Their inital appearance saw them originate from some point in the far future, but had also been temporarily living in both the Permian era and the present day.
In the second timeline Future Predators were apparently not natural creatures and were created in the ARC because of something Christine Johnson would apparently come to do after taking over the ARC, implying they were genetic mutants, created using cloning mechanisms. It is also possible that they were cloned from their future selves' DNA, creating a time paradox.
In a third change to the future timeline that was caused by the interruption of the 2011 Convergence by the opening of the New Dawn Anomaly (though how it affected them is unknown, though it is likely they changed to cope with surviving in the harsh landscape), the Future Predators have mutated into a different form.
It is unknown whether or not the Future Predators will be in the fourth version of the future, but it is possible, considering that they are one of the show's most iconic ceatures.