Quantifying defective and wild-type viruses from high-throughput RNA sequencing.

Motivation: Defective viral genomes (DVGs) are variants of the wild-type (wt) virus that lack the ability to complete autonomously an infectious cycle. However, in the presence of their parental (helper) wt virus, DVGs can interfere with the replication, encapsidation, and spread of functional genomes, acting as a significant selective force in viral evolution. DVGs also affect the host's immune responses and are linked to chronic infections and milder symptoms.

The geometry of admixture in population genetics: the blessing of dimensionality.

We present a geometry-based interpretation of the f-statistics framework, commonly used in population genetics to estimate phylogenetic relationships from genomic data. The focus is on the determination of the mixing coefficients in population admixture events subject to post-admixture drift. The interpretation takes advantage of the high dimension of the dataset and analyzes the problem as a dimensional reduction issue.

Mutations along human chromosomes: How randomly scattered are they?

The diversity of mutations in human chromosomes is nowadays very well documented. The mutations characterize populations in the world as well as genetic causes of diseases. In the approach that we follow, we study the patterns of gaps between mutations by means of the rescaled range analysis and the fractal dimension estimates.

A Geometrical Framework for f-Statistics.

A detailed derivation of the f-statistics formalism is made from a geometrical framework. It is shown that the f-statistics appear when a genetic distance matrix is constrained to describe a four population phylogenetic tree. The choice of genetic metric is crucial and plays an outstanding role as regards the tree-like-ness criterion.

Evolutionary distances corrected for purifying selection and ancestral polymorphisms.

Evolutionary distance formulas that take into account effects due to ancestral polymorphisms and purifying selection are obtained on the basis of the full solution of Jukes-Cantor and Kimura DNA substitution models. In the case of purifying selection two different methods are developed. It is shown that avoiding the dimensional reduction implicitly carried out in the conventional model solving is instrumental to incorporate the quoted effects into the formalism.