(1) As used in this act:

    (a) "Animals" means cattle, horses, sheep, or swine.

    (b) "Department" means the department of natural resources and environment.

    (c) "Director" means the director of the department of natural resources and environment.

    (2) The owner of any animal shall not allow the animal to run at large or graze upon any lands owned by or under the control of the department except under authority of a written permit issued by the director.

    (3) The owner of any swine shall not permit the swine to run at large or graze upon any lands owned by or under the control of the department. Swine running at large are a public nuisance.