麻雀の遺伝

I had an interesting discussion last night with a friend who wanted to learn how to play Mahjong.

I told them that a trait for latent Mahjong talent was in my lineage. My grandmother (father's side) has this trait but my grandfather does not, her daughter (my aunt) has it as well, but my father does not. My mother and my brother do not have it but I do. 

Based on this information, we can rule out that it is not a sex-linked trait, since there is no immediate evidence that males have the trait more than females (in fact, quite the opposite with this data!); therefore the trait is autosomal.  Now we can draw a simple pedigree to see the relationships:

A quick note for those that have forgotten, or have not studied Mendelian genetics:

• Males are represented as squares; females as circles
• An individual with the particular trait in question is filled in (black); an individual who does not have the trait is not filled in (black outline)
• P Generation is the first set of parents, or the Parental Generation
• F1 is Filial 1, the offspring that result from the P Generation
• F2 is Filial 2, the offspring that result from the F1 Generation, and so on

I am represented as the black square with the blue outline. This pedigree gives us a visual representation of the data we had to start with.

The question now is whether latent Mahjong ability (our phenotype in question) is a dominant or a recessive trait. To find this out, we fill use Punett squares.

It might be hard to determine the genotype of the P Generation at first glance, but through deductive reasoning it is a simple task.

Our P Generation consists of one parent who has the trait, and one parent who does not. Let us assume that the trait in question is dominant, and that the female is homozygous dominant for the trait. Our Punett squares would be as follows:

Recall that a capital letter represents a dominant allele, and a lower case letter represents the recessive allele. Red represents female and blue represents male for distinction purposes.

Our first Punett square depicts a homozygous recessive male, which would result in all offspring being heterozygous. This would mean all offspring have the phenotype. But from our Pedigree, we see that is not true. Therefore, our P Generation male cannot be homozygous recessive.

Our second Punett square depicts a heterozygous male, and that results in a 50% chance of being homozygous dominant, and a 50% chance of being heterozygous. But again, in both cases, all offspring should have the phenotype, and that is not true.

This rules out that our female cannot be homozygous dominant. However, it does not rule out that latent Mahjong ability is a dominant trait. We now redo our Punett squares; this time with a heterozygous female:

As you can see, this time our Punett squares comply with our Pedigree. Here is where a problem arises. Since our sample space is so small (P Generation only produce 2 offspring), it becomes a challenge to determine whether the male is heterozygous or homozygous recessive. However, that is not the question we are interested in; we are interested in seeing if the phenotype is a dominant or a recessive trait. From our analysis so far, we could conclude that it is a dominant trait, but that would be an incomplete conclusion. Why? Let's examine the problem more.

We now divert our attention to F1 Generation (Or my parents). Since my father does not show this trait, he must be homozygous recessive. Again, this doesn't tell us whether my grandfather was heterozygous or homozygous recessive, but we don't care at this point. My mother does not show this trait as well, and as a result she is homozygous recessive. Let's do our usual Punett square:

It doesn't take a genius to figure out two homozygous recessive parents will produce homozygous recessive offspring all the time. So if the phenotype were in fact a dominant trait, then through genetics, I would not possess it. This is why I said before that it would be inconclusive to conclude it was dominant; looking at one generation of offspring is not enough.

Through all this work, we conclude that the phenotype is recessive. To provide support for this, we repeat the process from before, except with a homozygous recessive grandmother:

Once again, two homozygous recessive parents always produce homozygous recessive offspring. A homozygous parent who mates with a homozygous recessive parent will always produce heterozygous offspring. Therefore, my grandfather must be a heterozygous (Mm), my grandmother homozygous recessive (mm), and their son is heterozygous (Mm). It is interesting to note that our dominant calculations never concluded which genotype the grandfather was, but our recessive calculations do. This can be a dead giveaway that the phenotype in question is recessive.

Finally, we look at the F1 Generation to justify our conclusion:

My mother cannot be homozygous dominant; otherwise I would not have inherited both recessive alleles. In the end, we can conclude that my mother is heterozygous as well, which means that there is a 25% chance of inheriting the phenotype of latent Mahjong ability.

To wrap things up, we fill in our Pedigree with the proper genotypes:

One final note. If you ever have to solve a problem like this, most likely you will be provided with more information than I had, such as the phenotype of the P generation, etc. This is just the procedure to use if that information ceases to exist. Also, it is better to assume that the phenotype in question is recessive, since if you can prove that, then you can skip all the work necessary to prove that the dominant possibility is false.

PS: Latent Mahjong ability is not a real trait, though I probably didn't have to tell you that. I learned the game at the age of 5 and it has taken me years to get to the skill level I am now. So even though it's in the blood, I still had to work for it.