




Rune Lyngsø,
Yun S. Song and
Jotun Hein. Accurate Computation of Likelihoods in the Coalescent with Recombination via Parsimony. In RECOMB08, Vol. 4955:463477 of LNCS, springer, 2008. Keywords: coalescent, likelihood, phylogenetic network, phylogeny, recombination, statistical model. Note: http://dx.doi.org/10.1007/9783540788393_41.
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"Understanding the variation of recombination rates across a given genome is crucial for disease gene mapping and for detecting signatures of selection, to name just a couple of applications. A widelyused method of estimating recombination rates is the maximum likelihood approach, and the problem of accurately computing likelihoods in the coalescent with recombination has received much attention in the past. A variety of sampling and approximation methods have been proposed, but no single method seems to perform consistently better than the rest, and there still is great value in developing better statistical methods for accurately computing likelihoods. So far, with the exception of some twolocus models, it has remained unknown how the true likelihood exactly behaves as a function of model parameters, or how close estimated likelihoods are to the true likelihood. In this paper, we develop a deterministic, parsimonybased method of accurately computing the likelihood for multilocus input data of moderate size. We first find the set of all ancestral configurations (ACs) that occur in evolutionary histories with at most k crossover recombinations. Then, we compute the likelihood by summing over all evolutionary histories that can be constructed only using the ACs in that set. We allow for an arbitrary number of crossing over, coalescent and mutation events in a history, as long as the transitions stay within that restricted set of ACs. For given parameter values, by gradually increasing the bound k until the likelihood stabilizes, we can obtain an accurate estimate of the likelihood. At least for moderate crossover rates, the algorithmbased method described here opens up a new window of opportunities for testing and finetuning statistical methods for computing likelihoods. © 2008 SpringerVerlag Berlin Heidelberg."






Joanna L. Davies,
Frantisek Simancík,
Rune Lyngsø,
Thomas Mailund and
Jotun Hein. On RecombinationInduced Multiple and Simultaneous Coalescent Events. In GEN, Vol. 177:21512160, 2007. Keywords: coalescent, phylogenetic network, phylogeny, recombination, statistical model. Note: http://dx.doi.org/10.1534/genetics.107.071126.
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"Coalescent theory deals with the dynamics of how sampled genetic material has spread through a population from a single ancestor over many generations and is ubiquitous in contemporary molecular population genetics. Inherent in most applications is a continuoustime approximation that is derived under the assumption that sample size is small relative to the actual population size. In effect, this precludes multiple and simultaneous coalescent events that take place in the history of large samples. If sequences do not recombine, the number of sequences ancestral to a large sample is reduced sufficiently after relatively few generations such that use of the continuoustime approximation is justified. However, in tracing the history of large chromosomal segments, a large recombination rate per generation will consistently maintain a large number of ancestors. This can create a major disparity between discretetime and continuoustime models and we analyze its importance, illustrated with model parameters typical of the human genome. The presence of gene conversion exacerbates the disparity and could seriously undermine applications of coalescent theory to complete genomes. However, we show that multiple and simultaneous coalescent events influence global quantities, such as total number of ancestors, but have negligible effect on local quantities, such as linkage disequilibrium. Reassuringly, most applications of the coalescent model with recombination (including association mapping) focus on local quantities. Copyright © 2007 by the Genetics Society of America."








Rune Lyngsø,
Yun S. Song and
Jotun Hein. Minimum Recombination Histories by Branch and Bound. In WABI05, Vol. 3692:239250 of LNCS, springer, 2005. Keywords: ARG, branch and bound, from sequences, minimum number, Program Beagle, recombination, reconstruction, software. Note: http://www.cs.ucdavis.edu/~yssong/Pub/WABI05239.pdf.








Yun S. Song and
Jotun Hein. On the Minimum Number of Recombination Events in the Evolutionary History of DNA Sequences. In JOMB, Vol. 48(2):160186, 2004. Keywords: minimum number, recombination. Note: http://dx.doi.org/10.1007/s0028500302275.
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"In representing the evolutionary history of a set of binary DNA sequences by a connected graph, a set theoretical approach is introduced for studying recombination events. We show that set theoretical constraints have direct implications on the number of recombination events. We define a new lower bound on the number of recombination events and demonstrate the usefulness of our new approach through several explicit examples. © SpringerVerlag 2003."










Jotun Hein. A heuristic method to reconstruct the history of sequences subject to recombination. In JME, Vol. 36(4):396405, 1993. Keywords: explicit network, from sequences, heuristic, parsimony, phylogenetic network, phylogeny, Program RecPars, recombination, recombination detection, software. Note: http://dx.doi.org/10.1007/BF00182187.






Jotun Hein. Reconstructing evolution of sequences subject to recombination using parsimony. In MBIO, Vol. 98(2):185200, 1990. Note: http://dx.doi.org/10.1016/00255564(90)90123G.
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"The parsimony principle states that a history of a set of sequences that minimizes the amount of evolution is a good approximation to the real evolutionary history of the sequences. This principle is applied to the reconstruction of the evolution of homologous sequences where recombinations or horizontal transfer can occur. First it is demonstrated that the appropriate structure to represent the evolution of sequences with recombinations is a family of trees each describing the evolution of a segment of the sequence. Two trees for neighboring segments will differ by exactly the transfer of a subtree within the whole tree. This leads to a metric between trees based on the smallest number of such operations needed to convert one tree into the other. An algorithm is presented that calculates this metric. This metric is used to formulate a dynamic programming algorithm that finds the most parsimonious history that fits a given set of sequences. The algorithm is potentially very practical, since many groups of sequences defy analysis by methods that ignore recombinations. These methods give ambiguous or contradictory results because the sequence history cannot be described by one phylogeny, but only a family of phylogenies that each describe the history of a segment of the sequences. The generalization of the algorithm to reconstruct gene conversions and the possibility for heuristic versions of the algorithm for larger data sets are discussed. © 1990."



