Rate of coalescence of lineage pairs in the Spatial Λ-Fleming-Viot process.

We revisit the Spatial Λ-Fleming-Viot process introduced in Barton and Kelleher (2010). Particularly, we are interested in the time T0 to the most recent common ancestor for two lineages. We distinguish between the cases where the process acts on the two-dimensional plane and on a finite rectangle. Utilizing a differential equation linking T0 with the physical distance between the lineages, we arrive at computationally efficient and reasonably accurate approximation schemes for both cases. Furthermore, our analysis enables us to address the question of whether the genealogical process of the model "comes down from infinity", which has been partly answered before in Véber and Wakolbinger (2015).

The Evolving Moran Genealogy.

We study the evolution of the population genealogy in the classic neutral Moran Model of finite size n∈N and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise to a process on a state space consisting of n-sized binary increasing trees. We derive a number of properties of this process, and show that they are in agreement with existing results on the infinite-population limit of the Moran Model. Most importantly, this process admits time reversal, which makes it possible to simplify the mechanisms determining state changes, and allows for a thorough investigation of the Most Recent Common Ancestorprocess.

A common genomic code for chromatin architecture and recombination landscape.

Recent findings established a link between DNA sequence composition and interphase chromatin architecture and explained the evolutionary conservation of TADs (Topologically Associated Domains) and LADs (Lamina Associated Domains) in mammals. This prompted us to analyse conformation capture and recombination rate data to study the relationship between chromatin architecture and recombination landscape of human and mouse genomes. The results reveal that: (1) low recombination domains and blocks of elevated linkage disequilibrium tend to coincide with TADs and isochores, indicating co-evolving regulatory elements and genes in insulated neighbourhoods; (2) double strand break (DSB) and recombination frequencies increase in the short loops of GC-rich TADs, whereas recombination cold spots are typical of LADs and (3) the binding and loading of proteins, which are critical for DSB and meiotic recombination (SPO11, DMC1, H3K4me3 and PRMD9) are higher in GC-rich TADs. One explanation for these observations is that the occurrence of DSB and recombination in meiotic cells are associated with compositional and epigenetic features (genomic code) that influence DNA stiffness/flexibility and appear to be similar to those guiding the chromatin architecture in the interphase nucleus of pre-leptotene cells.

Topological linkage disequilibrium calculated from coalescent genealogies.

We revisit the classical, and introduce a novel, concept of two-locus linkage disequilibrium (LD). In contrast to defining haplotypes as allele combinations at two marker loci, we concentrate on the clustering of a sample of chromosomes induced by their coalescent genealogy. The root of a binary coalescent tree defines two clusters of chromosomes, each one of them containing the left and right descendants of the root. At two different loci this assignment may be different as a result of recombination. We show that the proportion of shared chromosomes among clusters at two different loci, measured by the squared correlation, constitutes a natural measure of LD. We call this topological LD (tLD) since it is induced by the topology of the coalescent tree. We find that it is, on average, larger than classical LD for any given distance between loci. Furthermore, tLD has a smaller coefficient of variation, which should provide an advantage, compared to the use of classical LD, for any kind of mapping purposes. We conclude with a practical application to the LCT region in human populations.