  Clustered regularly interspaced short palindromic repeats (CRISPR) in
bacterial and archaeal DNA have recently been shown to be a new type of
anti-viral immune system in these organisms. We here study the diversity of
spacers in CRISPR under selective pressure. We propose a population dynamics
model that explains the biological observation that the leader-proximal end of
CRISPR is more diversified and the leader-distal end of CRISPR is more
conserved. This result is shown to be in agreement with recent experiments. Our
results show thatthe CRISPR spacer structure is influenced by and provides a
record of the viral challenges that bacteria face.
