[lkrubner]

If a mutation in a given gene leads to death 99.9999% of the time, but leads to oxygen transport the rest of the time, and the mutation happens many millions of times, then it is reasonable to think it could have been invented twice. Most of the time the mutation leads to death, but every once in a million times it leads to a happy result. Over the course of a few million years, the mutation happens many millions of times. In that scenario you would expect to happen at least twice, and probably much more often.

As an example, write a simple program that randomly generates strings of letters from 1 to 20 characters in length. Then include an English dictionary in the program. Compare the randomly generated strings with the words in the dictionary. How often does the random process generate actual words? Not often, but sometimes, and that is all that is needed.

[Sharlin]

If genetics were that fickle life would have never happened. The vast majority of mutations are neutral or affect the functionality of the resulting protein only by a matter of degree.

Your example totally ignores how selection works. Life does not generate genes randomly and see what sticks. Prebiotic chemistry might have worked like that to some degree. But at the point oxygen transport was invented every gene in an organism would already been subjected to billions of years of selection pressure and the gene or genes that eventually came to code for hemoglobin would already have had some other, related purpose.

[lkrubner]

"Your example totally ignores how selection works."

What do you think the word "selection" means? It means that stuff dies. It means that there is constant random mutation, most of which leads to death. Of the mutations that are useful, we say they are selected. When we speak of a gene being selected, we should recall that many mutations are failed mutations that lead to death. It is a random process. If you think there is some guiding force that leads genes down the correct path, then you are basically making a religious argument.

[Sharlin]

Your understanding of selection and evolution is inadequate. As I said, the majority of mutations are neutral. Of the rest, the vast majority have some small effect on the reproductive fitness of the organism. More often negative than positive, yes. But it's about "on average x±ε offspring instead of x" and not "99.999% likely to cause death pre reproduction, 0.001% likely to make the gene code for hemoglobin when it previously did something completely different". A gene that fickle would never get selected for in the first place; any line carrying such a ticking timebomb would go extinct very quickly. The biochemistry of genetics is itself subject to selection; the most critical genes are selected for being extra robust against harmful mutations. You proposed a mechanism for the same gene to separately evolve more than once, but that argument is irrelevant because the real world doesn't work like that.

[lkrubner]

Neutral mutations can simply be ignored for answering the question posed above. Gort asked:

"isn't it possible, at least in theory, that mutation happened more than once?"

The answer is obviously "yes". Even taking your own words, the answer is clearly "yes", so I'm not clear why you are arguing. Even in the extreme case, where mutations lead to death 99.9999% of the time, the answer would remain "yes". Your own math shows the answer is "yes". I'm sure you know what convergent evolution is:

http://www.zo.utexas.edu/courses/thoc/convergence.html

As it says there:

"Molecules can evolve convergently"

I think you wanted to make the point that this is rare. You should have said so. You could have answered gort by saying "Yes, but this is rare." Instead, you've taken an indefensible position.

[reubenswartz]

Keep in mind that a lot of evolutionary advances come from crossover, not just mutation.

[rlpb]

What if there are a million different possible genes that produce hemoglobin? In that case, if two different species were found to produce hemoglobin but use the same gene, then what would that imply? I think this is what grandparent meant by "You could easily have quite different genes doing similar things".

[gort]

Sure, but this is only possible if the original (shared) gene was really quite close to being able to transport oxygen.