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. The results for chromosomes 1 to 22 and X indicate the existence of the so-called Hurst phenomenon in all of them. The interpretation of this outcome entails the presence of long-range correlations and we propose an explanation based on the genomic feature dubbed linkage disequilibrium, a nonrandom association of alleles at different loci. An unexpected outcome is the noteworthy uniform reduction in the Hurst phenomenon when considering the centimorgan metric instead of base position units. By contrast, such uniform reduction is not observed with the fractal dimension values.

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. The case of lack of treeness is interpreted in the formalism as the presence of population admixture. In this respect, four formulas are given to estimate the admixture proportions. One of them is the so-called [Formula: see text]-ratio estimate and we show that a second one is related to a known result developed in terms of the fixation index [Formula: see text]. An illustrative numerical simulation of admixture proportion estimates is included. Relationships of the formalism with coalescence times and pairwise sequence differences are also provided.

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. The problem of estimating the numerical values of the model parameters, as well as those of the correction terms, is not addressed.