“Phillip had been drinking, and later he repeatedly told people close to him that he’d taken LSD that night. Somewhere behind him was a grizzly, and Harry’s flashlight was lost. Phillip stumbled downhill through the forest and burst into the moonlight on Geyser Hill. He dodged the steaming pools, got to the boardwalk, and ran toward the lights. At 1:10 a.m., he crashed through the door into the lobby of the Old Faithful Inn and fell on the floor in front of the registration desk, weeping and begging for someone to help Harry.”

This passage from my book Engineering Eden: The True Story of a Violent Death, a Trial, and the Fight Over Controlling Nature describes the aftermath of a 1972 grizzly bear attack at Old Faithful, in Yellowstone National Park. The victim, Harry Eugene Walker of Anniston, Alabama, was killed almost instantly. He had been partially eaten when his body was found. His friend, Phillip Bradberry, survived, but he never got over what happened that night.

Harry Walker’s death occurred at a time of conflict between people and the remaining handful of grizzlies in the United States—one small band around Yellowstone and one around Glacier National Park, to the north. For eight decades, bears had been allowed, even encouraged, to feed on groceries and garbage in the national parks. The feedings taught bears to close what had generally been a wide berth they instinctively gave humans. Meanwhile, the numbers of human visitors in bear habitat burgeoned. Then, in a single night in August 1967, two young women were killed by different grizzlies in separate attacks at Glacier National Park. There had not been a death from a grizzly attack in Glacier since the park was established in 1910. In the years that followed, to disconnect the relationship between unnatural feeding and changes in bear behavior, the Park Service and other land management agencies worked to make foods of human origin unavailable to bears. Open garbage pits in and around national parks at which grizzlies had been feeding for decades were covered over, but the operation was inconsistent and poorly planned. Notably, garbage dumps were closed before safe food storage was available to visitors in campgrounds, and before conversion to secure disposal of garbage was completed. This was not only true at Yellowstone, but at Yosemite, Sequoia, Kings Canyon, and Shenandoah national parks. Coming as it did in the midst of this process, Harry Walker’s 1972 death was the first human fatality from a bear attack at Yellowstone in 30 years, and only the third in the park’s history. But as grizzlies charged into developed areas looking for food, many more bears than people were killed in protective actions by rangers. After his death, Harry Walker’s parents sued the Park Service, alleging mismanagement of grizzlies, and in 1975, the year the Walker case went to trial, the grizzly was listed as threatened under the Endangered Species Act.

Much has been learned since then. One retired biologist told me that for years after the garbage dumps at Yellowstone were closed, she found evidence of bears—which have tremendous memories about where they got food in the past—digging in the earth fill over the old dumps. But those bears are long dead now, and during my research for Engineering Eden, wildlife biologist Kerry Gunther, Yellowstone National Park’s longtime bear management specialist, told me that bears conditioned to look for foods of human origin are so rare at Yellowstone as to be almost unknown. But, Gunther cautioned me, the park now gets more than four million visitors a year, and with that many people doing outdoor activities in grizzly habitat, occasionally an encounter between the two species goes badly. That happened once last year, when Lance Crosby, 63, of Billings, Montana, was killed by a grizzly. He was hiking alone. Experts like Yellowstone National Park historian Lee Whittlesey, who records an extensive study of Yellowstone’s grizzly attacks in his book Death in Yellowstone, say hiking alone can be a contributing factor in grizzly attacks.

On June 29 this year, tragedy struck again at the other stronghold of the American grizzly, the area now known as the “Crown of the Continent Ecosystem,” including Glacier National Park. Brad Treat, 38, an off-duty Forest Service law enforcement officer, was attacked and killed by a grizzly while mountain biking with another man just outside Glacier’s west entrance. It is too early to say definitively what caused that attack pending a complete investigation by wildlife authorities, but grizzlies—and particularly females with cubs or bears feeding on a dead animal—have been known to charge if startled by the rapid approach of people. And in a small number of cases, grizzlies will attack human beings without provocation.

As a friend of mine says, “We humans are hard-wired for the Paleolithic.” Human evolution proceeds at a relative snail’s pace. It takes a couple of decades for our genes to express themselves in the next generation. (Bacteria and viruses do it several times a day.) So we may drive Priuses and Instagram each other on our tablets, but our mentalities were formed during tens of thousands of years of dark nights huddled around campfires, glancing nervously over our shoulders. For most of the time we have been on earth, we humans have been medium-sized snacks for a suite of predators that once included formidable but now-extinct creatures such as the cave bear, the dire wolf, and the Smilodon. And nothing brings forth our inner caveman and cavewoman better than the sound of a snapping twig outside the tent in the dark—generally nothing more than a deer ambling through the campground on its way to drink at the creek. But really, how worried should we be about keeping company with grizzlies, wolves, and mountain lions at Glacier and Yellowstone this summer?

The simple answer is, the incidence of attacks by wildlife of all kinds on human beings in the American national parks is almost negligibly low. Yellowstone has never had an attack on a human being by a cougar or a wolf. And more common than bear attacks there are injuries to park visitors by bison—five of them in 2015 alone.

