Genetic structure of a trait with six discrete phenotypes

Question

In my world magic is conferred genetically. Their are five "types" of magic, which never mix. You either have one type, or you have another (or none at all, the sixth option), you never have a mix of two.

In real life we see this behavior frequently with two discrete options. By that I mean two distinct options, either one or the other, not a mix or a gradation. For example, we have the green or yellow pods of the famous Mendalian peas. They are either green or yellow, and don't mix between the two. However, for most traits with a lot of options, we have a gradation, like skin color or height, and not discrete phenotypes.

What would the genetics look like for six phenotypes rather than two?

Assume that inheritance works exactly like it does for humans on Earth. No magic is involved in reproduction or inheritance. For this reason, this question is science-based.

Answer 1

All of the answers so far either do some hand-waving with DNA bases or amino acid codes, or try to construct six discrete phenotypes from a mixture of different alleles. I'd like to offer / describe a biologically possible solution, that is at the same time very 'basic': You can have five different variants of a genes (or six with one being magically 'inactive'), one for each type of magic, but still have only one active in each person.

The biological trick for this is called allelic exclusion. In humans the body uses it to suppress one of the two X-chromosomes in females (they only need one) and - more to the point - to prevent certain specific genes from being expressed from two alleles. (This is important in the immune system, where any given B-cell should only produce exactly one version of the B-cell receptor/antibody).

In your case you would have six different possible alleles. While each person will have two different ones in their genome, only one will be active in each person. This also means that children can inherit a magic type (including 'no magic') that their parents are not actively showing, as long as they carry the genes for it.

Edit, a few more things:

• This system works both with the 6 gene variant (-> no magic has a gene) and with the 5 variant (-> no magic is simply the absence of any gene). The latter version will mean that magic is always dominant over 'no-magic', because persons with only one gene, will obviously express it.

• The silencing of gene normally has to happen in the 1-cell embryo stage, otherwise you can get people with one half of their cells 'fire' magic and the other half 'water' (spotted colouring of cats works that way). Of course, if you wanted to, some freak of nature like this could still exist with two different half powers

• If anyone ever asks for an evolutionary reason to have allelic exclusion on the magic gene: maybe having two competing kinds of magic in a single cell just mean bad things for that organism.

Answer 2

Blood type, there are six alleles for blood type with four phenotypes. Just use a similar plan and make them all co-dominant instead the normal setup (O does code for a protein it just doesn't work). So now you have six genotypes and 6 phenotypes. basically take this chart and ignore the blood type column. so A+O would be its own thing and not the same as A+A.

this also gives you a frequency you can map. So some types will be more common than others.

If those genes are not the end result but instead code for the activation protein for different pathways, then cofactors don't even have to be related to each other.

AA = type 1

AB = BA = type 2

BB = type 3

AO = OA = type 4

BO = OB = type 5

OO = type 6

Of course you could have the super rare chimera individual who expresses all three and thus is something else, because they are not actually one person biologically. Biological chimera are extremely rare and are a product of zygote fusion. These may occur no matter how you decide to establish the genetics. You can also just ignore these individuals and say they self destruct in the womb.

Answer 3

You are in luck! Six variations fits quite nicely into the genetic code; look here at the DNA to Protein Table.

There are four DNA 'letters', ATCG. It takes 3 letters to specify a code for one of our amino acids; or one of the control codes ('Start', 'Stop'). That is 22 results for 64 possible combinations ($4^3$) so 42 of the 64 codes must duplicate some result.

The 'winner' for this is Leucine, which has SIX distinct genetic codes: TTA, TTG, CTA, CTT, CTC, CTG.

Proteins are a link of such amino acids that fold into some specific sequence. IRL of course, Leucine is Leucine is Leucine; the ribosome translates all six of these things into the same amino acid.

However, for fictional magic purposes, the construction of your magical organ must depend upon DNA, and you make which type of magic a person can do depend upon seeing the correct variant of Leucine in one or more places within this organ.

If you want the magic to be fairly common; this could be in one place. If you want it to be more rare, demand it in multiple places: Say the chances of one variant appearing is 1/6, then getting the same variant in two places is 1/36, getting the same variant in 3 places is 1/216, etc. People with a mixture have no magic.

