The time to the ancestor along sequences with recombination

Mitochondrial introgression and interspecies recombination in the Fusarium fujikuroi species complex

The Fusarium fujikuroi species complex (FFSC) is an economically important monophyletic lineage in the genus Fusarium. Incongruence observed among mitochondrial gene trees, as well as the multiple non-orthologous copies of the internal transcribed spacer region of the ribosomal RNA genes, suggests that the origin and history of this complex likely involved interspecies gene flow. Based on this hypothesis, the mitochondrial genomes of non-conspecific species should harbour signatures of introgression or introgressive hybridization. The aim of this study was therefore to search for recombination between the mitochondrial genomes of different species in the FFSC. Using methods based on mt genome sequence similarity, five significant recombinant regions in both gene and intergenic regions were detected. Using coalescent-based methods and the sequences for individual mt genes, various ancestral recombination events between different lineages of the FFSC were also detected. These findings suggest that interspecies gene flow and introgression are likely to have played key roles in the evolution of the FFSC at both ancient and more recent time scales.

Coalescence computations for large samples drawn from populations of time-varying sizes

We present new results concerning probability distributions of times in the coalescence tree and expected allele frequencies for coalescent with large sample size. The obtained results are based on computational methodologies, which involve combining coalescence time scale changes with techniques of integral transformations and using analytical formulae for infinite products. We show applications of the proposed methodologies for computing probability distributions of times in the coalescence tree and their limits, for evaluation of accuracy of approximate expressions for times in the coalescence tree and expected allele frequencies, and for analysis of large human mitochondrial DNA dataset.

Ancestral recombinations graph: a reconstructability perspective using random-graphs framework

We present a random graphs framework to study pedigree history in an ideal (Wright Fisher) population. This framework correlates the underlying mathematical objects in, for example, pedigree graph, mtDNA or NRY Chr tree, ARG (Ancestral Recombinations Graph), and HUD used in literature, into a single unified random graph framework. It also gives a natural definition, based solely on the topology, of an ARG, one of the most interesting as well as useful mathematical objects in this area. The random graphs framework gives an alternative parametrization of the ARG that does not use the recombination rate q and instead uses a parameter M based on the (estimate of ) the number of non-mixing segments in the extant units. This seems more natural in a setting that attempts to tease apart the population dynamics from the biology of the units. This framework also gives a purely topological definition of GMRCA, analogous to MRCA on trees (which has a purely topological description i.e., it is a root, graph-theoretically speaking, of a tree). Secondly, with a natural extension of the ideas from random-graphs we present a sampling (simulation) algorithm to construct random instances of ARG/unilinear transmission graph. This is the first (to the best of the author's knowledge) algorithm that guarantees uniform sampling of the space of ARG instances, reflecting the ideal population model. Finally, using a measure of reconstructability of the past historical events given a collection of extant sequences, we conclude for a given set of extant sequences, the joint history of local segments along a chromosome is reconstructible.

Approximating the coalescent with recombination

The coalescent with recombination describes the distribution of genealogical histories and resulting patterns of genetic variation in samples of DNA sequences from natural populations. However, using the model as the basis for inference is currently severely restricted by the computational challenge of estimating the likelihood. We discuss why the coalescent with recombination is so challenging to work with and explore whether simpler models, under which inference is more tractable, may prove useful for genealogy-based inference. We introduce a simplification of the coalescent process in which coalescence between lineages with no overlapping ancestral material is banned. The resulting process has a simple Markovian structure when generating genealogies sequentially along a sequence, yet has very similar properties to the full model, both in terms of describing patterns of genetic variation and as the basis for statistical inference.

Maximum-likelihood estimation of rates of recombination within mating-type regions

Features common to many mating-type regions include recombination suppression over large genomic tracts and cosegregation of genes of various functions, not necessarily related to reproduction. Model systems for homomorphic self-incompatibility (SI) in flowering plants share these characteristics. We introduce a method for the exact computation of the joint probability of numbers of neutral mutations segregating at the determinant of mating type and at a linked marker locus. The underlying Markov model incorporates strong balancing selection into a two-locus coalescent. We apply the method to obtain a maximum-likelihood estimate of the rate of recombination between a marker locus, 48A, and S-RNase, the determinant of SI specificity in pistils of Nicotiana alata. Even though the sampled haplotypes show complete allelic linkage disequilibrium and recombinants have never been detected, a highly significant deficiency of synonymous substitutions at 48A compared to S-RNase suggests a history of recombination. Our maximum-likelihood estimate indicates a rate of recombination of perhaps 3 orders of magnitude greater than the rate of synonymous mutation. This approach may facilitate the construction of genetic maps of regions tightly linked to targets of strong balancing selection.

The distribution of surviving blocks of an ancestral genome

What is the chance that some part of a stretch of genome will survive? In a population of constant size, and with no selection, the probability of survival of some part of a stretch of map length y < 1 approaches y/log(yt/2) for log(yt) > or = 1. Thus, the whole genome is certain to be lost, but the rate of loss is extremely slow. This solution extends to give the whole distribution of surviving block sizes as a function of time. We show that the expected number of blocks at time t is 1+yt and give expressions for the moments of the number of blocks and the total amount of genome that survives for a given time. The solution is based on a branching process and assumes complete interference between crossovers, so that each descendant carries only a single block of ancestral material. We consider cases where most individuals carry multiple blocks, either because there are multiple crossovers in a long genetic map, or because enough time has passed that most individuals in the population are related to each other. For species such as ours, which have a long genetic map, the genome of any individual which leaves descendants (approximately 80% of the population for a Poisson offspring number with mean two) is likely to persist for an extremely long time, in the form of a few short blocks of genome.

A note on distributions of times to coalescence, under time-dependent population size

Expressions for marginal distributions of times in the time-varying coalescence process are derived. The proposed method allows also for computation of joint probability distribution for pairs, triples, etc. of coalescence times. The expressions derived are useful for (1) extending several statistics from time constant to time-varying case, (2) increasing efficiency and accuracy of simulations in time-varying evolution, and (3) debugging coalescence simulation software.

Consequences of recombination on traditional phylogenetic analysis

We investigate the shape of a phylogenetic tree reconstructed from sequences evolving under the coalescent with recombination. The motivation is that evolutionary inferences are often made from phylogenetic trees reconstructed from population data even though recombination may well occur (mtDNA or viral sequences) or does occur (nuclear sequences). We investigate the size and direction of biases when a single tree is reconstructed ignoring recombination. Standard software (PHYLIP) was used to construct the best phylogenetic tree from sequences simulated under the coalescent with recombination. With recombination present, the length of terminal branches and the total branch length are larger, and the time to the most recent common ancestor smaller, than for a tree reconstructed from sequences evolving with no recombination. The effects are pronounced even for small levels of recombination that may not be immediately detectable in a data set. The phylogenies when recombination is present superficially resemble phylogenies for sequences from an exponentially growing population. However, exponential growth has a different effect on statistics such as Tajima's D. Furthermore, ignoring recombination leads to a large overestimation of the substitution rate heterogeneity and the loss of the molecular clock. These results are discussed in relation to viral and mtDNA data sets.