Anomalistic Abilities, while genetic in nature, could be, in fact, emotionally developed. Where it seems that people gain abilities from having a certain genetic marker, and can indeed develop abilities, these abilities are wide in range and form. There seems to be little agreement between the nature of the abilities in question and the fact that every individual on the current list of determined "specials" shares that genetic marker. However, close study needs to be given to the emotional state the individual is in when using their ability, the kind of personality they have as a reflection of their emotions, even their emotional reaction to the way their ability works or appears to work. For the most part, it seems that these individuals are dispositioned to develop a certain kind of ability based on their emotional state and personality.
Could an individual with the genetic marker, if driven to a slow but steady depression, or even chronically depressed as a result of constant buried anger, develop the ability to unleash a nuclear holocaust purely because of the pain experienced while depressed or otherwise stressed? Could an individual with this emotional state have full control over their abilities, those abilities being a result of the strain on their emotions? To this extent, it would make sense that the abilities are directly tied to emotions. The adaptive ability that the genetic marker gives the individual is enormous, but only if these abilities are not just conscious decisions but unconscious reflexes in the characteristic human defensive response of "fight or flight". To this end, the best way the brain would be able to handle the release of the ability would be in response to whatever sudden and specific emotional responses are elicited within the subject. If the anomalistic abilities are tied to emotions in this way, the formation of personality and shaping of emotional responses in the individual would only logically give rise to specific ability development.
Consider an individual with the genetic marker that grows up with a sick mother. The individual, a loving and caring son or daughter would grow the sense of wanting to be able to help the sickly in any way they could. The strong feelings of compassion and caring for others, not just oneself would or at least could endow that individual with the ability to do so. In this scenario, the individual that felt so strongly this way could develop the ability to heal and repair others. Or consider instead the impoverished individual that grows up in a home where the parents are constantly fighting. Their words are like knives, cruel and commanding, and powerful. Hypothetically, the individual is also silenced by these arguments, a voice unheard because of the fighting between his or her parents. The sense of being almost powerless because they cannot be heard is fostered, and finally in an angry outburst of their own, that individual develops the ability to, naturally, control and persuade others just by the application of the voice. Think instead of the carefree, personable person that grows into a friendly kind of individual, constantly thinking of others and trying hard to be there and be friends with everyone. Logically then, this individual could develop the ability to hear another's thoughts, in order to become intimately aware of what the other person is feeling or thinking, in order to better understand and further their attempts at fostering trust and companionship within the other.
When these considerations are taken into account, the list of anomalistic abilities can be subsequently organized and understood by study of the individual that develops them. Furthermore, the list of individuals with the potential for anomalistic abilities could be better dissected with regard to those that have not yet developed abilities, or even when further understanding of how the process works is gained, prediction of abilities or even predictive abilities in the next generation of the "special" individual's offspring.
With these theories considered, there could also be a means of tracking down specific abilities based upon the tracking of standard Mendelian genotypes such as hair and eye color. Two unrelated individuals could have the exact same ability, but have lived separate lives entirely in separate locations and times. The only similarities being physical characteristics such as hair, eye, and skin color. This could aid in determining if, like some diseases, specific genotypes or social groups are more prone to developing a certain series of related abilities than others and in which generations they might occur. Lingering close to eugenetics, this is still a morally tricky subject.
It is also possible that these evolutions are the result of contact with some unknown agent, that has occurred in recent era, thus the Activating Agent, could be Biological (a virus or Transposon) Chemical (such as mutagens) or Radiological (extraterrestrial radiation, sunspot, supernova, or man made). If for instance a large number of people possessing such abilities were descendants of the survivors of Hiroshima and Nagasaki then a radiological cause would be likely. However, it might be something as mundane as living near electrical pylons or eating certain foods. What will happen? Who knows.
It is also possible that such a giant leap in evolution is in fact a human sub species, which had interbred with Homo sapiens, re-emerging because sufficient quantities of genetic material once dispersed have gathered in specific individuals. This could be plausible because of much lower mortality rates, the once common practice of persecuting witches, may in fact been genocide of this race; and now that such practices have ceased, the diffuse genetic material is re-emerging from the Homo sapiens gene pool.
Single Mutation Theory
Accelerated Evolution assumes that a higher mutation rate of many loci, or punctuated equilibrium, is responsible for creating individuals of interest. However, it is possible that regular, natural mutation of a single gene could be responsible for these individuals.
In nature, there are some genes that are poorly regulated by the cells natural genetic repair mechanisms, making them susceptible to frequent mutation. In such genes, allele a1 can easily mutate to allele a2, which can easily back-mutate to allele a1 again. These mutations are not the result of doubling mutation rates across all loci or accelerated chromosomes. Indeed, since mutations are random, having fifty times the natural mutation rate would likely result in multiple malformations.
How a single natural mutation could cause individuals of interest is simple. A single gene that codes for a protein or enzyme in brain function could have a dozen or more possible alleles. One of those alleles (allele p12) could be the precursor for the special allele (allele P12). Allele p12 could easily mutate to P12, and even back-mutate to p12 again. This adds another avenue for finding potential individuals of interest. One could look for the special allele (P12) in current generation. However, one could also look for the precursor allele (p12) in the parental generation. If a parent was homozygous for the precursor (p12p12 instead of p12p11), the odds of the child having at least one special allele by natural mutation would increase. If both parents had the precursor, it would further increase the odds. In this way, it might be possible to find individuals of interest even if you do not have direct genetic data from them. One could analyze genetic data from their relatives, even if their relatives were not individuals of interest. If you find out which gene becomes p12 naturally, (for instance, if p7 commonly mutates to p12, and p12 commonly becomes P12) you could go back even more generations. A complex algorithm would be necessary to sift through all the information, but might provide a way to find individuals of interest.
As for how one gene could manifest in so many different ways- that too is simple. The notion that one gene causes one phenotypic trait is an old way of thinking. Many genes impact other genes indirectly. It is possible that the individual's specific genome, including all of their regular genes, helps determine how the special gene will manifest. Also, many traits are subject to phenotypic plasticity. For example, two people with the same genetics for height may be over a foot apart when they reach maturity, depending on how well they were fed, how large their mother was during pregnancy, and whether they were born prematurely or late. Similarly, the special gene (P12) may be subject to a great deal of natural phenotypic plasticity.
Of course, if there is only one gene separating individuals of interest from regular individuals, they are most decidedly not a separate species.