An improved sequence measure used to scan genomes for regions of recent gene flow

Anthony J. Geneva, Christina A. Muirhead, LeAnne M. Lovato, Sarah B. Kingan, Daniel Garrigan
(Submitted on 6 Mar 2014)

The study of complex speciation, or speciation with gene flow, requires the identification of genomic regions that are either unusually divergent or that have experienced recent gene flow. Furthermore, the rapid growth of population genomic datasets relevant to studying complex speciation requires that analytical tools be scalable to the level of whole-genome analysis. We present a simple sequence measure, Gmin which is specifically designed to identify regions of diverging genomes as candidates for experiencing recent gene flow. Gmin is defined as the ratio of the minimum number of nucleotide differences between sequences from two different populations to the average number of between-population differences. We compare the sensitivity of Gmin to that of the widely used index of population differentiation, Fst. Extensive computer simulations demonstrate that Gmin has greater sensitivity and specificity to detect gene flow than Fst. Additionally, the sensitivity of Gmin to detect gene flow is robust with respect to both the population mutation and recombination rates, suggesting that it is flexible and can be applied to a variety of biological scenarios. Finally, a scan of Gmin across the X~chromosome of Drosophila melanogaster identifies candidate regions of introgression between sub-Saharan African and cosmopolitan populations that were previously missed by other methods. These results demonstrate that Gmin is a biologically straightforward, yet powerful, alternative to Fst, as well as to more computationally intensive model-based methods for detecting gene flow.

A renewal theory approach to IBD sharing

Shai Carmi, Itsik Pe’er
(Submitted on 6 Mar 2014)

Long genomic segments that are nearly identical between a pair of individuals and are inherited from a recent common ancestor without recombination are called identical-by-descent (IBD) segments. IBD sharing has numerous applications in genetics, from demographic inference to phasing, imputation, pedigree reconstruction, and disease mapping. Here, we provide a theoretical analysis of IBD sharing under Markovian approximations of the coalescent with recombination. We describe a general framework for the IBD process along the chromosome under the Markovian models (SMC/SMC’), as well as introduce and justify a new model, which we term the renewal approximation, under which lengths of successive segments are independent. Then, considering the infinite-chromosome limit of the IBD process, we recover previous results (for SMC) and derive new results (for SMC’) for the average fraction of the chromosome found in long shared segments and the average number of such segments. A number of new results for tree heights in SMC’ are proved as lemmas. We then use renewal theory to derive an expression (in Laplace space) for the distribution of the number of shared segments and demonstrate implications for demographic inference. We also use renewal theory to compute the distribution of the fraction of the chromosome shared. While the expression is again in Laplace space, we could invert the first two moments and compare a number of approximations. Finally, we generalized all results to populations with variable historical effective size.

Decoding coalescent hidden Markov models in linear time

Kelley Harris, Sara Sheehan, John A. Kamm, Yun S. Song
(Submitted on 4 Mar 2014)

In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population.