(1) (a) The owners of at least fifty-one percent of the sheep, or the owners of at least fifty-one percent of the cattle, or the owners of at least fifty-one percent of both sheep and cattle acting jointly in the county, as shown by the assessment rolls of the last preceding assessment, may petition the board of county commissioners to establish a predatory animal control program as provided for in this part 2.

(b) The petition shall be filed on or before the first of November in any year at a regularly scheduled meeting of the board of county commissioners. After examination of the petition, if the board finds the petition in order and properly signed by the owners of at least fifty-one percent of the sheep or cattle, or both, in the county, the board shall establish the predatory animal control program provided for in this part 2 to commence the following calendar year on the first of February of said year; but the license fee as fixed under the provisions of section 35-40-205 shall be assessed only against the owners of sheep if only said owners of sheep petition for the establishment of said program, and only against the owners of cattle if only said owners of cattle so petition, and against both the owners of sheep and cattle if both said owners of sheep and cattle, acting jointly, so petition.

(c) Likewise, the question of an increase or decrease in the license fee, or the question of the discontinuance of the program, as provided in subsection (2) of this section, shall be determined only by the owners of sheep if they petitioned the establishment of the program, and only by the owners of cattle if they petitioned the establishment of the program, and jointly by the owners of both sheep and cattle if they, acting jointly, petitioned the establishment of the program.

(2) The license fee to defray the cost of any program established under the provisions of this part 2, as fixed by the board of county commissioners under the provisions of section 35-40-205, shall remain in full force and effect from year to year without change, unless there is filed with the board a petition signed by the owners of at least fifty-one percent of the sheep, or the owners of at least fifty-one percent of the cattle, or the owners of at least fifty-one percent of both the sheep and cattle acting jointly, in the county, requesting repeal of said license fee in total and discontinuance of the program, or for an increase in said license fee, subject to the limits provided in section 35-40-205, or for a decrease in said license fee, in either of which events, the board of county commissioners shall fix a new license fee to continue from year to year and provide for the continuation of the program within the limits of the aggregate amount of the license fees as collected from year to year.