Something like:
endogenous
- having an internal cause or origin.
- growing or originating from within an organism.
Genous, you can think of it as analogous with genesys, it's the root word for creation.
When it comes to viruses though, there's one more very fascinating hypothesis. That the cell nucleus itself was once actually a virus that took over some bacteria to do its bidding.
Thus we have some species nurturing their young (most mammals, marsupials, and birds) as opposed to spawning them and then going on to other things (e.g. fish, insects).
The most extreme case of this is humans: females live well beyond their fertile age and, effectively, so do men (while technically fertile in their 70s, the offspring are not as vigorous, in the evolutionary sense, as those conceived when the father was in his 20s). It is believed that this is because older humans have learned lots of things that can be useful in keeping kids alive and effective until they can propagate their genes.
Although 99+% of evolutionary psychology is utter bullshit this is nonetheless fascinating.
Biological immortality means after some point mortality rates don't increase with age - you can still grow old, it just won't directly kill you. Biologically immortal organisms don't have a max lifespan, if they're lucky they can just keep on going, but they may be dramatically more feeble than their younger counterparts.
No virus needed. Humans are currently (or were very recently) under enormous evolutionary pressure to get smarter. The ability to adapt is likely itself a trait as you suggest, but it makes sense that it can vary over time as needed depending on environmental factors.