My IP specialty was copyrights, not patent law, but I did have to take patent law classes . . . More than a decade ago . . .
To be patentable it must be a new thing/techhnique/process that take a “novel step” that differentiates itself from any prior art. A new patent must be novel, non-obvious, and useful. You cannot patent stuff in public domain. You also cannot patent stuff even you yourself have made and have previously sold/exhibited but not patented yet. So, provable or not, if genetics are out there and being sold or exhibited, technically you should have an uphill battle to patent. Even if it would otherwise be patentable. Famous case/precedent was about corsets.
Egbert v. Lippmann - Wikipedia (public use of invention bars patentability)
But a little change in the dna would make it new and novel. How big a change to make it a novel step? Thats what patent examiners and court are for. Even if initially granted you can sue to invalidate a patent on novel grounds and win. Good luck having the pockets to fund such a legal attack against a big company though.
Arguments abound over whether you should be able to patent a genome but currently you can, or could completelty when I studied it. Dont know about the last two years as asked on another thread but monsanto has absolutely sued farmers due to accidental pollenation of the farmers heirloom soybean crop with monsanto pollen/genetics from a farmer next door. Claimed the seeds produced from the unintended breeding were monsanto IP/property if I rememebr properly. Law may have changed since I looked at, as it does, but Monsanto had the legal leverage back then, and used it.