This is likely how you would ensure heritable magic (or none at all), the chances of 2 nucleotides mutating exactly the same way in an offspring are very remote. However, you could have SNP (single nucleotide polymorphism) mutations (just one nucleotide changed) with a very low % chance that make the offspring of two same-magic parents have mixed leucine types and thus no magic at all.

Answer 4

There are plenty of ways of doing that, you should presumably choose one that fits your story the best.

1) A person can have active mage gene from A-F or 0 (not working). A person is a mage when has two the same copies like AA or CC. Any other combination is simply not functional. Means that a mage should marry someone of his genetic group, which may create interesting inbreeding.

2) A magic is passed in genes that don't follow Mendelian rules - either in Y chromosome or mitochondria. Wizardy is being spread only in male/female line.

3) You may just pick some combination of dominant/recessive genes, where someone technically has some gene, but there is no continuum.

Answer 5

One locus with three alleles are enough to make six phenontypes.

Let's suppose that magic ability is linked to a locus M for which there are three alleles, M₀ (null magic, "muggle"), M₁ (standard magic) and M₂ (super magic); furthermore, M₀ is partially dominant over M₁ and M₂, and M₁ is partially dominant over M₂. Now you have the following genotypes and phenotypes:

1. M₀M₀ - completely non-magical, a pure muggle.

2. M₀M₁ - weak magical of the first kind; M₀ is partially dominant over M₁, with the effect that the carrier has a little magic, but less than an M₁M₁.

3. M₀M₂ - weak magical of the second kind; M₀ is partially dominant over M₂, with the effect that the carrier has a little magic, but less than an M₂M₂.

4. M₁M₁ - standard magical ability.

5. M₁M₂ - increased magical ability; M₁ is partially dominant over M₂, so that the carrier has more magical ability than M₁M₁ but less than M₂M₂.

6. M₂M₂ - super-magical; the carrier has highest magical ability.

Answer 6

DNA is fundamentally a discrete structure (a finite sequence built from a finite alphabet), so at a genetic level, all traits are discrete. However, there may be so many genes involved that there are many, many possible phenotypes, making the trait appear continuous. Also environmental factors like nutrition and sun exposure may play a role in traits such as height and skin color. But at the enzymatic level, all traits are discrete, and since inherent magic probably falls outside the realm of environmental effects, I'm going to assume that having a particularly magic type has a direct correspondence to enzyme activity. The tricky part is coming up with a set of enzymes and enzyme variants with exactly 6 phenotypes.

The biggest obstacle to overcome is avoiding the effect of codominance. Perhaps the most obvious solution is to have a single gene with 6 alleles--but remember that humans are diploid and thus, everyone has two copies of every gene. Since every allele corresponds directly a magic type, and every person has two alleles, we wind up with 21 total phenotypes.

We can get around this in a couple of ways. We could put the gene on the X chromosome. Males have only one copy and females only express one copy. But this has the effect that males always inherit their magic type from their mother, while females could wind up with either their mother's or their father's type with about equal likelihood.

Alternatively, we could reduce the number of alleles to 3, which would result in 6 phenotypes. Each magic type is now the result of the combination of two alleles. For example:

1. AA
2. BB
3. CC
4. AB
5. AC
6. BC

This system has a few problems of its own however. Inheritance becomes a bit messy; based on the above system, a type 1 and a type 4 could have either type 1 or type 4 children, but a type 1 and a type 3 would always have type 5 children, and a type 5 and a type 6 could have either type 3, type 4, type 5, or type 6 children.

Also, it's difficult to justify why one particular combination would be non-magical but all other combinations were of equal strength. We can't just make allele C nonfunctional, because then there'd be no difference between types 1 and 5 and between types 2 and 6. You could get around this by making allele C be unable to function on its own, making type 3 non-magical, but to change the effect of allele A or B if its also present. This is perfectly biologically valid, but it still ties types 1 and 5 and types 2 and together somewhat. So this is now getting into the realm of exactly what these types of magic are, how they relate to each other and what common features they might have.

An alternative explanation could be that two of the alleles, say A and B, have "opposite" effects that cancel each other out. Maybe the A and B enzymes recognize each other as foreign and try to consume each other, but don't mind themselves (obviously) and are okay with enzyme C. Or maybe the molecules they produce destructively react together (imagine if A gives you magic through the power of baking soda, C through the power of water, and B through the power of vinegar. Stupid example but hopefully it makes my point). This would be very similar to how blood type works, as discussed in John's answer.

