Actually, I'm asking the opposite, if by 'fixation' you mean wholesale presence, i.e. how does a single mutation that appears today become fixated in the population as a whole over time? And I'm not restricting the question to the human population, but it seems more apt to ask it in that context given the more limited scope for natural selection compared to, say, wild animals that fall victim to prey.
20 Million Amerinds were in the wrong place at the wrong time when Europeans arrived, and their genetic bad luck meant they were vulnerable to new plagues that Old World human populations had adapted to. Maybe a quarter of the world died in fifty years. That was only 400 years ago.
More recently, humans have proven to be the most efficient species on earth for eliminating competing genes. More than accomodating for any slack from our moral compunctions. Wild animals may eliminate alleles one competitor at at time, but humans have applied technology to the process. The European dictatorships between 1920 and 1950 made quick work of perhaps 40 million 'different' people.
I don't think it's this simple, because you make a huge assumption, namely that the mutation to which you allude leads to a greater chance of survival. What if we're talking about an 'indifferent' mutation? This is why I chose humans as the specimen species, because there can, presumably, be many mutations, even 'detrimental' varieties, that, because of human protectionism (medicine, lack of natural threats, social security, etc), do not lead to premature death prior to procreation.
In Southwind's defense, your question had an assumption that all alleles eventually become dominant. The mental image that I suggest is to just accept that over time, there are more and more alleles, some are uncompetitive, and die out; some are more competitive, and become more abundant; most are what we call 'silent' mutations, and their frequency grows with the chance growth of the founder's descendants. Luck plays a role, too. Not all alleles are exterminated by competition: some are just a matter of being in the right/wrong place at a certain time. Consider a species of bug unique to the island of Krakatoa. Bad luck, is all.
Let's say we use the arguably ludicrous hypothetical example of somebody acquiring a sixth finger on each (or one!) hand. Assuming that person procreates we should, presumably, expect to see the number of six-fingered people increasing over time. But the number of five-fingered people is also increasing, generally directly proportionally. Should we expect everybody in the future to have six fingers, given a geological timescale? If not, how did the vast majority of current members of each species essentially come to be biologically identical (I don't know many six-fingered people!)?
The condition is called polydactyly, and it's autosomal dominant. It runs in families, as you suggest, and I think you're right: there's no obvious reason to consider this allele to lead to more succesful offspring. The proportion in the population is not noticeably growing or shrinking.
The problem with this assumption, though, is that we don't know whether some day, there will be some unexpected advantage or disadvantage to polydactyly.
Another factor is that genes are 'linked' to their neighbours. When a mutation occurs, it's going to be on a particular chromosome, and in a particular cluster of other genes. The cluster may or may not be related. For example, freckles and red hair are physically very close on the genome. So, if it turns out that freckles are useful, and people without freckles are selected against... well, red hair is also favoured by sheer luck.
In the case of polydactyly specifically... that one's probably been selected against until recently. Many animals show nervousness around any physical shape or behavior that seems outside the 'accepted' form. People with what might be considered 'deformities' have been less likely to reproduce in the past, and still face these challenges today. This is a disappointing finding of a series of studies that marketing or anthropology use to learn about what looks good on TV for advertising. Assymetry, especially in the face, is a real turnoff. Extra or missing limbs or digits is also rated by focus-groups as 'unattractive'.
Yes, I suppose so, because I think I understand the 'selection' process, which is largely eliminated from the human species, compared to, say, wild animals, that is (or does that demonstrate that I don't understand it as well as I'd like to think I do?!

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Based on my above response, you can see where I stand on the issue: I think we are a very successful species, and our huge population means there is a lot of diversity. But we are sensitive to alleles that produce visible differences, and can be very efficient in being our own hostile and selective environment, producing a counter-selection for monoculture.
But surely all of the mutations that have occurred in the past that have led to humans being what they now are, and essentially the same in all of us, were not all subject to selective pressures for their replication, or were they?
Twins aside, we're all genetically distinct. Each person has about 6 new mutations that were not inherited from either parent. Our selection pressures are unique to each individual. However, if you looked at the planet 2,500 years ago, you couldn't help but notice that many allele distributions were regional. Even more recently, we have examples of alleles that have exploded from only a few founders, because of local selective pressures.
Specifically, consider what was originally a rare 'silent' mutation to CCR12. Turns out that it conveys resistance to bubonic plague. When the plague propagated across Europe, people without the allele were cut down, and it was selected for. In fact, there were twenty different *types* of mutations to this gene, all probably sitting dormant in the population, and who could have predicted that after the plague, 90% of the population would have this allele? And today, new mutations have happened in this gene, so there are more new alleles, and that particular CCR12 morphology is only something like 30% of the population.
But we've seen a second explosion of this allele in cities like Goa or Calcutta, where prostitution is rampant, because these alleles also provide protection against HIV infection.
I'm sorry, I didn't mean to use that term as a biologist or geneticist might. By 'essentially come to be biologically identical' I mean two arms, two legs, upright walking, useless(?) appendix, limb proportions, hairy parts, etc.).
Appendix is more an example of something that was selected
against and is much smaller in moderns than in our ancestors. A caecum made sense for our arboreal primate ancestors, but the benefit/cost ratio shifted as later ancestors added scavenged food. The main problem with a caecum is that it can become colonized by parasites or can trap fecoliths and become septic. Consider how tiny a cavity it is today, and it's still a lethal hazard.
Do you think a baby born today with six fingers is unlikely to reach adulthood and procreate?
Unlikely, no;
less likely, yes.
Maybe this is the gist of what's eluding me. Are you able to elaborate on 'occur often enough'? That, to me, suggests identical mutations occurring simultaneoously in different parts of the population. Is that what you mean? If so, is that generally accepted by the evolution gurus?
It's rare for there to be two simultaneous
identical mutations. What's not rare, though, is for
different silent mutations to have occured in the same gene in different places at different times, which might all have the same effect when exposed to some environmental pressure. As we speak, I wouldn't be surprised to learn that you and I could have different mutations, but in the same gene, that may have the same phenotype.
A recent example is Tay-Sach's, which is a condition that causes children to die young if they have two copies. If they have one copy, they are only slightly affected.
These mutations were rare over the human population, but there was one population that was socially thrust into a physical environment that actually favoured this. Diaspora Jews were forbidden to own land, and had to live in very close quarters, later ghettoes. Turns out all these different mutations that produce Tay-Sach's also provide protection from tuberculosis. Azekenashi Jewish families who weren't carriers of these alleles were more likely to have tuberculosis, or have children with tuberculosis, so Azekenashi Tay-Sach's families became a huge proportion of the population. Concievably, given enough time and a consistent environment, this allele could have become the rule, but we're only talking about a dozen generations, here.