Evolving Populations, and Speciation

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Fixation is when one allele of a gene outcompetes all other alleles and becomes the only allele for that gene that any individual possesses.

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Not exactly. Competition implies that there is some increase in fitness for an organism that bears an allele.Fixation is more likely to occur in small populations where the selection is weak. Genetic drift in small populations will overcome such weak selection and as a result the offspring may actually be less adapted to the environment than the preceeding ancestral population.For example, a population may have 100 breeding pairs that produce 100 more breeding pairs in the next generation. In the first generation you may have an exact 50/50 mix of a certain allele. The chance that you will see the same 50/50 mix is 1% as is the chance that you will get a 100/0 and a 0/100...all of the potential percentages have an equal chance of occuring. But any deviation away from the 50/50 could have a drastic effect on the following generation. So if you have the next generation with a 40/60 mix of the allele in question, the chances that you will get a 50/50 mix is quite a bit less than 1% and the chances that you will get even less than 40/60 is even greater.

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A parent gives rise to a child who happens to be in posession of a beneficial mutation. This mutation proves to be so useful that the child manages to reproduce with no problem. If its children also posess the beneficial mutation, then that family line will soon dominate the population, until all members of the population posess the mutation.

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IMO, there is way too much attention paid to mutations and not enough to the novel combinations that existing genes may be shuffled into new forms.The basic textbook definition of evolution is: "The change in gene frequencies in a population over time." It says nothing about mutations accumulating or even if they occur at all.You could also have a novel combination of existing alleles that would result a new species. Consider the African Elephant that has had its population severly impacted by poaching for its ivory. The result we now have is that there is an increase in the percentage of tuskless males. We also see an increase in the percentage of surviving "loner" males. (These are males that seem to prefer to live away from the herd.)The end result is that the most likely males to survive to breeding age are tuskless/"loner" males. Both of these alleles already occur in the population and they occur independently. The novel combination would be to have the genes for tusklessness and for males to live away from a herd. These two strategies both work, but in different ways. But given enough time, we will have a genetic bottleneck.If we were to jump forward a million years and look back at the fossil record, we could possibly see a sudden change in the morphology of elephants and from that it could be assumed that a new species had evolved even though no mutations had actually occured in the population. Evolution had happened with the same gens that had always been there.