It doesn't have to be one gene, however. There could be two genes essential for magic, or three, or six. There are many increasingly complex ways this could work. I'll write more if I think of any that are particularly interesting.

Answer 7

Pseudo-science and real science to follow

First, a caveat - I don't know much about genetics, but I do know that it is complicated (read artistic licensing can be applied more or less liberally) and I'm really good with the Punnet Squares. Depending on how much you want to be tied to real principles of genetics, there are LOTS of ways to do this. The variables of note are (1) the number of "genes" used, (2) the number of "traits" used, and (3) how the geneotypes manifest phenotypes (including traditional dominant vs. recessive and more hypothetical (read likely not realistic) dominance schemes), and one assumption: possessing magic is beneficial and culturally desirable (this is import for consequences), and a few very, very needful simplifications. I shall refer to a person who has inherited magic as a Mage, a person who has not inherited magic as a Non, and the five magical branches as A, B, C, D, and E respectively.

1 gene, 5 traits, magic is recessive

$$ \begin{array}{c|c c} & \text{A} & \text{B} & \text{C} & \text{D} & \text{E} \\ \hline \text{A} & \textbf{AA} & \text{AB} & \text{AC} & \text{AD} & \text{AE} \\ \text{B} & \text{BA} & \textbf{BB} & \text{BC} & \text{BD} & \text{BE} \\ \text{C} & \text{CA} & \text{CB} & \textbf{CC} & \text{CD} & \text{CE} \\ \text{D} & \text{DA} & \text{DB} & \text{DC} & \textbf{DD} & \text{DE} \\ \text{E} & \text{EA} & \text{EB} & \text{EC} & \text{ED} & \textbf{EE} \end{array} $$ Inheritence
Mage/Mage
$$ \begin{array}{l|l l} 1 & \text{A} & \text{A} \\ \hline \text{A} & \text{AA} & \text{AA} \\ \text{A} & \text{AA} & \text{AA} \\ \end{array} \space{}\space{}\space{}\space{} \begin{array} {c| c c} 2 & \text{B} & \text{B} \\ \hline \text{A} & \text{AB} & \text{AB} \\ \text{A} & \text{AB} & \text{AB} \end{array} $$ [1] A pair of Mages of the same branch will always produce a Mage of that branch
[2] A pair of Mages of different branches will always produce a Non
Mage/Non
$$ \begin{array}{c|c c} 3 & \text{B} & \text{C} \\ \hline \text{A} & \text{AB} & \text{AC} \\ \text{A} & \text{AB} & \text{AC} \\ \end{array} \space{}\space{}\space{}\space{} \begin{array} {c| c c} 4 & \text{A} & \text{C} \\ \hline \text{A} & \text{AA} & \text{AC} \\ \text{A} & \text{AA} & \text{AC} \end{array} $$ [3] A Mage and a Non with no common traits will always produce a Non
[4] A Mage and a Non with a common trait will produce a Mage of that branch (0.5) or a Non (0.5)
Non/Non
$$ \begin{array}{c|c c} 5 & \text{C} & \text{D} \\ \hline \text{A} & \text{AC} & \text{AC} \\ \text{B} & \text{BC} & \text{BD} \\ \end{array} \space{}\space{}\space{}\space{} \begin{array} {c| c c} 6 & \text{A} & \text{C} \\ \hline \text{A} & \text{AA} & \text{AC} \\ \text{B} & \text{BA} & \text{BC} \end{array} \space{}\space{}\space{}\space{} \begin{array} {c| c c} 7 & \text{A} & \text{B} \\ \hline \text{A} & \text{AA} & \text{AB} \\ \text{B} & \text{BA} & \text{BB} \end{array} $$ [5] Two Nons with no common traits will always produce a Non
[6] Two Nons with one common trait will produce a Mage of that branch (0.25) or a Non (0.75)
[7] Two Nons with both traits common will produce a Mage of one branch (0.25) or the other (0.25) or a Non (0.5)

Consequences
This would likely produce a natural caste system where 'noble' houses intermarry with noble houses of the same magical branch and carefully control the bloodlines. The common folk will periodically produce a mage by accident, quite scandalous! Some of these would periodically get married into the noble lines because the heart wants what the heart wants or to deliberately help with genetic diversity.

