How rare are they? I will let you decide. We have over 6,000 genetic disorders due to mutations and your side can only point to a handfull of beneficial mutations. Beneficial mutations they say can be added to the genepool because they are less likely to be noticed and eliminated. Why is that when we can only point to a few beneficial mutations that has been added to the genepool but we can point to many more harmful mutations that have been added to the genepool.
Wow... If we thought like you did throughout history, we wouldn't have gotten very far. No offense. It's intellectual laziness on your part. To get to the point, you are not able to show that the chances are too small for a beneficial mutation to occur. In fact, its ridiculous to rule this out, and you are committing a logical fallacy, once again: "proof by assertion." If you have no evidence for something, you don't get to simply assert it as fact. Again, intuition does not count as evidence.
The answer to your question is quite simple. it is more probable that a mutation is either neutral or harmful, simply because what constitutes fitness for any given animal is a narrow set of features. Relative to the possible mutations, only a narrow set of mutations would actually increase the chances for an organism to survive. Therefore, it is statistically improbable that a random change in the alleles will produce anything desirable. Occasionally, we do see people with beneficial mutations, but we might not even notice it. They may simply be the "prodigies" we all admire. By definition, any mutation we see, wouldn't be a huge mutation, because that's not really possible, or highly unlikely. It would be a small mutation, something we might not even notice, like greater intelligence, or a greater proclivity to understand math or music, english, etc... who knows. You seem to be expecting someone with wings or something ridiculous, I am guessing.
I did a post on mutation fixation a while back and the conditions that need to be met for a mutation to become fixated in the population and the problems for this to happen. You have enzymes also working against fixation . I am not gonna search for that post but here read this article and you will see one of your own explaining the conditions that have to be met for fixation to take place plus the enzymes working to correct these copying errors and the chances are impossible no matter how many years you give it.
Mutation Fixation: A Dead End for Macro-evolution
by E. Calvin Beisner, M.A.
Most arguments against the possibility of mutation as a mechanism for evolution revolve around two premises: that mutations are almost always harmful, and that the idea of their improving rather than harming organisms is contrary to the Second Law of Thermodynamics, which tells us that matter and energy naturally tend toward greater randomness rather than greater order and complexity. These are two sides of the same coin, actually, the latter arguing from principle and the former from empirical observation.
Rarely, though, do arguments against mutation as the mechanism for evolution consider at once the many conditions that must be met if mutation is to bring about macro-evolutionary change (that is, change from one basic kind of life to another). Yet examining the probabilities of these conditions all being met together provides excellent evidence against evolution and in favor of creation.
NINE CONDITIONS FOR MUTATION FIXATION
Fortunately, geneticist R.H. Byles has made the job easy for us by discussing nine important conditions in an article on the subject. 1
1. Natural Environment
Byles's first condition is: "Natural selection must be inconsequential at the locus or loci under investigation." This is because natural selection tends to work against fixation of mutations--in other words, it tends to prevent their becoming a permanent part of the gene pool of a population. Natural selection keeps things stable rather than helping them to change. B. Clarke points out that even so-called advantageous mutations are harmful in that, because of increased competition, they can reduce population size, making their fixation nearly impossible. He adds that they will almost certainly lead to extinction of the mutant gene or organism, and possibly even the entire population. 2
The effect of Byles's first condition is that the environment must be selectively neutral, or else the mutant gene will never be retained in the population, preventing even slight change. But according to J.T. Giesel, most locations are almost certainly not selectively neutral. 3 Thus, in the vast majority of cases, Byles's first condition will not be met.
2. No Structural Change
Byles's second condition is: "There must be no pleiotropic effect involved with the locus or loci, or, if such effect exists, all the phenotypic structures involved must be selectively neutral." This means that there either must be no changes in physical structure involved, or they must be selectively neutral. If none are involved, then of course evolution does not occur. But if only those occur that are selectively neutral, then they are of no advantage to the mutant and survival of the fittest does not affect it or its non-mutant relatives; again, no evolution.
Not only would mutations that met this condition appear to contribute little or nothing to evolution, but also they would appear never to happen--or nearly never, anyway. G. Ledyard Stebbins tells us that within the gene there is no such thing as an inactive site at which a mutation will not affect the adaptive properties of the gene. 4 "Every character of an organism is affected by all genes," writes Ernst Mayr, "and every gene affects all characters. It is this interaction that accounts for the closely knit functional integration of the genotype as a whole." 5
In other words, there may well be no such thing as a mutation having no structural change in the organism. Yet Byles says that a requirement for the fixation of a mutation is that it have none, or that the effect it has must be selectively neutral. Neither case appears ever to happen, and even if the latter did, it would not lead to macro-evolution since it would leave the mutant no more "fit" than any of its relatives. Indeed it would probably be less "fit" because of the tendency of natural selection to weed out rather than preserve mutations in a gene pool.
