It was autumn, and Patricia van Tighem and her husband, Trevor Janz, were hiking in Waterton Lakes National Park, Canada. As they passed into a dense pine forest, Patricia had a sense of foreboding. Something was not right. Trevor called her paranoid, and they resumed their climb. It was a popular trail. There seemed no reason for concern. Yet as they came into view of a waterfall, Patricia stopped again. An awful smell hit her, but Trevor dismissed it. A bighorn sheep had died just off the trail and though she didn't know it, she could smell its decomposing body. Patricia worried aloud about bears, but Trevor's enthusiasm won out and they pressed on up the trail.

Trevor rushed ahead, eager as always to plunge onward. He disappeared round a bend and Patricia hurried to follow. But as she came within sight of him, something was out of place. It took a moment before she could comprehend what she was seeing. Trevor was down and a bear's jaws were around his leg.

The bear charged Patricia so fast that she could scarcely take it in. Their eyes met for a moment. Then the bear took her head in its mouth and began chewing. She could feel its teeth scraping across her skull, ripping away her eye and half of her face. Patricia thought of her mother and of all the people who would be destroyed by her death, and she reached up and twisted the huge black nose before her. The bear barked and stood aside. It began pacing in front of her. Patricia played dead.

Silence fell at last. Patricia began to stand and felt that something was wrong with her head. She was in the snow, hypothermic and near death, when hikers came to her aid. Somehow they managed to get her down the trail and to find a search-and-rescue team. Not until she reached the hospital did she learn that Trevor was expected to live.

Her stay in the hospital was a torture of surgical procedures interrupted by hallucinations, flashbacks and nightmares. The bear was in the hall, stalking Patricia in her dreams. For weeks of that autumn, in 1983, she was completely blind, adding to her disorientation. The bear took not only her skin and scalp but the muscles of the neck that held up her head. The surgeons took part of her back muscle and grafted it in place as a substitute. Skin from her buttocks was taken to cover her neck and head. That procedure alone took 12 hours. She was informed that her left eye, where the bear had eaten away the cheekbone, would never see or move again.

Patricia was 24. She had been working as a hospital nurse, and Trevor was a third-year medical student. A month after the attack, they were able to leave the hospital, to visit her parents. On that outing, it first became clear that Patricia and Trevor were about to take radically divergent courses. Patricia's response was terror and shame at her disfigurement. She felt weak and vulnerable, apprehensive that the car would crash on the way home. She now experienced the world around her as an intensely hazardous place. Arriving at the home where she had grown up, she felt overwhelmed. "I am a stranger in some way," she said, echoing many who survive severe trauma.

Trevor was disfigured, too, his head and face crisscrossed with stitches, his jaw broken, his leg ripped open and sewn back together. And yet, as they left the hospital that day, he was singing, despite the fact that his jaw was wired shut. Again and again, he said he felt lucky and grateful to be alive. One evening, he smuggled a wheelchair to Patricia's room and sneaked her out of the ward to see the beautiful view. That night he said he wanted to get out of the hospital and go ice climbing. In his mind, he was rapidly moving on from the experience.

Although they had survived almost the same experience, the differences in their responses grew greater over time. Patricia simply longed for the return of a normal life. Trevor's response seemed to be: I'm a new man. Let's see what I can do. Neither Patricia nor Trevor could eat solid food at first. But while Patricia grew thinner, Trevor took a blender to the hospital and put in ice-cream and lasagne, so he could ingest enough calories to gain weight. By the time they were able to leave the hospital, Trevor was losing patience with Patricia for reliving the incident. They stayed at Patricia's parents' house at first, and she would sit in the living room looking out of the window, vigilant, expecting at any moment to see a grizzly bear heaving into view. Trevor and her parents went out for walks, but Patricia was too afraid to join them. Exasperated, alone in the house, she would shout out loud at herself, "There is nothing out there! Stop it. Stop looking!"

She and Trevor sought help from a psychotherapist. Trevor voiced his frustration with his wife. They had tried to go on a hike together, but after 15 minutes Patricia was ill with trepidation and had to turn back. That night, she had terrifying dreams.

