In article <Pine.A188.8.131.520815144016.39360Bfirstname.lastname@example.org> Andrew Singer <email@example.com> writes: > "..the mathematician D.S. Ulam argued that it was highly >improbable that the eye could have evolved by the accumulation of small >mutations, because the number of mutations would have to be so large and >the time available was not nearly long enough for them to appear..."
>1- How does someone determine how long it would take for a series of >mutations to occur (all being presumably favorable mutations)?
In my opinion we are nowhere near being able to pose this question for a structure such as the vertebrate eye. How many mutations *does* it take to make an eye? It depends, critically, on how much of the code was created more or less *de novo* and how much was cribbed from other applications. If a lot of the stuff needed to make an eye is already implicit in the genome, serving other functions, you might be able to make an eye very easily indeed. Need a muscle to focus the lens? Just tweak the muscle that closes the eyelid.
To know how probable the eye is, we would have to know how many different ways you could use a reasonable number of mutations to adapt the pre-existing code into an eye. But since we don't know how many ways there are to make an eye (at least three, as another poster points out) or what the details of the pre-existing code were, there is no way to make a meaningful probability estimate.
You could get a start by identifying all the eye genes, and then asking where they seemed to have come from--do they have close relatives in other systems, or are they new genes? How different are they from their neighbors? We have not done this yet, except for a very few genes. The genes that make human red-detecting and green-detecting pigment are siblings--about half a dozen mutations were needed to change from bichromatic to trichromatic vision. But eyes are old, and some of the evidence may be lost in history.
It's also worth noting that not all successful mutations are favorable mutations; many mutations occur and persist by chance because they are not harmful, or not too harmful. I suspect that the genetic quirk which makes my lineage blonde as children and brunette as adults has no use at the moment, but it's available for subsequent mutations that would *give* it a use (for example, the control sequences that let the hair-color gene tell a child from an adult could be attached to something else).
In my opinion we cannot make meaningful estimates of the probability of evolution for any complex structure, much less all of life; we just don't know enough. We certainly can't say with any confidence that it was too improbable to happen.