Larger animals tend to have larger eyes, but faster animals tend to have larger eyes too:
“If you can think of mammals that are fast like a cheetah or horse, you can almost guarantee they’ve got really big eyes,” says Kirk. “This gives them better vision to avoid colliding with obstacles in their environment when they’re moving very quickly.”
Kirk and physical anthropology doctoral student Amber Heard-Booth are the first to apply Leuckart’s Law — a hypothesis that was developed specifically for birds and speed of flight — to 50 species of mammals. The paper is forthcoming in the journal Anatomical Record. Heard-Booth presented the findings at the 2011 American Association of Physical Anthropology Meeting, where she was awarded the Mildred Trotter Prize for exceptional graduate research in evolutionary morphology.
Previously it was thought that the time of day that an animal is active (nocturnal or diurnal) would be the main factor driving the evolution of mammalian eye size. However, comparative research on the anatomy of the eye has shown that although nocturnal and diurnal species differ in eye shape, they often have similar eye sizes. Although nocturnal species may appear to have bigger eyes because more of the cornea is exposed to let in more light, activity pattern only has a modest effect on eye size.
By comparison, body mass plus maximum running speed together can explain 89 percent of the variation in eye size among mammals.
The researchers controlled for body size and evolutionary relationships, and found that the relationship between eye diameter and maximum running speed is stronger than the relationship between body mass and running speed.
Seems to work at our place. My Golden Retriever is mid-speed and maybe 70 lbs. The herd are 1400 lbs. and can run pretty darn fast when they want to. Big Cow Eyes beat Puppy Dog Eyes.