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DNA/RNA simply replicate themselves correct? How is death a factor here?
Technically speaking, they don't replicate themselves. They code for instructions for how to do it (saying that, some RNAs do have catalytic ability and some are involved in DNA replication - but by themselves they can't do it). This is all very philosophical, but "death" for DNA would be when it is degraded to nucleic acids, I suppose. In any case, I would not say that DNA "dies" with the organism considering that other organisms might still engulf it and potentially incorporate it. On the other hand, it is not really the actual molecules as such that make DNA important, but rather the information they carry. In this sense, DNA would "die" when it no longer carries any meaningful information. This is all just random thoughts, of course...
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Multi cellular organisms seek to maintian their reaction. This is not a factor in the case of DNA/RNA.
It is not the case for proteins or fats either. In fact, you can't point to any singular molecule in an organism and say that is seeks to maintain anything.
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At some point the individual organism began to exist for itself beyond replication. What was the advantage of this and was this when death as we understand it became a factor?
I'm again just being philosophical without presenting any actual data - but that kind of suits the questions anyway, methinks...
I would probably say that death, as I understand you to refer to it (i.e. ageing), would have started whenever organisms became multicellular AND had cells with specialized functions. The question then becomes: why aren't non-reproductive cells immortal so as to allow indefinite reproduction? Well, for starters, there has to be a balance between maintaining the non-reproductive cells versus reproducing. Combine that with the fact that there is a cumulative probability of death (from disasters, predation) one can see why it would be good to have a larger population rather than investing too many resources on growing old when you might die anyway. One can also speculate that perhaps faster reproducing organisms were better at adapting to changing environments, so that longevity is in fact restricted because of competition with members of the same species. So, the answer here as to why we die of age would be that selective forces have come to a balance between the benefits of ageing and reproduction.
To find out the advantage of such a system I suppose one should start looking at organisms that are multicellular but don't have specialised cells (e.g. sponges). Is there, for these organisms, an advantage to live as colonies? Next you can start looking at organism that have just a few specialised cells types and see what kind of advantage this has over organisms such as sponges. I'll leave that as an excercise to those that have the time to look it up (I seem to remember reading about this at some stage, so I THINK that some material might be available).