The Definition of Congenital Amusia
Amusia can be defined as "an inability to appreciate music" or "a disinterest in music". Congenital amusia is amusia which has a substantial genetic cause. (To be exact, "congenital" actually refers to any disability which is evident at birth, and a more accurate term might be "genetic amusia", or "genetically-caused amusia". But "congenital" seems to be the preferred term, so I will keep using it.)
Amusia and "Musical Genes"
In the context of music science, the most interesting kind of congenital amusia would be amusia which is caused by some mutation or alteration to a "musical gene", i.e. some gene which can be considered to be for music.
This raises the general question of what it means for any gene to be a gene for something. A simplistic answer to this question is:
A gene X is a gene for an attribute Y, if the determination of attribute Y by gene X was what caused a new allele of gene X to be favoured by natural selection when it first appeared.
This definition is obviously historical in nature. When attempting to determine whether a gene is a gene for something now, based only on observations of an organism in the present, we must assume that the relevant relationship between the gene, the attributes determined by the gene and the effect of those attributes on natural selection have not been too much altered by other changes to the organism and its environment that have occurred in the time since the gene first appeared.
The Genetics of Disabilities
Suppose that an alteration to gene X causes a disability related to function Y of an organism. Does this mean that gene X is a gene for Y?
Not necessarily, because the change in gene X may cause some more general deficit in some other function Z which is a prerequisite for function Y. In other words, the gene X is actually a gene for function Z.
Amusia and "Tone-Deafness"
Amusia is sometimes defined as being "tone-deafness". But tone-deafness is conceptually distinct from "inability to appreciate music", as it refers to an inability to discriminate pitch values.
Discriminating pitch values is not the same thing as appreciating music.
Consider some computer software. If I write a program which can analyse a digital sound recording and identify the pitches of tones occurring in the recording, have I written a program that appreciates music?
It would seem obvious that I haven't. I could give my program in a recording of the world's greatest pianist playing some of the world's greatest classical music, and I could give the program a recording of my cat walking across the piano keyboard. The software would probably have equal success in discriminating the tones in each case, but it would not be appreciating the music, in the sense that it would not be able to tell me which recording was music and which wasn't. Nor would I be able to write any simple extension to the software to add this capability.
If we characterise amusia as being the same as tone-deafness, we are incorrectly identifying music appreciation with pitch discrimination.
Tone-Deafness is One Cause of Amusia
A more reasonable statement about tone-deafness is that it causes amusia. In other words, the appreciation of music depends on pitch discrimination, and if a person cannot discriminate pitch values, then they cannot appreciate music. This is quite different to saying that tone-deafness is amusia.
Amusia May Cause Tone-Deafness
It is possible that amusia could cause tone-deafness, in the sense that the parts of the brain which discriminate pitch values fail to develop in the absence of any motivating interest in music. There does not appear to be any reason for people to have the level of pitch discrimination that they have other than the appreciation of music. For example, the level of pitch discrimination required to perceive the melodic components of language is much less than the precision of pitch perception which underlies most people's ability to appreciate music.
So it is at least plausible that pitch discrimination may be lost if there is no appreciation of music, because the neurons whose job it is to do the discrimination might fail to develop in the absence of any feedback received from the neurons whose job it is to signal the appreciation of music.
But even if amusia does cause tone-deafness in this sense (and this is by no means certain, I am just raising it as a possibility), this is still not the same thing as amusia actually being tone-deafness.
An Analogy with "AWalkia"
If you search for "awalkia" on Google, you will realise it's a word that I just made up. Its definition, by analogy with "amusia", is "an inability to walk on two legs", and/or, "a disinterest in walking on two legs".
Now there are many people in the world who cannot walk, and some of those people cannot walk as a result of a genetic disorder. We might describe the latter group as having "genetic awalkia".
But how many genetic walking disorders are caused by genes for walking?
One would presume that somewhere in the human genome there are genes for walking, in the historical sense described above. After all, the evolution of walking was a specific event in the evolution of our ancestors, which occurred only a few million years ago, and it seems reasonable to suppose that the genes involved still exist in the current human population, and still have an identifiable causal relationship with the ability to walk.
