How many films with animals in the title won the Oscar for Best Picture?

There have been several films with animals in the title to win the Oscar for Best Picture

1. Dances with Wolves,
2. The Deer Hunter,
3. One Flew Over the Cuckoo's Nest
4. Silence of the Lambs

Other nominees for Best Picture with animals in the title

1. Crouching Tiger Hidden Dragon,
2. Kiss of the Spider Woman,
3. The Elephant Man,
4. Raging Bull,
5. A Lion in Winter,
6. To Kill a Mockingbird,
7. Cat on a Hat Tin Roof,
8. The Snake Pit,
9. The Maltese Falcon,
10. The Little Foxes,
11. Of Mice and Men