Wyo. Stat. § 41-9-504
When a majority of the lands within the district are unentered public lands, a majority of the commissioners of the district, who shall be residents of the state, may be appointed by the secretary of the interior, and shall be subject to removal from office by him and any vacancy so created may be filled by further appointment by the secretary of the interior. Commissioners thus appointed by the secretary of the interior shall hold office until such time that the unentered public lands within the district constitute a minority of the total area, after which they shall be appointed or elected as otherwise provided by this chapter 76, Wyoming Compiled Statutes, 1920, and all acts amendatory thereof or supplementary thereto; if a majority of the commissioners of the district are so appointed by the secretary of the interior, then the remaining commissioners shall be appointed or elected at large within the entire drainage district for terms of two (2) years each, which terms, however, shall be limited to and expire on the first Tuesday in July next following the date when the unentered public lands within the district constitute less than a majority of the total acreage within the district, after which the commissioners shall be appointed or elected in the same manner and for the same terms as provided for in the case of first appointment or election of commissioners under the said statutes.
W.S. 41-9-504