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Next Generation Sequencing (NGS) technologies generate large amounts of shortread data for many different organisms. The fact that NGS reads are generallyshort makes it challenging to assemble the reads and reconstruct the originalgenome sequence. For clustering genomes using such NGS data, word-count basedalignment-free sequence comparison is a promising approach, but for thisapproach, the underlying expected word counts are essential.  A plausible model for this underlying distribution of word counts is giventhrough modelling the DNA sequence as a Markov chain (MC). For single longsequences, efficient statistics are available to estimate the order of MCs andthe transition probability matrix for the sequences. As NGS data do not providea single long sequence, inference methods on Markovian properties of sequencesbased on single long sequences cannot be directly used for NGS short read data.  Here we derive a normal approximation for such word counts. We also show thatthe traditional Chi-square statistic has an approximate gamma distribution,using the Lander-Waterman model for physical mapping. We propose severalmethods to estimate the order of the MC based on NGS reads and evaluate themusing simulations. We illustrate the applications of our results by clusteringgenomic sequences of several vertebrate and tree species based on NGS readsusing alignment-free sequence dissimilarity measures. We find that theestimated order of the MC has a considerable effect on the clustering results,and that the clustering results that use a MC of the estimated order give aplausible clustering of the species.

Inference of Markovian Properties of Molecular Sequences from NGS Data and Applications to Comparative Genomics