If the gene to be a Metamorphai is a simply Mendalian genetic trait, then yes, this is plausible. However, maybe the gene needs a magical component (another gene?) to be active. Complex genetic traits (think height and weight) are really common and involve environmental factors as well as genetic factors. Some complex traits (height) rely less on environmental factors than other genetic traits. Also, development is all about certain genes being activated or repressed to make various proteins depending on what hormones and signaling molecules are available in the developing embryo.
We know that a Metamorphai doesn't need to be a pureblood witch or wizard, but can a witch or wizard with a Muggle parent possibly be a Metamorphagus?
This question is actually easier to answer than the first from a genetics standpoint. I think your first assumption of recessive or a carrier is probably the easiest one to make. I would say Tonks is a recessive carrier. It's probably easiest to think of a Metamorphai gene as a single gene trait (one gene codes for one trait) that follows simple, Mendelian rules (think Punnett squares). There are plenty of human petigrees available that show the lineage of carriers of recessive traits. Sex linked (X chromosome) recessive traits tend to be fairly common, and this is how hemophelia is transmitted. The really famous hemophelia lineage is of Queen Victoria and the royal family. The most important thing about an X chromosome linked recessive trait are these things: 1)the trait is rare and 2)only male progeny can inherit it. If Tonks is double recessive for whatever gene goes with becoming a Metamorphagus, then ALL her sons will be Metamorphagus, but none of her daughters will be. You should also assume Lupin doesn't have this trait because it is rare.
I assume the gene for the abilities of a Metamorphagus are either recessive or carrier. Do you think the fact that Tonks herself is a Metamorphagus increased the chances of Teddy being born with the ability? Does anyone know of any genetic illnesses I could study that you think would be at all similar to this ability?
Yup. This sounds correct. Lupin's somatic cells are infected, but his germ cells seem to be fine (aka his sperm). It's like cutting off your finger. Your children won't inherit it, but you're always going to be minus a finger.
I agree with you that it could have something to do with Lupin, but I doubt it has anything to do with his Lycantrophy. Teddy seems to be fine in the werewolf-department, and I doubt that being a werewolf would change Lupin in his stem cells.
I wrote about X-linked recessive traits, which are linked to the sex chromosomes (specifically, the X chromosome since Tonks is a Metamorphagus). However, if the trait is a somatic recessive single gene trait (it's a recessive gene that codes for one discrete trait on some other chromosome besides the sex chromosomes), then you have to make different assumptions. First, Lupin has to be heterozygous for the trait. This DOES NOT mean that a grandparent or former family member has to have carried the trait. Second, Tonks must be homozygous recessive for the trait. Third, assume it is just one gene coding for one trait and this follows simple Mendelian genetics. Therefore, Tonks and Lupin have a 1:1 chance of producing a Metamorghagus child of EITHER sex.
Then, if the gene was recessive and only came to show if there was some trace of it in both parents, that would explain why it happened with Teddy - and why, apparently, none of Tonks' parents are Metamorphmagi, but she is. I don't have names of any specific illnesses here right now, but I'm almost 100% sure that there are illnesses that require both parents to carry a certain gene.
None of the family members in either Tonks or Lupin's families had to be a Metamorphmagus prior to Tonks or Teddy being a Metamorphmagus. First, the trait is rare, so this means that the majority of the population is probably homozygous dominant or completely normal. However, what Lupin DOES have to have is one dominant and one recessive copy of the gene (he must be heterozygous). This applies to Tonks's parents as well. They BOTH must have been heterozygous because you cannot have a homozygous recessive child with one parent that is homozygous dominant. If one parent is homozygous dominant, ALL the children will be normal because they all inherit the dominant allele from the one parent.
Trying with an example... Lupin's paternal great great great great grandfather (I'll call him F from now) was a Metamorphmagus; his wife, however, was not, and no one in the Lupin family met/married a Metamorphmagus from then. However, all the descendants of that F had the gene to potentially produce a Metamorphmagus.
Along the lines of diseases that work this way, there are plenty. Sickle cell anemia, Tay-Sachs, and cystic fibrosis are single gene traits that are all somatic homozygous recessive.