There is a small literature on the genetics of whisker trimming in animals.
I don't think that the specific genes are known, but it does seem to have a
genetic component as well as a social dominance heirarcy component.  Below
is an abstract discussing this topic in lab mice (unless this is copyright
protected and BIG just leaves the reference).  Max
 
"Strozik E, Festing MF(1981) Whisker trimming in mice. _Lab Anim_ 15:309-312
 
Whisker trimming is extremely common in strain A2G mice, with an incidence
which progresses with age.  Over 75% of cages containing 2-3 mice have 1 or
more active trimmers by the time the mice are about 60 days old.  When male
A2G mice were housed with mice of other strains there was a tendency for
trimming to occur most in cages where the A2G male was socially dominant
(as judged by a tube test).  The number of animals per cage did not seem to
influence this behaviour.  In groups of male mice there was usually I with
untrimmed whiskers, presumably because he was socially dominant.  However,
with females there were always several active trimmers.  There was some
evidence that when females became pregnant they were able to resist whisker
trimming by their mates."
 
[Moderator's note: That seems to be an abstract of the article and is
probably OK for it to appear on the FML. BIG]
[Posted in FML issue 2360]