In all cases where there is a contest or conflict between applicants for a lease to the same piece or parcel of land growing out of a prior occupation or improvements, such conflicting claims shall be determined by the department at a meeting scheduled by the department after notice to each of the claimants of the time and place of hearing, and in such cases depositions may be taken by any claimant in the manner provided for taking depositions in the circuit courts of this state. Any party considering himself or herself aggrieved by any decision of the department refusing to grant him or her a lease under the provisions of this part, whether in case of conflict, contest, or otherwise, has the right of appeal to the circuit court for the county in which the land is situated, and the proceedings to take the appeal and the trial of the appeal in any of those courts shall be in accordance with the statutes providing for appeals from district courts of this state, or the aggrieved party may take such other action at law or in equity as provided by the statutes and laws of this state.