Basic Genetics II: Multiple Loci
Usually more than one gene locus is involved in coat color. We'll
take one of the simplest, in which the two loci each have two alleles,
with a simple dominant-recessive relationship. The model we will use is
the Labrador Retriever. One locus we have already examined: the brown
locus. We will now add a second locus, on a different chromosome, called
E. An EE or Ee dog will show whatever eumelanin pigment is possible. An
ee dog apparently can manufacture only phaeomelanin in the hair, though
the skin and eye pigment still includes melanin (of whatever color is
allowed by the B series).
A black Lab may be BBEE, BBEe, BbEE or BbEe - any combination that
includes at least one B and one E gene.
A chocolate (brown) Lab may be bbEE or bbEe.
A yellow Lab with a black nose may be BBee or Bbee
A yellow Lab with a liver nose is bbee - but since ee dogs tend in
many cases to lose nose pigment in winter, this may not be easy to
distinguish from BBee or Bbee.
Suppose we mate two BbEe dogs, both blacks carrying brown and yellow:
| |
BE |
Be |
bE |
be |
| BE |
BBEE (pure for black) |
BBEe (black carrying yellow) |
BbEE (black carrying brown) |
BbEe (black carrying brown and yellow) |
| Be |
BBEe (black carrying yellow) |
BBee (pure for yellow, black nose) |
BbEe (black carrying brown and yellow) |
Bbee (yellow carrying brown) |
| bE |
BbEE (black carrying brown) |
BbEe (black carrying brown and yellow) |
bbEE (pure for brown) |
bbEe (brown carrying yellow)
|
| be |
BbEe (black carrying brown and yellow) |
Bbee (yellow carrying brown) |
bbEe (brown carrying yellow)
|
bbee (brown-nosed
yellow) |
Each puppy has one chance in sixteen of having the combination shown
in any section of the table above. In this mating between two black dogs
both carrying brown and yellow, there is a 9/16 probability that a
particular pup will be black, a 3/16 probability that the pup will be
brown, a 3/16 probability that the pup will be a black-nosed yellow, and
a 1/16 probability of a brown-nosed yellow. Since nose color does not
come into registration, the registered colors would be 9 black:3 brown:4
yellow.
What happens if more than two loci are involved? The basic principle
is the same - put all of the possible combinations in a sperm cell along
the top and all of the possible combinations in an egg cell along the
left side. The problem is that the number of possible combinations
doubles for each additional locus. For a single locus, we had a 2 x 2
square with 4 cells. For two loci, we had a 4 x 4 square with 16 cells.
With three loci, we have an 8 x 8 square with 64 cells. Besides, we've
pretty well exhausted the acceptable colors for Labs.
Shetland Sheepdogs might be a good model for our three-locus model.
For the moment we'll omit the recessive black, and consider that Sheltie
color is determined by three loci.
At the A (agouti) locus, ay is sable and at is
tan-point (black and tan = referred to as tricolor if a white spotting
gene is present.) An ayat dog is sable, but
generally somewhat darker than an ayay dog. The
difference is generally of the same order as the difference within ayay
or within ayat, so it is not possible to be
absolutely sure whether at is present by looking at the dog.
At the M locus, Shelties have both M and m, as discussed earlier. Mm
produces blue merle in atat dogs and sable merle
on ayat and ayay.
At the S (spotting) locus most correctly marked Shelties have two
copies of si, Irish spotting. A sisi
dog generally ranges from white on the chest and feet to high white
stockings, white tail tip, and a full shawl collar. The probability of
the full collar, as well as white stifles, seems to be somewhat enhanced
if the dog is sisw, so sw, color headed
white, tends to be maintained in the breed as well. (I am keeping it
simple by ignoring sp, piebald, which may also occur in
Shelties.) swsw dogs are predominantly white with
color on the head and perhaps a few body spots. While healthy, they
cannot be shown.
Suppose we mate two white-factored, tri-factored sable merles (not a
likely mating, but this is an illustration!) The genetic formula for
each parent is ayatMmsisw.