These nobles would likely blend (a mixed region/country), resulting in few common born mages (because of genetic diversity), or separate (mono-branch region/country), leading to a higher frequency of common born mages (due to lack of diversity of nobles - sewn oats and all that). Mono-branch regions would have an incentive take prisoners from other mono-branch regions to diversify (and oppress) the common stock. Mixed regions seems the most likely if different branches can accomplish different things, but if similar effects can be achieved with each branch then both would be likely to occur.

1 gene, 6 traits, magic is dominant

As above, but a 6th trait N is introduced. All co-dominant pairings can be exclusively Nons or exclusively Mages if following some dominance rules (AB always manifests as A, etc. -- several rock, paper, scissors, lizard, Spock style diagrams could map out all pairings) or some combination (AB always manifests as A, AC is always a Non, etc.). All A-E/N pairings are a Mage of the appropriate branch. All NN pairings are Nons.

Consequences
If co-dominant pairings are Nons, Mages are still rare, similar as magic recessive above. Pure Mages (AA) could be more powerful (due to purity) or less powerful (due to latent effects of N, perhaps a larger pool of power from which to draw -- hence NN are Nons that could theoretically be considered Mages with large pools to draw from but no way to expend it). If Pure Mages are more powerful then there will be little dilution in the bloodlines. If *N Mages are more powerful, bloodlines will be mixed and some children will be Nons and thus possibly shunned, cast off, executed, exiled, used for purely political marriages, etc.

If co-dominant pairings (AB) are Mages, then Mages will likely be VERY common. If Pure Mages (AA or AB) are more powerful than Non-Mage mixes (*N) then Nons will be second class citizens in many places. If Pure Mages are weaker than Non-Mage mixes then Nons will valuable property/breeding stock in some places and key figures of important houses in others.

2+ genes, 3+ traits

Mages have one or more genes that determine if they are a Mage and one gene with 3 or more traits that determine what Branch of magic they have. If magic is recessive, the more genes required to be a Mage the fewer Mages there will be. If magic is dominant, the more genes that create Mages the more Mages there will be. With 3 traits, you would have 6 distinct pairs (AA, AB, AC, BB, BC, CC) or 8 permutations (treating AB and BA as different, etc.), which would be enough to map out to 5. The more combinations belong to a branch the more populous that branch will be, so this set up would be ideal if you wanted a magical ruling class (rare branches) and a magical laboring/middle class (common branches). You need 5 (or a multiple of 5, but 5 would be the most simple) to have all branches be roughly equally represented (see rock/paper/scissors/lizard/Spock comment above for how to chart that).

A pairing of mixed people from mixed branches $$ \begin{array}{c|c c} 1 & \text{MA} & \text{MB} & \text{NA} & \text{NB} \\ \hline \text{MA} & \text{MMAA} & \text{MMAB} & \text{MNAA} & \text{MNAB} \\ \text{MC} & \text{MMCA} & \text{MMCB} & \text{MNCA} & \text{MNCB} \\ \text{NA} & \text{NMAA} & \text{NMAB} & \text{NNAA} & \text{NNAB} \\ \text{NC} & \text{NMCA} & \text{NMCB} & \text{NNCA} & \text{NNCB} \\ \end{array} $$ M is the gene for Mages and N is the gene for Nons. If magic is dominant, MN could be a Mage or a Non depending on how you treat mixed branches (if A or B is dominant over the other, then it is still a Mage, if traits are co-recessive then it is a Non). If magic is recessive, MN is a Non regardless of branch traits. For multiple magic genes, it is similar, but the portion that is magic/non-magic shifts appropriately.

Answer 8

There's some good answers so far, but they have some issues.

The blood type-style inheritance is on the right track, but you'd end up with a ton of children who didn't have the same magic type as either parent. For example, if a AA parent pairs with a BB parent, all the children will be AB, which would be a completely different phenotype than either parent. The allelic exclusion answer sort of works, but humans don't have the same allele inactive in all of their cells. Can't add another link, but google "Why women are stripey" for a bit more info.

I'd like to suggest a sort of rock-paper-scissors inheritance instead, with 6 possible alleles at one locus. Here's a quick diagram to show what I mean:

• A dominant to B and C
• B beats C, D, E
• C beats D, E
• D beats E, F, A
• E beats F, A
• F beats A, B, C

A punnet square color-coded by the resulting phenotype (I'm using MS Paint right now) looks like this:

Assuming that the 6 possible alleles are evenly distributed throughout the population, you'd end up with each phenotype represented by between about 14% and 20% of the population, which is a pretty even split. You can adjust the allele frequency or the rock-paper-scissors ring if you want a different distribution of phenotypes.

