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Today, the CRISPR (clustered regularly interspaced short palindromic repeats)region within bacterial and archaeal genomes is known to encode an adaptiveimmune system. We rely on previous results on the evolution of the CRISPRarrays, which led to the ordered independent loss model, introduced by Kupczokand Bollback (2013). When focusing on the spacers (between the repeats), newelements enter a CRISPR array at rate $\theta$ at the leader end of the array,while all spacers present are lost at rate $\rho$ along the phylogeny relatingthe sample. Within this model, we compute the distribution of distances ofspacers which are present in all arrays in samples of size $n=2$ and $n=3$. Weuse these results to estimate the loss rate $\rho$ from spacer array data.

The independent loss model with ordered insertions for the evolution of CRISPR spacers