A gene doesn't necessarily "escape" the effects of evolution to remain conserved. There are often strong balancing selection forces on essential genes. Basically, some gene's function is so absolutely required for life or survival, that any random changes in their code is rapidly purged from the population as any change is almost always highly detrimental to fitness, or outright lethal.
But, a gene under strong balancing selection is not removed from or immune to the forces of evolution. It is those very forces that keep it in check and prevent change.
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A gene doesn't necessarily "escape" the effects of evolution to remain conserved. There are often strong balancing selection forces on essential genes. Basically, some gene's function is so absolutely required for life or survival, that any random changes in their code is rapidly purged from the population as any change is almost always highly detrimental to fitness, or outright lethal.
But, a gene under strong balancing selection is not removed from or immune to the forces of evolution. It is those very forces that keep it in check and prevent change.
No DNA sequence escapes evolution. The conserved regions that are observed are a reflection of the relatedness of the organisms looked at and the selective pressure on the DNA segment either directly or through the product it encodes. So if a gene encodes a protein that has limited capacity to change, you would not expect to see much change in the DNA sequence except perhaps at the 3rd position. The amount of change here is to some degree a reflection of the evolutionary distance of the organisms you are comparing as well as the constraints of the translational machinery for those codons. But nothing escapes evolution, you may just be looking at something that is perhaps fully optimized.
I see it as a function of protein. most of the conserved residues in a protein are either necessary for protein structure stability or its function e.g. enzyme activity- as in the active site of enzymes. If a conserved residue is mutated in the course of evolution making the protein/enzyme inactive in any case, it will be diluted out of the population and we might not know if that was mutated at all.