Trevor had nightmares sometimes, too, but his response was not to think about it. He just put it out of his mind. Psychiatrist George Vaillant, in his Study Of Adult Development, found that this type of suppression was straightforward, practical, and it worked. "Of all the coping mechanisms," he wrote, "suppression alters the world the least and best accepts the terms life offers." Contrary to what many psychologists would have you believe, he says, simply suppressing a traumatic experience and getting on with business is "the defensive style most closely associated with successful adaptation". Trevor forced this hard-nosed logic to dominate over emotion, telling his wife, "We won't be attacked again, Trish. We're predisastered." (In quoting from the movie The World According To Garp, he was employing one of the best strategies for successful adaptation: humour.) In the midst of the attack, Trevor recalled feeling distant and philosophical about it. He had seen the bear attack Patricia and was under the impression that she had been killed. When the bear returned to attack Trevor for a second time, he later told his wife that he was convinced he'd die, but his only reaction was curiosity. He thought: "So this is how I die." Patricia's response to the bear was pure panic and terror.

Patricia had been more severely injured than her husband, which may explain to some extent the differences in their responses. Because the bear bit into her face, she had repeated operations on her sinuses. Within weeks of each surgery, infection would set in again. More surgery would follow. Her head and face ached all the time. Patricia needed to experience her body healing in order to make progress, and that just wasn't happening.

Also, their experiences of the attack had been different in one crucial way. Trevor had had no premonition about the bear. Patricia had ignored the clear warning she had felt.

Lisette duPré Brieger had premonitions, too. She and Marshall Johnson worked in the same office. At the annual Christmas party, she saw him sharpening an axe. She thought it odd, but they worked for an oil company that owned a 400-acre farm in the Virginia countryside. Maybe the axe was for chopping firewood out there.

Lisette liked Marshall. A friend had driven her to the party, but when Marshall offered her a ride home, Lisette accepted. As they drove, Marshall asked if she'd ever been out to the farm. She had not. Marshall drove out into the countryside, parking by the farm, then reached into the back seat for the axe. Without having to think about it, Lisette threw open the door and began running across the snow-covered ground in her high heels. She was struggling towards the farmhouse when she glanced back and saw Marshall standing in the illumination from the headlights, looking puzzled.

"What are you doing?" he called out.

She hesitated. What was that in his hands? Not the axe. A little box. Lisette walked back, now conscious of how wet her feet were, how terrified she had been.

"Open it," he said. "What were you doing?"

"I thought you might be about to murder me with that axe."

"I'm hardly an axe murderer," he said with a chuckle. All at once it was a joke. And the flicker of something sinister that she had seen in the car subsided beneath the surface once again.

The box contained a necklace. She was the administrative assistant at the company, and he was technically one of her bosses, so this was in keeping with the Christmas tradition. Even so, Lisette was touched. How silly of me, she thought. And what an odd thing to think, that he wanted to kill me. Where had that come from?

By October 4 2009, Lisette and Marshall had been married for 21 years. They had two children, Graham, just turned 10, and Natalie, 11. The psychological and verbal abuse had become extreme. Lisette had told Marshall she was leaving.

Lisette had felt a sense of foreboding the day before. She had celebrated their son Graham's birthday with eight of his friends. There had been Toy Story at the cinema and birthday cake at home. That evening, Marshall was acting strange. He had been threatening her, first saying that he'd never see the children again if she left and then that she'd never get custody because she was crazy.

The next morning was Sunday. She had plans to meet her friend Gretchen, but found her husband sitting on the bed in the guest room looking upset. Lisette turned and went to her bedroom. Marshall followed, saying, "I want to know how you are going to live when you leave here. What are you going to live on?" He stormed out. Lisette sat to check her email. Then Marshall returned with a towel over his hand.

Lisette stood immediately, suddenly knowing. She stood at the exact moment he pulled the trigger, firing point blank at her head. And because she stood, instead of sitting there in disbelief, the bullet struck her not in the head but halfway between her collarbone and her right breast. She bolted for the open door and he fired a second time, hitting her in the abdomen. As she ran across the yard, she screamed for the children. He fired again, hitting her in the back. She could hear her daughter screaming, "What's wrong? What's happened?"

Lisette managed to call out, "Daddy shot me!" She heard another shot but felt nothing: that last shot had been for him. She collapsed in a pile of leaves.

