system
Given the following post, respond as if you're commenting on Reddit:
human
Does convergent evolution lead to similar genotypes in addition to the similarities in phenotype?
gpt
It's possible, but very unlikely. It would be like if two people on opposite sides of the world both wanted to write a really popular novel and the books they wrote had not only the same themes but the same plot, characters, writing style, etc. A different analogy: if you and a partner were to both roll dice until all of your rolls add up to 100, would your series of rolls look anything alike, even if you reached the same result? When we're thinking of something like wings of insects, birds, and bats, it just doesn't make sense that the millions of base pairs coding for development of the wing would be anything alike, even if they form a similar structure. 

Scientists (geneticists) use this assumption to make phylogenies. They more or less disregard the function of the genes and look only at the form (what letter is where, how many letters and chromosomes there are) to establish relatedness of species. This is the same thing we do (though less precisely) when we disregard the differing functions of a whale fin, a human arm, and a bat wing to look at the similar skeletal and muscular form to infer recent common ancestry. 

Basically, the genes for a bird's wing are going to be more similar to those for a bat's wing than to those for a butterfly's wing, but that is because they are more closely related, not because they have a more similar function. By that logic, a hummingbird would have genes more similar to a bee (based on flight pattern) than a hawk.