...of nature evolving more advanced compression algorithms in more complex organisms.
lol, I'm guessing you're joking.
But just in case some people don't realize this is a joke, I will add that there are several reasons why it doesn't quite work like that. To name a few:
1. The idea of "more advanced" assumes a linearity to evolution that does not fit with natural selection (the "escalator fallacy" discussed by Mary Midgley)
2. While many genes perform multiple functions, these are not in any way planned, as though a gene becomes established because it does both A and B and therefore can replace two separate genes that each do only one task. Since genes operate by dictating the production of amino acids, in most cases their multiple operations are mere coincidence. Governed by natural selection, if such coincidences happen to be useful enough to promote the organism's survival over others, then the gene becomes established.
3. It is actually much simpler to suppose that excessively large genomes evolved by mere chance. In the first place, it is not as though so-called less-evolved organisms all have large genomes while advanced organisms have small ones. It is true that many apparently simple plants have huge genomes, but this does not mean that the line of evolution passes from large to small genomes. Rather, earlier versions of plants had simpler genomes which became much larger because strange copyerrors ended up producing some benefit. For example, a cell accidentally doubled a chromosome, but by pure chance this doubling did not lead to its death but ended up being read in such a way that it provided a benefit.
Importantly, what is especially facinating is that not all DNA really adds new information. For example, since we have two of every chromosome, much of our DNA is essentially just backup. I remember being in high school pondering how so much complexity about the human person could be encoded into DNA. I did some simple math, and discovered that human DNA is only about as much information as a clean installation of Windows XP! Clearly there must be more to what makes us human than just DNA, because we certainly seem at least a little more complex than Windows XP. Of course, epigenetics helps to explain the gap a bit. But at the same time, it's important to see that much of what we are is really a product of our individual development/environment, and is not strictly encoded into DNA.
When all else fails, read the instructions.