Lisette was given 10 units of blood in the emergency room. Both of her lungs had collapsed. She still has one of the bullets in her liver. But she got up by herself in the first week. She returned to work, took care of the children. She functioned.

She took the children to visit her family for New Year and, like Patricia, Lisette began to feel how such extreme survival sets you apart. "I was surrounded by love," she said, "but I had this odd sense of isolation. Difference. Like I knew something they didn't."

The children experienced hysterical crying jags. Lisette had to stand in the middle of it, trying to calm them when she, too, felt like curling up in a ball and falling apart. Back at home during the first week of 2010, she went through the motions. She took Graham and Natalie to school, had a shower, made a business call. Then hung up and burst into tears. This is part of me now, she thought. Part of who I am. "You have to be all right," she told herself, "because you have to take care of the children."

Spring came. The woods that surrounded the house were exploding with life. Lisette was cleaning out the linen closet when she discovered the bullet hole in the wall. She stared at it, marvelling at how the bullet could have passed through her husband's brain and then through the bedroom wall and through this wall as well. She felt a new sense of peace and detachment.

Lisette began giving talks for the police at the domestic violence task force. Talking, helping others, gave her strength. Her emotions were still just below the surface, but she gradually began to feel grateful for having any feelings at all. She began to realise how long she had been completely numb in her marriage. She used to feel lonely all the time. Now that she was really alone, she rarely felt true loneliness.

Then something remarkable happened. Lisette was sitting in the waiting room while Graham was in therapy. An 11-year-old girl named Betty struck up a conversation. Betty told Lisette that she had been shot in the neck and that the bullet was still there. Lisette told her that she, too, had a bullet in her abdomen. Betty said that her mother had been shot twice and her brother was shot four times. Her father had done the shooting. Her brother, aged 10, was in the hospital on a ventilator.

Lisette was trying to hold it together as she listened to this. She told Betty and her sister Ruth that they would be happy one day, because she was happy. They exchanged phone numbers and, since their mother couldn't drive a car yet, Lisette promised to take the girls to their appointments. She had found something apart from herself to care about. She struggled on, both for the sake of her children and for Betty and Ruth. In that way, she became a rescuer, and left behind the persona of the victim.

Micki Glenn's screensaver of the shark that attacked her

For Micki Glenn, confronting the trauma she survived became the key to recovery. She had been on an expedition to scuba dive and photograph sharks off Caicos Bank in the West Indies. Micki managed her husband's practice as a trauma surgeon. Among the others on the boat were a vascular surgeon and a nurse in an intensive care unit.

Micki was snorkelling, while her husband Mike was in scuba gear, photographing beneath the surface. Looking down, she was not surprised to see a 7ft-long female shark just beneath her fins. It was their fifth day of diving and Micki and her companions had become accustomed to having sharks nearby.

The female shark stopped beneath Micki's fins and changed direction. Then the animal moved slowly upright, aligning its body with Micki's until the two were staring at each other. "I was looking right into her eye, just inches away. I saw the slit of her mouth, and the hair was standing up on the back of my neck. I thought I was the luckiest person ever." Micki held her breath as the shark moved slowly against her, then glided away.

As she let out her breath, Micki felt a powerful surge of water hit her side, as the shark flipped around and took Micki's arm in its mouth. The shark's upper rows of teeth were across Micki's back all the way to the spine. She felt no pain, only pressure "like I was in a vice". Like many people caught in a life-threatening emergency, Micki described "time slowing down so that I could perceive the most minute details". Like a razor, the lower jaw sliced her breast. The upper jaw took half her armpit. Then the shark began thrashing with such force that Micki suffered whiplash. At the same time, she was trying to power her left hand around to strike the shark and drive it away. At last the shark slid beneath the boat, taking a huge chunk of meat with it. It was about eight in the morning, a beautiful sunny day, on November 14 2002.

Micki looked around and saw four other sharks. The water all around her was not just red but deep crimson. She saw the ragged flesh and the bone of her arm. "The rest of my arm was in the water. I was beyond terror." She began kicking as hard as she could toward the boat, paddling with her uninjured left arm.

