Upon the passage of the proposal in the county, the governing body of the county shall, by order, declare the agricultural commodity research district to be incorporated and, within thirty days after the district has been declared organized, shall call a meeting of the landowners of the county subject to the fee for the purpose of electing a board of supervisors for the district to consist of five members to be selected from among the landowners of the county subject to the fee. At the time of calling the meeting, the governing body of the county shall give notice thereof by publication once a week for two consecutive weeks in a newspaper of general circulation within the county, the last publication to be at least ten days before the day of the meeting. The notice shall state the day, hour and place of the meeting. At the meeting, the landowners of the county subject to the fee shall elect a board of five supervisors, to be comprised of owners of real estate in the county subject to the fee. The landowners when assembled shall organize by the election of a chairperson and a secretary of the meeting who shall conduct the election. At the election, each and every acre of land in the county subject to the fee shall represent one vote and the five persons receiving the highest number of votes shall be declared elected as supervisors. Members of the board shall serve for a term of four years, except that, the members of the board shall determine by lot the terms of office for the members of the first board so that two shall be elected for a term of one year, one shall be elected for a term of two years, one shall be elected for a term of three years, and one shall be elected for a term of four years. Members of the board shall receive no compensation for their services, but shall be reimbursed for their actual and necessary expenses incurred in the performance of their duties out of funds of the district. In the same month of each year after the election of the first board of supervisors, the board of supervisors shall call a meeting of the landowners of the county subject to the fee in the same manner as provided for the calling of the first meeting, and the landowners shall meet at the time and place set by the board of supervisors and elect a supervisor as a successor to those supervisors whose terms of office are expiring. In the case of a vacancy in any office of supervisor, the remaining supervisors may fill such vacancy until the next annual meeting, when a successor shall be elected for the unexpired term.