The best replacement for bighorn sheep is mountain goat.

The best alternatives to bighorn sheep are rated as following:
★★★★★  mountain goat
★★★★★  mountain lion
★★  rocky mountain bighorn sheep
★  dall sheep
  mountain goats

Your alternative for bighorn sheep is not listed? Suggest!
Speaking about bighorn sheep, one probably shouldn't forget about heart shot.

Other search terms related to bighorn sheep and their ratings are:
★★★★★ heart shot
You have in mind a companion for bighorn sheep and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of bighorn sheep in all years. Click on graph for more.
bighorn sheep
mountain goat
mountain lion