  Today, the CRISPR (clustered regularly interspaced short palindromic repeats)
region within bacterial and archaeal genomes is known to encode an adaptive
immune system. We rely on previous results on the evolution of the CRISPR
arrays, which led to the ordered independent loss model, introduced by Kupczok
and Bollback (2013). When focusing on the spacers (between the repeats), new
elements 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 relating
the sample. Within this model, we compute the distribution of distances of
spacers which are present in all arrays in samples of size $n=2$ and $n=3$. We
use these results to estimate the loss rate $\rho$ from spacer array data.
