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The Clustered Regularly Interspaced Short Palindromic Repeats-system (or CRISPR- Cas system) is known as the immune system of bacteria against phages. Albeit the general function is similar across the different CRISPR systems, the known systems are highly diverged, and a classification system is required that identifies the different components and their function. In addition, for any given CRISPR system, a population sample may have different spacers, which calls for a population genetic model for the spacer sequences. In future work, such a model can be used to determine rates for spacer gain and loss depending on the type of the CRISPR system.