On the boat, Mike, the vascular surgeon and the ICU nurse were on hand with their medical equipment, brought along as a precaution against just such an emergency. Mike groped for the torn end of Micki's brachial artery, which was ejecting a fountain of blood. "That's when the pain hit," Micki said. "It was surgery without anaesthesia. I started screaming so loud that I couldn't hear." They put her on an IV. "I still didn't think I was going to live through it. I refused pain meds because I didn't want to relax and lose the ability to fight and stay alive."

Micki knew it was important to stay awake and that the pain could help her accomplish that. She developed a mantra: pain is my friend. Micki's mantra carried her through the excruciating journey to the hospital, by dinghy, police boat, helicopter, ambulance and, at last, a Coast Guard jet. When they reached the hospital, a surgeon reconstructed her arm. She underwent six operations over the next two weeks.

But the more profound drama, the ordeal of trying to re-enter the world, began while she was still in hospital. "If I didn't focus on something every minute, as soon as I relaxed, it was like the wall in the hospital would turn into the sea again, and I relived the shark attack over and over and over." To take her mind off the shark, she returned to work just 16 days after the attack, still wearing bandages and plaster.

"The Micki I loved was loud and clear in my head," she told me. "But the new fearful, injured, careful, timid person emerged as the dominant me and, to my dismay, she controlled my actions, my body. The old familiar me had a strong voice and sense of who I should be, but she had no control. She was a ghost. I aligned myself with her, and we hated the alien Micki."

Mike had managed to photograph the shark just before it attacked Micki. Now he put a close-up image of that very shark on her computer, as her screensaver. "Every time I walked in, I had to look at her again," she said. "It took a week or two, but I was gradually desensitised."

After the accident, Micki had told her husband to get rid of her scuba gear. She never wanted to see it again. He kept it anyway. Two years passed. Then a friend coaxed Micki into taking a trip to Dominica in the Caribbean – and for two days sat holding Micki's hand at the edge of the water. "The first day I actually went to dive, I threw up my breakfast."

When she was 80ft down, a big barracuda surprised her. "All I saw were teeth. I came completely unglued and crashed into the wall and cried into my mask and got all snotty." She forced herself to stay in the water and work through it. "After Dominica, I felt that I was whole again," she told me.

A decade after their bear attack, Patricia still had not moved on. She and Trevor had children but, while he was working as a doctor, for many days she lay curled up in her room with a blanket over her head, unable to function. Trevor had attacked the world in much the same way as Micki, by seeking new pursuits. When he was in hospital, Trevor had sustained himself in part by dreaming that he would one day go ice climbing. He made that dream a reality. He went mountaineering. He bought a sailboard and went windsurfing. He built a house to live in and built the furniture for it. And he became, in effect, a single parent.

Patricia, who had been perfectly well-adjusted before setting out for that hike at the age of 24, now began her passage through a series of psychiatric hospitals, through electro-convulsive therapy, through drugs and therapy and more surgery, through more and more pain and depression.

Fifteen years passed after the attack, yet still Patricia read obsessively about bears and people being attacked by bears, and wrote compulsively about her experience. She had a big family and good social support from her many siblings and friends. But their well-meaning attempts to cheer her up ("At least you're alive") merely sent her into a rage again. When her book The Bear's Embrace was published, it became a bestseller. Yet nothing seemed to help her get over the attack.

Patricia's temperament actually might have prevented the accident. When they were going up the trail, she had sensed something. She smelled the dead sheep and knew it was a warning signal. She was consciously afraid of bears at that moment. (The grizzly was feeding on the dead sheep and attacked them in an attempt to protect its find.) Left to her own devices, she might well have turned back. Instead, Trevor's boldness won out. His personality proved much more resilient in the aftermath. And Patricia's apprehension, the very sensitivity that might have saved them, became her greatest liability in the years to come.

On December 14 2005, Patricia van Tighem checked into a hotel in Kelowna, British Columbia, and took her own life, leaving behind Trevor and four children. She had fought the bear for 22 years.

• Extracted from Surviving Survival: The Art And Science of Resilience by Laurence Gonzales, published by WW Norton on 9 November at £18.99. To order a copy for £15.19, with free UK p&p, go to guardian.co.uk/bookshop or call 0330 333 6846.