The inheritance of scalation
The inheritance of scalation is controlled by two genes, associated with their mutants or alleles. The gene S we shall use to designate SCALED FISH. Its allele, s, will be used to designate the mutant gene which stops the formation of scales. Every normal fish must have an S gene, but they can also have either another normal S gene or an abnormal s gene. Fish which have two of the same genes for a single characteristic are called HOMOZYGOUS. Fish with two different genes are called HETEROZYGOUS. Homozygous fish usually always look either normal or abnormal depending upon which genes they carry. Heterozygous fish look normal but may have an abnormal gene.
The second factor controlling scales is the factor N which stands for NO SCALES. We use the letter n to designate the allele which is a mutant gene meaning scaled. Thus an nn fish is normal while an NN or Nn fish would have abnormal scales. NN fish never live. The SS fish is normally scaled as is the Ss, but the ss fish would be abnormal.
Thus we talk about GENOTYPE and PHENOTYPE. The genotype of a fish is what genes it has; the phenotype is what it looks like. We must always be concerned with both of these genetic characteristics in order to selectively breed Koi with special scalation.
When a male and female fish breed, a single sperm from the male unites with a single egg to produce a single offspring. As with all things of nature, there are rare exceptions. These rare exceptions produce Siamese twins, fraternal twins and/or identical twins in humans. There are equivalent random fertilizations in fishes, too.
The single sperm and the single egg carry genes for many characteristics. When the sperm and combine, the male's gene for S or s combines with the female's gene for S or s; the same is true for the other gene controlling scaleless condition, the N or n gene. Using a handy little table called a Punnett square, we can show the POSSIBILITIES of genetic combinations based upon PRESUMED genetic makeups of the parents based upon what they look like. It is only normal looking fish which are difficult to determine genetically but by inbreeding two normal fish and then inbreeding their offspring, a skilled geneticist can usually determine the genetic makeup, the genotype, of the original breeders.
Our situation here is different. We can see the phenotype, thus we have some idea of the genotype. The probable genetic formula for the different Doitsu are as follows:
NORMALLY SCALED KOI: they are either homozygotic SSnn or heterozygotic, Ssnn. No other genetic combination can produce a fully scaled carp. SSnn individuals when bred together can never produce anything but fully scaled individuals unless there is a genetic accident (mutation). You shouldn't count on anything like this happening. When using the Punnett square technique, we can visualize what the possibilities are. The male sperm can release either an S or an s together with a normal n gene. Thus breeding two individuals together, we have the possibility or breeding either two SSnn's, two Ssnn's or one of each, an Ssnn and a SSnn.