In the case of a district which contains unincorporated territory and the territory of one or more cities, the district board may be elected or appointed by the county board of supervisors and the city councils in which the district is located. If the district board is to be appointed, the board of supervisors and the city council or councils shall appoint directors according to the proportionate share of population of that portion of the county and each city within the district, provided that the board of supervisors and each city council shall appoint at least one director.