“…Some themes have emerged from experimental studies of CRISPR immunity: (a) high spacer diversity relative to phage diversity increases the likelihood of phage extinction ( van Houte et al, 2016 ; Common et al, 2020 ; Guillemet et al, 2021 ), (b) bacteria become more immune to phages over time ( Laanto et al, 2017 ; Morley et al, 2017 ; Common et al, 2019 ; Pyenson and Marraffini, 2020 ), and (c) phages readily gain mutations ( Weinberger et al, 2012a ; Paez-Espino et al, 2013 ; Levin et al, 2013 ; Pyenson et al, 2017 ; Watson et al, 2019 ; Pyenson and Marraffini, 2020 ; Guillemet et al, 2021 ; Guerrero et al, 2021a ) and sometimes genome rearrangements ( Paez-Espino et al, 2015 ) to escape CRISPR targeting. Explorations of CRISPR immunity in natural environments have also documented ongoing spacer acquisition and phage escape mutations ( Weinberger et al, 2012a ; Guerrero et al, 2021a ). Likewise, previous theoretical work has addressed the impact of parameters such as spacer acquisition rate and phage mutation rate on spacer diversity ( Childs et al, 2012 ; Han et al, 2013 ; Han and Deem, 2017 ) and population survival and extinction ( Weinberger et al, 2012b ), how costs of CRISPR immunity impact bacteria-phage coexistence ( Skanata and Kussell, 2021 ) and the maintenance of CRISPR immunity ( Levin, 2010 ; Weinberger et al, 2012b ; Westra et al, 2015 ; Gurney et al, 2019 ), how spacer diversity impacts population outcomes ( He and Deem, 2010 ; Weinberger et al, 2012a ; Childs et al, 2012 ; Haerter and Sneppen, 2012 ; Han et al, 2013 ; Childs et al, 2014 ; Bradde et al, 2017 ; Han and Deem, 2017 ), and how stochasticity and initial conditions impact population survival ( Bradde et al, 2019 ; Chabas et al, 2018 ).…”