The single-engine tailwheel-equipped airplane was performing a predator control flight while on a public use mission for a government agency. The 5,843-hour commercial pilot reported that the flight profile of the flight required operation at low altitude. The pilot reported that about an hour and fifty minutes into the flight, the airplane settled into a mesquite tree thicket while maneuvering. The pilot was able to add full power, arrest the descent, and eventually fly out of the thicket. The pilot found an open pasture about 1/2 mile from the location of the mishap, and landed to survey the damage to the airplane. The pilot found structural damage had incurred to the tail section of the airplane.