Bison are happy grazing around paths in developed areas and appear docile and slow-moving, like dairy cows. Not so, says park biologist emeritus Mary Meagher, who did the first modern study of Yellowstone bison for her doctoral dissertation in the ’60s and later served as Yellowstone’s chief scientist. “One thing people fail to understand about bison is, they are not cattle,” she says. People have been gored while putting their arms over the beasts’ giant necks to have their picture taken. National Park Service public affairs specialist Charissa Reid, who grew up in Yellowstone, once watched in horror as a foreign visitor walked up to a bison and fired a flash camera right by its face, as the animal raised its tail—a warning sign—and prepared to defend itself. Somehow the situation didn’t prove fatal.

Reid says that visitors sometimes assume that because they are allowed to mix freely with wild animals the animals must be safe to be around. But she urges visitors not to crowd them. Like bison, moose need to be given a wide berth. Even elk and deer can be aggressive during the fall rut, and they have been involved in many collisions with motor vehicles, some resulting in serious injury and death to the occupants. So at Yellowstone and other parks, rangers stringently enforce a 45-mile-per-hour speed limit on many park roads to protect both people and animals. And they ask park visitors to prevent problems with wildlife in camping areas by practicing proper food storage and disposal of refuse. Campgrounds now feature bear-proof food lockers and garbage receptacles, but they don’t work if people don’t use them. Every trace of food needs to be cleaned up when you’re not eating, even during the day.

Poisonous snakes are present in some parks in the West, Southwest, and South, but they go out of their way to avoid trouble and are responsible for relatively few incidents if visitors exercise reasonable caution. Snakebite claimed a single human life in the entire national park system between 2007 and 2013, the same death toll as choking on hot dogs. Grizzly bears killed four. And during the same period 210 visitors were killed in car crashes and 365 people drowned in national parks.

Overall, notwithstanding the stuff of our ancient nightmares, the most pernicious animal threats in the national parks may be the smallest. Bee and wasp stings can be serious for those allergic to them. Mosquito bites can transmit West Nile Virus and perhaps soon, in some areas of the South, Zika. However these risks are no greater in a national park than at a suburban backyard barbeque, so you may as well go and enjoy nature’s grandeur. But be especially vigilant about prevention and proper treatment of tick bites. According to a 2013 estimate from the Federal Centers for Disease Control and Prevention, ticks transmit 300,000 new cases of Lyme disease in the United States each year. And in addition to Lyme, North American ticks commonly carry a dozen other illnesses, including babesiosis, Bartonella, Rocky Mountain spotted fever, tick-borne relapsing and Q fevers, Powassan virus, and anaplasmosis.

Statistics kept by the Park Service show that with all of the high-risk outdoor sports practiced in parks—climbing Mt. Denali and El Capitan, kayaking the Colorado River, and even jumping off cliffs with parachutes (which is illegal in many areas), the rate of accidental death among national park users is astoundingly low: 0.57 deaths per million visitors, according to Jennifer Proctor, chief of the Park Service’s Office of Risk Management in Washington, D.C. And, the most common causes of death on national park vacations are far more prosaic than those in our Paleolithic night terrors. They are, in order: drowning, automobile accidents, and falls. So yes, store your food safely and put your garbage away to keep bears out of camp. Be vigilant about tick bites. But for Pete’s sake, keep an eye on your children around fast-moving streams and ocean surf, carry and use personal floatation devices when boating, and don’t mix alcohol with aquatic activities—a frequent contributor to tragedy.

With all of those cautions, Dr. Sara Newman, chief of Risk Management’s neighboring branch, the Park Service’s Office of Public Health, proposes that the benefits to your wellbeing from national park visits far outweigh the risks. “National Parks are a great place to get healthy,” says Newman. As I point out in Engineering Eden, the physical and spiritual benefits of awe-inspiring natural beauty and outdoor recreation away from urban stressors were among the original reasons cited by 19th century advocates for the creation of national parks, such as Central Park designer Frederick Law Olmsted and Yosemite naturalist John Muir. Today, 144 years after Congress designated Yellowstone a national park, those attributes benefit record numbers of Americans and foreign visitors. Take-home message: Wildlife attacks are rare, the parks are safe, but you, the visitor, are an important part of keeping them that way. Conditions outdoors are constantly changing. Park Service Risk Management chief Jennifer Proctor recommends checking with rangers about your activities and obeying park regulations such as those regarding proper food storage, speed limits, and how far away to stay away from large animals.

In the end, communing with our inner cavewoman and caveman brings us far more good than it does psychic distress from the occasional snapping twig at night. After a few days in the out-of-doors we feel renewed. Our appetites are ravenous; everything seems to taste better. Our sense of smell and hearing become more acute. There is something very restful to the eyes about looking into the far distance, or lying on your back watching clouds pass over. Watching bison, elk, and pronghorn antelope awakes in us the ancient and mysterious beauty of wild animals that so fascinated our distant ancestors, as evident in their cave paintings. We fill our lungs with sweet air after months of shallow breathing.

Anyway, whether you go away to the parks this weekend or decide to catch up on home projects, just exercise reasonable caution. A lot of people get hurt in falls from ladders.

Jordan Fisher Smith spent 21 years as a park ranger and rescue medic in California, Wyoming, Idaho, and Alaska. His ranger memoir, Nature Noir, was a Wall Street Journal Summer Reading pick and an Audubon Magazine Editor’s Choice. His Engineering Eden, covering the bear attack on Harry Walker and the struggle to live peacefully with wildlife in the national parks, was published in June by Crown and the accompanying audio book was released by Blackstone.