3. Net Effect Must be Unidirectional
Byles's third condition is: ". . . the mutational event must be recurrent and, furthermore, the rate of back mutation must be so small as to be irrelevant." Byles himself admits, though, that even recurrent mutations are almost never retained in the population: ". . . non-recurrent mutations have a very low probability of remaining in the genepool at all . . . the odds against a recurrent mutation being retained in the gene pool for any significant number of generations are very high." And even "most recurrent mutations have been observed to retain the potential for back mutation." It seems that neither part of his third condition will be fulfilled; yet Byles makes it clear in his article that all the conditions must be fulfilled in order for mutations to be fixed in a population.
4. High Mutation Rate
Byles's fourth condition is: "The mutation rate at the relevant locus or loci must be very large." Yet Francisco Ayala says, "It is probably fair to estimate the frequency of a majority of mutations in higher organisms between one in ten thousand and one in a million per gene per generation." 6
Byles himself comments on Lerner's estimate of one hundred mutations per one million gametes (one in ten thousand). "Obviously, a mutation rate this small, even given a complete absence of back mutation (which appears never to occur), would result in a very small change in a given gene pool, even given large numbers of generations. This has long been considered one of the major stumbling blocks to the [Probably Mutation Effect] . . . In order for the P.M.E. to be effective, very high mutation rates are clearly necessary."
So it appears that this condition, too, is likely never met in nature.
5. Large Population
Byles's fifth condition is that the population involved must be large. He stipulates this because small populations can easily be destroyed by a mutation. And, as population size decreases, the probability that a mutation will be eliminated increases.
Dobzhansky, Hecht, and Steers, however, postulate that a small population with much inbreeding is important: ". . . the ideal conditions for rapid evolution . . . are provided by a species which is divided into a number of small local sub-populations that are nearly but not completely isolated and small enough so that a moderate degree of inbreeding takes place. . . . The division of a species into two or more subspecies is of course dependent on complete isolation being achieved in some way." 7
It seems that evolutionists themselves have realized a great problem but are unable to deal with it. In a small population, a mutation will almost certainly be eliminated. Yet a small population is needed for evolution to occur. Here indeed is an impasse. But the problem gets worse.
Byles adds (in contradiction of Dobzhansky, Hecht, and Steere), "If the investigator is dealing with a population which is undergoing contact with genetically dissimilar neighbors, the effect of the mutation is inevitably so minor as to be undetectable. Therefore, to argue that mutation is the cause of change in the population's genetic structure, one must also of necessity argue that this population is not undergoing a process of hybridization." In other words, if the population is large, the effect of the mutation is almost nil. Even when Byles's condition is met, then, the effects of the mutations are almost zero on the entire population. And, furthermore, while Dobzhansky, Hecht, and Steere say some interbreeding between dissimilar populations is necessary, Byles says it is death to evolutionary change.
6. Selective Neutrality of Polygenes
Byles's sixth condition is: "Polygenes are not relevant to this argument, unless the entire anatomical complex is itself selectively neutral." This means that for organisms of many genes, the mutation cannot be fixed unless the whole anatomical structure of the organism is selectively neutral relative to the gene which mutates. That this does not occur was shown in our discussion of the second condition.
7. Little Hybridization
Byles's seventh condition is: "There must be little or no hybridizing admixture." This of course is to avoid making the mutation itself insignificant. But if the effect is actually significant, then this contradicts his second condition, which was that the mutation must cause no significant structural change (see under point 2 above). Furthermore, the only way in which to have no hybridizing admixture is to have a small population that is isolated from others of the same kind. This contradicts his fifth condition. If the population is small, the probability of a mutant gene's being eliminated rises steeply.
This seventh condition, if fulfilled, makes evolution impossible because the mutation would not be retained due to the necessarily small population. But if unfulfilled, it leaves evolution impossible due to the insignificance of the effect of the mutation.
8. Necessity of High Penetrance
Byles's eighth condition is: "The genetic structures involved must have high 'penetrance.'" Put simply, this means that the genes must be highly susceptible to mutation. It thus means almost the same as Condition Four.
Yet it occasions another problem. As soon as the structure becomes highly susceptible to mutation, it must also become highly susceptible to back mutation. But his third condition states that the rate of back mutation must be irrelevant. Again there is contradiction: fulfill Condition Eight and you can't fulfill Condition Three. Fulfill Condition Three and you can't fulfill Condition Eight. Yet Byles says that all of the conditions must be fulfilled for mutation fixation to occur; and without mutation fixation there is no macro-evolution.
9. High Heritability
Byles's ninth condition is: "The phenotype must have high heritability." This condition is almost never met for mutational phenotypes. Byles himself told us that the probability of retaining even a recurring mutation is "very low."
TALLYING THE SCORE
It appears that the probability of meeting any one of these conditions in nature is extremely low, if not non-existent. Recall now that the fifth and seventh conditions effectively cancel each other out, as do the third and eighth, and we are forced to the conclusion that it is impossible to meet all the conditions. Mutation cannot be the mechanism for macro-evolution.
Mutation Fixation: A Dead End for Macro-evolution