Scale invariant correlations between genes and SNPs on Human chromosome 1 reveal potential evolutionary mechanisms

Abstract

The local density of gene structures and single nucleotide polymorphisms (SNPs) along human chromosomes appears inhomogeneous. In chromosome 1, the density patterns from both these elements are shown here to exhibit similar scale invariant clustering, as well as long-ranged and scale invariant auto- and cross-correlations. The local densities of these elements sites can be accurately represented by the scale invariant exponential dispersion models, a group of stochastic models that act as limiting distributions for a wide range of generalized linear models. The scale invariant Poisson-gamma (PG) distribution is the most applicable of these models, since it describes the above findings and it lends itself to a stochastic mechanism for the accumulation of segmental chromosomal changes. This PG model describes the summation of neutral chromosomal mutations, deletions, rearrangements and recombinations, within chromosomal segments that are distinguished by their evolutionary genealogies. Scale invariance is a necessary property if such a description is to remain valid at different measurement scales. The observed density patterns, and proposed model, presumably represent the convergent summation of multiple stochastic processes within the evolutionary history of the chromosome.