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We propose an original statistical method to estimate how the occurrences of a given process along a genome, genes or motifs for instance, may be  influenced by the occurrences of a second process. More precisely, the aim is to detect avoided and/or favored distances between two motifs, for instance,  suggesting possible interactions at a molecular level.  For this, we consider occurrences along the genome as point processes and we use the so-called Hawkes' model. In such model, the intensity at position t depends linearly on the distances to  past occurrences of both processes via two unknown profile functions to estimate. We perform a non parametric estimation of both profiles by using B-spline decompositions and a constrained maximum likelihood method. Finally, we use the AIC criterion for the model selection. Simulations show the excellent behavior of our estimation procedure. We then apply it to study (i) the dependence between gene occurrences along the E. coli genome and the occurrences of a motif known to be part of the major promoter for this bacterium, and (ii) the dependence between the yeast S. cerevisiae genes and the occurrences of putative polyadenylation signals. The results are coherent with known biological properties or previous predictions, meaning this method can be of great interest for functional motif detection, or to improve knowledge of some biological mechanisms.

FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model