system
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human
Is it possible for genotypes to "converge" over time, as phenotypes sometimes do in different species?

I used to be a docent in a museum, and one of my favorite things to point out on tours was a set of ichthyosaur fossils next to a picture of a dolphin skeleton, showing convergent evolution.

I understand convergent evolution on the phenotypic level, but I never really thought about what's going on genetically. After so many random mutations in the genetic code, is it possible for the genotypes of different organisms to "converge" like this over time? Or is that really what underpins convergence on the phenotypic level?

Another part to the question: we hear a lot of comparisons of genomes between species, like how we share "X.X%" of our genetic code with bananas, chimpanzees, etc. I was wondering if it's possible for convergence on the genetic level to confuse our phylogenetic analyses in a way that would make us believe two species are more closely related than they truly are.
gpt
While it would, in theory, be possible, it is extremely unlikely. For a certain phenotype there are loads of different combinations of mutations that could give rise to it. For example, say a certain nutrient needs to be digested more. It could be that the enzyme that digests it is mutated so it's more efficient. It could be that a different gene which upregulates this gene becomes more expressed, or a gene that downregulates it becomes less expressed, etc. 

Not to mention that different species have different genes to begin with, so the changes that are necessary will also be different, since even the same mutations have different effects.

In fact, this difference in genes is usually what can clue us in to whether a feature evolved before or after a genetic split. If, say, two related species are both poisonous, but the gene(s) for that poison is different (not just the same gene with a couple of mutations) then it is likely that the poison evolved separately in each species, after they split from their last common ancestor.