Sabine Mercier

Exact distribution for the local score of one i.i.d. random sequence.

Let X(1)...X(n) be a sequence of i.i.d. positive or negative integer-valued random variables and H(n) = max(0 < or = i < or = j < or = n)(X(i) +...+ X(j)) be the local score of the sequence. The exact distribution of H(n) is obtained using a simple Markov chain. This result is applied to the scoring of DNA and protein sequences in molecular biology.

Accounting for Linkage Disequilibrium in genome scans for selection without individual genotypes : the local score approach

Detecting genomic footprints of selection is an important step in the understanding of evolution. Accounting for linkage disequilibrium in genome scans increases detection power, but haplotype‐based methods require individual genotypes and are not applicable on pool‐sequenced samples. We propose to take advantage of the local score approach to account for linkage disequilibrium in genome scans for selection, cumulating (possibly small) signals from single markers over a genomic segment, to clearly pinpoint a selection signal. Using computer simulations, we demonstrate that this approach detects selection with higher power than several state‐of‐the‐art single‐marker, windowing or haplotype‐based approaches. We illustrate this on two benchmark data sets including individual genotypes, for which we obtain similar results with the local score and one haplotype‐based approach. Finally, we apply the local score approach to Pool‐Seq data obtained from a divergent selection experiment on behaviour in quail and obtain precise and biologically coherent selection signals: while competing methods fail to highlight any clear selection signature, our method detects several regions involving genes known to act on social responsiveness or autistic traits. Although we focus here on the detection of positive selection from multiple population data, the local score approach is general and can be applied to other genome scans for selection or other genomewide analyses such as GWAS.

Exact and Asymptotic Distribution of the Local Score of One i.i.d. Random Sequence

We propose two new and complementary methods to assess the statistical signiFIcance of high scoring segments, within both long and short sequences. The numerical results show that these methods improve the work of Karlin et al. implemented in BLAST for the comparison of two sequences.

Back to the Local Score in the Logarithmic Case: A Direct and Simple Proof

Let X1, ... , Xn be a sequence of i.i.d. integer valued random variables and Hn the local score of the sequence. A recent result shows that Hn is actually the maximum of an integer valued Lindley process. Therefore known results about the asymptotic distribution of the maximum of a weakly dependent process, give readily the expected result about the asymptotic behavior of the local score in the logarithmic case, with a simple way for computing the needed constants. Genomic sequence scoring is one of the most important applications of the local score. An example of an application of the local score on protein sequences is therefore given in the paper.

H-Tuple Approach to Evaluate Statistical Significance of Biological Sequence Comparison with Gaps

We propose an approximate distribution for the gapped local score of a two sequence comparison. Our method stands on combining an adapted scoring scheme that includes the gaps and an approximate distribution of the ungapped local score of two independent sequences of i.i.d. random variables. The new scoring scheme is defined on h-tuples of the sequences, using the gapped global score. The influence of h and the accuracy of the p-value are numerically studied and compared with obtained p-value of BLAST. The numerical experiments emphasize that our approximate p-values outperform the BLAST ones, particularly for both simulated and real short sequences.

Statistical significance based on length and position of the local score in a model of i.i.d. sequences

Motivation: The local score of a biological sequence analysis is a mathematical tool largely used to analyse biological sequences. Consequently, determining an accurate estimation of its distribution is crucial. Results: First, we study the accuracy of classical results on the local score distribution in independent and identically distributed model using a Kolmogorov‐Smirnov goodness of fit test. Second, we highlight how the length of the segment that realizes the local score improves the classical setting based on local score only. Finally, we study which part of the sequence contributes to the local score. Contact: mercier@univ‐tlse2.fr