Compared to the blood type example, you should end up with more children matching the phenotype of at least one parent. I believe that every pairing of parent genotypes would have, at worst, 50% of possible children matching at least one parent's phenotype.

Answer 9

Since you're looking for "clean breaks," you'd have to get "creative" with your application of genetics...

As I commented, doing 4 magics and a single mundane is fairly easy, since we have 4 bases. Assuming a single base in the magic gene is the determinant for affinity, this would make your phenotypes AA, CC, TT, GG, plus the six mixed bases (AC, AT, AG, CT, CG, TG). The "pure" phenotypes would be magical, and the mixed pairs would be mundane. This implies that half the population has no magical ability, and the remaining half is evenly divided among the four types.

If two people share the exact magic affinity, then they will have a child with that exact magic affinity. If they have differing magic affinities, then their child will ABSOLUTELY be mundane. BUT, if there is a magic and non-magic pair, the chance still exists for the child to share the affinity of the magic parent. Assuming you don't know the genetic makeup of the mundane parent, then the chance of them having no matching bases (and therefore will always have a mixed base child) is (3/4*2/4)=3/8ths, meaning there is a 5/8ths chance of sharing a base and a resulting 5/16th's chance of the child being magical.

For a mundane/mundane couple, each has 6 possible phenotypes, making 36 possibilities. Each has a single "opposite" phenotype with no chance of magical offspring (1/6 of magic not being possible). Matching mundane phenotypes (1/6 chance) would give a 1/2 chance of magical offspring of either of the base genotypes. The remaining 24 matches have single matches, which lead to a 1/4 chance of magical offspring.

Once you've got genetic sequencing, you can ensure that "matching bases" always exist among couples which raises your chance of a magical child to 1/2 for a magic/mundane couple, 1/2 for a mundane/mundane couple where both bases match, and 1/4 for a couple with only 1 matching base. Hypothetically, you could do this without sequencing if you prevented mundanes from marrying one another - that means a mundane from a given union will always have at least the base of the magical parent, and mixed magic union will have a mundane human with a known pair of phenotypes.

This gets us to 5 traits, though, not 6.

To quote Wikipedia:

The interaction between genotype and phenotype has often been conceptualized by the following relationship: genotype (G) + environment (E) → phenotype (P)

A more nuanced version of the relationship is: genotype (G) + environment (E) + genotype & environment interactions (GE) → phenotype (P)

Basically, add in an environmental factor controlling gene expression that is the determiner between two phenotypes. How exactly this works could be tweaked to modify how common you want magic to appear. (Note: capital letters (ACTG) are the actual alleles, while lower case (actg) represent environmental factors contributing to allele expression.)

If you want rare "pure" bloodlines, then the environmental factor MUST MATCH the inherited phenotypes in order for the offspring to be magical. So two AA's would NOT have magical offspring if the total phenotype is AA+(c,t,g factors). This would lead to cultures with highly regimented and ritualized environments created to preserve magic bloodlines.

Conversely, you can hold that environmental factors only operate as determinants when the phenotypes are different, which keeps magic bloodlines "secure" and would not necessarily result in the above cultural effects.

In either case, the final magic phenotype could exist among a "non-magic" mixed phenotype where the environmental determinant is unlike EITHER of the two bases. So an AC+(t or g) would be magical, while an AC+(a or c) would not. The environmental contribution basically "moderates" the two incompletely dominant magic alleles (normally mundane) and makes them "co-dominant," making this final phenotype "balanced" magic. This discrete magic phenotype could ONLY be brought about by marrying outside of your bloodline, and would presumably be a rare event.

Answer 10

To add a different solution, use a single gene expressed in 6 alleles: A-E, each corresponding with a magic type, and P providing power needed for the magic.

You need both a specific magic gene and power for your magic to work. So AP (and PA) expresses as magic type A. Combinations like AA, AB, and PP are non-magical.

This means that a magical couple has a 50% chance of getting a magical child and it doesn't matter if the parents express the same or a different kind of magic.

Moreover, two non-magical parents AA (or AB) and PP have a 100% chance of having a magical child (but e.g. combining AB and AC leads to a 0% chance). This may fuel some interesting story.

In case there's too much magic, add a non-functional allele N.