But the worst, by far, were the hyenas equipped with cheetah-like limbs and huge jaws full of ripping teeth.

''I don't think there's a predator alive today,'' said Dr. Byers, ''that would've been as ferocious as that long-legged hyena would've been -- its back as high as a person's waist and running in packs as it probably did. It would have been able to get on a group of pronghorns and drag them down and rip them apart. It would have been truly formidable.''

Once the pronghorn is envisioned amid such predators, its speed seems much less extraordinary and much more obligatory, as it is hard to imagine any save the fleetest getting out of the Pleistocene alive.

And fast they became. One researcher clocked pronghorns at 55 miles an hour, though biologists guess that they may go even faster. Others tracking pronghorns by light plane going at 45 miles an hour say they have seen pronghorns put on a little burst of speed and effortlessly slip away. Pronghorns are endurance runners as well, going at 45 miles an hour for several miles without showing any signs of exhaustion.

Despite the explanatory power of ghosts of predators past, those studying behavior rarely stop to consider such vanished enemies, which was one of the major reasons Dr. Byers said he decided to write the book.

Dr. Daniel Rubenstein, a behavioral ecologist at Princeton University, called Dr. Byers's work ''high quality'' and agreed, saying that typically behavioral researchers would only consider such historical explanations if forced to do so. ''Digging back into the past to see why traits originated is almost a last resort,'' said Dr. Rubenstein, who described it as an explanation used only after researchers could not find any current use for a behavior.

Part of the reluctance to entertain such ideas, is the difficulty of testing hypotheses in which the principal players are all extinct.