There are eight possible gametes for each sex:
| |
ayMsi |
ayMsw |
aymsi |
aymsw |
atMsi |
atMsw |
atmsi |
atmsw |
| ayMsi |
DMS |
DMS |
SM |
SM |
DMS |
DMS |
StM |
StM |
| ayMsw |
DMS |
DMS* |
SM |
WSM |
DMS |
DMS* |
StM |
WStM |
| aymsi |
SM |
SM |
S |
S |
StM |
StM |
St |
St |
| aymsw |
SM |
WSM |
S |
WS |
StM |
WStM |
St |
WSt |
| atMsi |
DMS |
DMS |
StM |
StM |
DM |
DM |
BM |
BM |
| atMsw |
DMS |
DMS* |
StM |
WStM |
DM |
DM* |
BM |
WBM |
| atmsi |
StM |
StM |
St |
St |
BM |
BM |
T |
T |
| atmsw |
StM |
WStM |
St |
WSt |
BM |
WBM |
T |
WT |
There is no way I could fill in this chart with the detail I used in
the 2-loci charts and still have it fit readably into a browser window,
so I have used a shorthand to indicate the apparent color:
- S = pure for sable with Irish markings (3)
- St = tri-factored sable with Irish markings (6)
- T = tricolor with Irish markings (3)
- SM = pure for sable merle with Irish markings (6)
- StM = tri-factored sable merle with Irish markings (12)
- BM = blue merle with Irish markings (6)
- WS = white with pure for sable head (1)
- WSt = white with trifactored sable head (2)
- WT = white with tricolor head (1)
- WSM = white with pure for sable merle head (2)
- WStM = white with tri-factored sable merle head (4)
- WBM = white with blue merle head. (2)
- DMS = homozygous merle, dilute sable markings (12)
- DM = normal homozygous merle (4)
I have not distinguished white-factored from Irish dogs, and I have
ignored the possibility that the MMswsw pups
(starred in chart) might not be viable. In practice such a breeding
would probably never be made, as Sheltie breeders tend to avoid breeding
merle to merle and white factor to white factor, but it does illustrate
the variety that can be obtained with two alleles at each of three loci.
In this case, all three loci are visibly affecting the color. The
only exception is the interaction between color-headed white and double
merle, and this is frankly an unknown. There are times, however, when a
particular gene combination at one locus can block expression of a gene
combination at another locus. I will follow Searle on nomenclature and
distinguish between a dominant-recessive relationship between alleles at
a particular locus and an epistatic-hypostatic relationship between two
loci.
The first example is very obvious, but only because the gene action
is clear-cut. Consider Cocker Spaniels. They have two alleles at the S
locus (S, fully colored, and sp, piebald.) An SS dog is solid
color, an Ssp dog may have minor white marking (and is often
unshowable) and an spsp dog is a parti-color. The
second gene is ticking. Ticking works by producing flecks of color in
white areas. TT produces ticks of color in any white areas on the dog,
tt has clear white areas, and Tt probably produces less ticking than TT,
with considerable variation among breeds. spsp and
probably Ssp dogs will show ticking if T is present, since
they have white areas that are "available" for ticking, though if the
base color is red, tan or cream the ticking may not be obvious. But if
the dog is SS, there are no white spots for the ticking to show up on.
SS is thus epistatic to ticking.
The final example involves the genes for dominant black, which may or
may not (my feeling is probably not, as there are records of dominant
black to tricolor producing both sables and tris) be the top dominant in
the A series where it is generally placed. I will assume it is at a
separate locus K, with K being dominant black, epistatic to anything at
the A series, while kk allows the A series to show through. We also have
the E series, in which E allows the A series to show through while ee
allows only red-yellow pigment in the hair. Functionally we can consider
that the A locus determines where eumelanin and phaeomelanin are
produced, the K locus allows only eumelanin to be produced if E is at
the E locus, but ee at the E locus overrides that to allow only
phaeomelanin production. Sounds like a mess? You bet it does! K at the K
locus is epistatic to the A locus, but ee (pure recessive at the E
locus) is epistatic to both the A and the K locus. But it agrees with
what is observed.
Let's look at a breed cross between two "red" dogs. We'll take an
accidental breeding I know of between a Belgian Tervuren (ayayEEkk)
and a Golden Retriever (??eeKK). Note that ee is epistatic to the A
series, so if dominant black is not at the A locus, we do not know what
the normal A allele is in the Golden. The gametes are ayEk
for the Terv and ?eK for the Golden. Every puppy inherits ay?EeKk
and is black, as was in fact observed (to the initial astonishment of
the owner.) If we mated two of these pups, we would get a 16/64
probability of ee which would be red regardless of what was at other
loci. Of the other 48/64 (Ee and EE dogs), 75% would be Kk or KK, and
hence black. so there is a 36/64 probability that a particular puppy
will be black. The remaining 12/64 will show what is present at the A
locus. Of the 12, we expect that 9 will have the ay gene in
at least one dose, and with dominant black moved to the K locus ay
is dominant over all other A alleles. So there is only a 3/64 chance
that a given puppy will actually show what A allele is normal in a
Golden - if in fact all Goldens have the same allele at A!
Note that in this particular case we can get identical results in the
first generation by postulating a top dominant As dominant
black at the A locus, with As- dogs having solid eumelanin
pigmentation (unless overridden by ee.) In this case the parent gametes
would be Ase and ayE, giving AsayEe
black pups. In the next generation we would again get 4/16 ee red, 9/16
As-E- black, and 3/16 ayayE- sables. If
we could be absolutely sure that the Terv used was not ayat,
the appearance of a tricolor would be good evidence for the first
hypothesis.
We still need to discuss penetrance, variable expression, and
threshold traits, as well as
linkage and
crossing over (and their influence on the accuracy of DNA testing),
test breeding,
and testing
whether a suspected allele is in fact at a particular locus. Some
further comments about merle are also in the works.
