseases or of human population histories. Standard pedigree-based approaches do not have the fine scale resolution that is needed to address this issue. In contrast, samples of deoxyribonucleic acid sequences from unrelated chromosomes in the population carry relevant information, but inference from such data is extremely challenging. Although there has been much recent interest in the development of full likelihood inference methods for estimating local recombination rates from such data, they are not currently practicable for data sets of the size being generated by modern experimental techniques. We introduce and study two approximate likelihood methods. The first, a marginal likelihood, ignores some of the data. A careful choice of what to ignore results in substantial computational savings with virtually no loss of relevant information. For larger sequences, we introduce a 'composite' likelihood, which approximates the model of interest by ignoring certain long-range dependences. An informal asymptotic analysis and a simulation study suggest that inference based on the composite likelihood is practicable and performs well. We combine both methods to reanalyse data from the lipoprotein lipase gene, and the results seriously question conclusions from some earlier studies of these data