The Rio Grande Turkey, Meleagris gallopavo, is a common bird in Texas, where introduction and reintroduction efforts have been very successful. Although I have never seen turkeys while hunting in Mexico, other hunters have reported to me that they have seen them in the western portion of the Mexico area south of the Texas city of Eagle Pass. The majority of turkeys killed by hunters in Texas are incidental to deer hunting, although there is an increased interest in the Spring hunt where the gobblers will respond to calls.
The common black-tailed jackrabbit, Lepus californicus, is a long eared rabbit of the open grasslands and desert scrub of South Texas and Mexico. Their natural enemy is the coyote; however I have seen them mingle peacefully where the coyotes were well fed on berries growing in Mexican lagunas. The jackrabbit depends on speed and its keen sense of hearing and sight to elude its enemies.
These rabbits tend to concentrate in pastures overgrazed by livestock and further deplete the vegetation. There have been studies that indicate that 128 jackrabbits will consume as much vegetation as seven sheep (18 rabbits equals one sheep..!). When the count of rabbits becomes 400 or more per 600 acres, the wise rancher will read the results as excessive overbrowsing by livestock.
Additional photos and comments.