(2) If the county is not made a weed control district or if the county weed control district does not include all such weeds or plants desired as included as noxious, interested parties may present a petition for a special weed control district. The petition shall describe the area to be included in the special weed control district and name the noxious weeds to be destroyed or prevented from blooming and producing seed within the district, and must be signed by more than half of the landowners in the area described in the petition who also own more than half of the acreage in the area. Upon presentation of such a petition, the county governing body shall declare such area a special weed control district and such weeds noxious within the district, in accordance with the petition. [Formerly 570.515]