Nevertheless, I suspect that almost all genetically caused walking disabilities are not due to mutations of actual "walking" genes. Rather they are disabilities for general functions, such as muscle contraction, nerve communication or structural development.
The Family with "True" Awalkia
The best evidence for this claim is the existence of one particular Turkish family which has a genetic disorder whose major consequence is an inability to walk on two legs (or actually, to stand, walk, run or anything else on two legs), as described in this BBC news story.
If you read that story, you will see that there is disagreement among various scientists as to whether this family's genetic disorder is a true "awalkia" (i.e. a deficit in a "walking" gene), or whether it is some more general deficit.
This article from traumaroom.com gives some more details, and introduces the term atavism, which specifically refers to a genetic defect which can be considered to "undo" some evolutionary change and "revert" a member of a species back to some earlier stage in that species' evolution (although the reversion obviously only applies to one particular aspect of the organism, and does not involve a complete reconstruction of the species' ancestral state).
Although the Turkish family was originally though to be unique, other families with similar disabilities (and possibly with similar genetic mutations), have been found as a result of the publicity surrounding publication of the studies done on that family.
If the evolution of walking has resulted from the evolution of many different genes, with none of them playing a more significant role than the others, then a full genetic "awalkia" will never occur at all, because the probability of mutations of all those genes coming together within one individual is just too remote.
Nevertheless, even with the uncertainty as to whether these families have true awalkia, we can still see that they have a genetic disorder which is more specific to walking than most other genetic disorders which affect the ability to walk as a result of causing more general deficits, and which is also rarer.
Back to Amusia
We might say that what we are looking for when studying amusia, is atavistic amusia, i.e. a disability caused by changes in genes which are for music in the sense that they were the genes which evolved when music "evolved" (or perhaps more precisely, when the appreciation of music evolved).
The Invisibility of Amusia
One difference between amusia and "awalkia", is that it is much less obvious when an individual does not like music. Amusia does not affect visible appearance, and it does not prevent a person from holding down a job.
At worst it may cause social difficulties, when other people are surprised, or even disapproving, when they discover that amusic individual just doesn't like music.
Various scientific studies have discovered rates of amusia of around 5%. But if we compare it to the example of "awalkia", then the occurrence of "true" or "atavistic" amusia may be much, much lower, like 0.0005%, or even 0.0000005% (which would still be 3500 people from a population of 7,000,000,000). The "true" amusics would be totally lost in the crowd, not even aware that there were scientists out there wanting to study them.
How to Find the "True" Amusics
I suggested above that amusia might cause tone-deafness (rather than the other way round), in which case it would be extra difficult to distinguish true amusia from amusia caused by poor pitch discrimination.
However, we can be a bit optimistic, and suppose that this is not the case, and that true amusia is independent of any deficit in pitch discrimination.
So what we need to search for is people who are not interested in music, but who do have a normal ability to discriminate different pitch values.
More generally, the more components of music perception which an individual has, while still being disinterested in music, the more interesting that person would be to study, and the more relevant the identification of genetic differences in that person would be to our understanding of the evolution and purpose of music and/or music appreciation.
Another Reason Why it Might be Hard to Find "True" Amusics
If music perception is a side-effect of some specific human mental faculty, then "true" amusia would be expected to correspond to a deficit in this faculty, whatever it might be.
As a result, such individuals may suffer from some mental disability, and this disability may be enough to prevent them from reading web pages advertising for amusic individuals to take part in scientific studies about amusia.
To discover such a person, i.e. an amusic individual who is also mentally disabled, it would be necessary for whoever was caring for them to know that the disabled person was unusually disinterested in music, to know that this was a topic of scientific interest, and to know or be willing to find out that the disabled person was not deficient in either pitch or tempo discrimination.
(Given the popularity of music therapy in treating various mental disorders, music therapists might be in a good position to identify disabled invididuals who have a surprising lack of interest in any kind of music.)