The gene
for white spotting is recessive, spotted mice are s/s.
PA245917: Piebalds in Recessive Yellow, Black, Chocolate
The amount of white is influenced by additional modifying factors, the k-factors. Both, the s-allele and the k-factors tend to show white tail tips or head spots, when they occur isolated from each other in self mice.
The allele “s”, when homozygous, usually produces distinct white spots, i.e., unpigmented and pigmented areas are clearly defined by sharp borders, without any intermingling of white and pigmented hairs. In general, the ventrum displays more white than the dorsum and according to Grüneberg "'centers of depigmentation' are the feet, the tail, particularly its distal part, an area round the umbilicus on the belly, a blaze between the eyes, and the tip of the nose. As a consequence of modifying factors, known as the "k" complex, the extent of all these centers is highly variable, and as they increase in size, they merge in numerous ways. Thus s/s may produce entirely or almost entirely unpigmented phenotypes, or it may produce only a few white spots on the belly, feet, and forehead ( Dunn, 1920).
P8024798
The "k" Complex As already noted stocks of s/s mice may differ widely with regard to the amount of white areas in their coats. Thus by selection and inbreeding it is possible to establish reasonably stable lines of piebald animals which are either essentially all white with very few pigmented areas (hereafter referred to as the "all-white" line), or, have very little spotting, amounting to 10% or less of the coat ( Dunn and Charles, 1937). Lines selected for intermediate amounts of spotting are much more variable.
The amount of white areas in the fur is depending on modifying factors. It seems evident that in the absence of " k" genes (or in the presence of their normal allelomorphs), s is almost completely recessive to + and in the absence of s the " k" genes too are almost completely recessive. On the other hand, these " k" genes act as semidominants in the presence of s/s. In other words "the dominance of s is influenced by the presence or absence of the ' k' genes, the dominance of the ' k' genes is influenced by the presence or absence of s" ( Grüneberg, 1952). The "k" complex has been analyzed further by Dunn ( 1942) and it seems to consist of a large number of genes which, individually, have very small effects. At least one of these genes is dominant since when spotted mice from a " k" stock were crossed with DBAs, a strain devoid of spotting and putatively devoid of " k" genes, all F1 animals were spotted either on the tail, belly, or both. The exact number of dominant " k" genes is not known, but the frequency of spotting in F2 and backcross populations of this outcross indicated that there was more than one and probably two. The citation for most parts of the above text and information is http://www.informatics.jax.org/wksilvers/index.shtml
PA245931
Conclusions: 1.) Mostly white piebald mice have a genetic background of s/s AND an accumulation of k-factors. 2.) Mostly dark mice with small white spottings on the front head, feet, belly and tail have a genetic background of s/s and no (or only a small number) of k-factors. Sometimes there are mostly dark mice, which look similar, but even have smaller white areas on the fronthead or tail only, which are s/+ or even +/+, but have a high number of k-factors. This is an important point to know! There are dark mice, which have very different genetic make-ups. Most times you will have mice from one make-up only, and therefore selection from inbred mice will not improve the pattern of spotting. 3. ) If you want to breed mice with 50% white and 50% dark areas, you start with animals which have this pattern. If you want to improve an all-white line or an all-dark-line, because other traits of your line are beautiful and you want to keep it, but want to improve the spotting, you should cross animals of both genetic make-up (all-white and all-dark) with each other. If you have a line with small areas of white spotting and want to increase the amount, there is need to outcross your mice to an all-white spotted partner. Again: selection will not lead to better spottings, since you simply lack the k-factors or just in opposite lack the s/s at all, see 2. 4.) If you do not want to breed spotted mice and have white tails or white spots on the forehead, you have to do a strong selection to erase all k-factors in your lines, which sometimes are difficult to notice and therefore difficult to erase, because there are a some white hairs only or they hide under light colours (eg albino).