Mapping whole genome sequencing of several strains of organism A to gene X

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I think you can just try it. The only thing that comes to my mind is that you maybe need to filter out some clipped reads. A mapping tool can clip the outsides of the read to make it map better to the reference. I don’t think it will be that much of a problem but it is the one thing that comes to my mind. You can also download the whole reference genome and check if your gen X is present in there with blast. And map against that full reference genome.