Calculating probabilities requires better knowledge in two areas:
In order to know all the possible outcomes, it is helpful to know how much of a genome is pure noise, and how much is already being used.
Not surprisingly, if one species has “x” amount of genome, and another species has “10 times x” in raw genome, more mutations can occur each generation.
If we don’t know how much of the genome is “almost ready” to become a gene with a specific use, how can we calculate a probability?
Probabilities work best when you know the universe of possibilities… like the heads and tails of a coin… or the number of possible sides a pair of dice have.
How do you calculate probabilities when someone gives you a pair of invisible dice, and only visible side is the one that is facing up? Your first task is to see how many sides there are … but as you slowly rotate the dice, the number keeps getting higher and higher … with no end in sight!
The logic of evolution becomes more important than the math:
Once one agrees that enough changes can aggregate in a population that makes them no longer reproductively compatible with another part of the population … all other things about evolution are possible!
 These changes could involve blood or ovarian chemistry;
 These changes could involve physical facilitation (if the male or female become so large or so small that many potential mating partners are physically unable to accomplish the deed);
 These changes could be changes in peripheral aspects of mating, like the song birds make to attract mates! In a single generation, a change can happen in a bird’s brain that triggers a different song … and the only ones willing to mate with it might be other descendants that share the same song change.
Once two groups of a single population no longer freely exchange genetic information, then one group will no longer experience the same set of mutations… and they will start traveling their own unique road of genotype and phenotype.
@colewd, I just read your post above… I hope you think my post touches on what you were describing.
Why did it need to have an antifreeze gene? Lots of fish get by fine without one. Getting one might have enabled some fish to exploit a new ecological niche (or exploit it better), but if no such gene had emerged . . . what? We wouldn’t be sitting around wondering why one didn’t exist. Which is to say, evolution isn’t striving to achieve some target.
Yeah, that site is perhaps not the best, overall source for beginning your inquiries, given the ‘what we believe’ statements here. For example:
Facts are always subject to interpretation by fallible people who do not possess all information. By definition, therefore, no interpretation of facts in any field, including history and chronology, can be valid if it contradicts the scriptural record.
I’m saying that there are only a few specialists in genetic probabilities… because for the most part, the kinds of probabilities you are asking about are only used to argue FOR or AGAINST evolution.
Someone who is already an Evolution scientist could care less about that debate.
Frankly, I think it is a loser for opening a discussion… though there is one application I would love to see take the center ring: nay-sayers love to talk about the odds of a specific genetic outcome being impossibly improbable:
The probability that enzyme A (as we know it) becomes enzyme B (as we know it) is 1 out of 99999999999. blah blah blah.
But this is like betting on the lottery: the probability that “Peter Derecskei” will win the Mega Ball would be a ridiculously speculative wager.
But if you had to use the probability that ANY single individual would win the Mega Ball… that becomes rather dull, right?
It’s a misleading term, since it suggests that the organism will be incomplete if it doesn’t get what it needs. It directs thought in the wrong direction, toward thinking in terms of the probability of a particular trait evolving, rather than of any beneficial trait evolving. The latter is a lot larger than the former.
Not that we can calculate any of these probabilities. We don’t know nearly enough about the space of possible proteins or possible traits to do such calculations. What we can do is observe overwhelming evidence that different species are related to each other by common descent, and strong evidence that the differences between them are the result of mutations and that new features (including new genes) arise by known processes from existing features.