This letter will probably be widely denounced as another simple solution to a complex problem. However, there is nothing in the cosmos that says that all complex problems require complex solutions. I have a simple solution to suggest.
Problem: Wild goats are overrunning San Clemente Island, despoiling the landscape and threatening native endangered species. Navy efforts seem to be ineffective in reducing the number of goats by trapping and relocation or (horrors) shooting.
Problem: Native mountain lions, after being protected for many years, are rapidly increasing from the predation on domesticated animals, particularly sheep. This is resulting in outcrys to kill them off, and such killing could threaten the survival of the species.
Solution: Capture the surplus mountain lions and ship them to San Clemente Island. The lions would prey on the surplus goats. Eventually both populations would stabilize. Predation would improve the health of the goat herds by culling out the sick and weak. The lions would multiply with their constraint being the goat population. The lions would not threaten domesticated species. The lions would do their work quietly, efficiently, and with the highest motivation. The two species would be saved and naturally controlled.