off towards the south part of the island. (Ch. 8)

As Karana spends her time on the island, she has to learn how to live without her tribe.  This is more than finding and making shelter, finding food, and minding her brother.  She also has to keep predators like the wild dogs away. 

I thought about these things for two days and on the third night when the wild dogs returned to the rock, I made up my mind that no matter what befell me I would make the weapons. (Ch. 9)

One day, Ramo is killed.  Karana finds him, and knows that the wild dogs have killed him.  She vows to kill all of them.  This demonstrates another change in her personality, from independent to vengeful.  At first she tries to obey the laws of her tribe that a woman cannot make weapons.  Then she decides that to protect herself, she needs to forget these laws.  This is a sign of her independence.

Eventually, Karana even forgets her vow to kill all of the wild dogs.  She befriends Fox Eyes and names him Rontu, and later his son, Rontu-Aru.  Karana has developed complete independence, and is alone from human contact.  She has overcome the laws and conventions of her people.  She has used her intelligence and wisdom to live on her own.

Karana is not really left behind accidentally; it is her brother, Ramo, who is left when the ship sails. Karana is told they cannot go back for him because the tides have made it dangerous to return at that time. Although she is assured her people will return for Ramo soon, and that he can survive for a short time by himself, she dives off the ship and swims back to the island to protect him.

Unfortunately, she cannot. Within a few days, Ramo is killed by a pack of wild dogs. Karana is then left to survive by herself. It is not clear how long this time will be, but it turns out to be 18 years. The "problem" of Karana's abandonment is not really solved. Rather, she learns to get along on her own, befriending first one of the wild dogs, some wild birds she tames, and then a sea otter pup that she raises after it has been wounded by Aleut hunters.

Over the course of her many years on the Island of the Blue Dolphins, Karana develops a close bond with the natural world. We read, "After that summer, after being friends with Won-a-nee and her young, I never killed another otter...Nor did I ever kill another cormorant...Nor did I kill seals for their sinew."

She tells us, "...animals and birds are like people, too...Without them, the earth would be an unhappy place."

Like the real Lost Woman of San Nicolas on whom the story is based, Karana is eventually "rescued" from the island and brought to a mission in Santa Barbara.

Island of the Blue Dolphins is a historical children's novel by Scott O'Dell.

Karana, the protagonist, is marooned on an island after her tribe is attacked. Throughout the book, she shows a drive for self-reliance, personal responsibility, and success. Her main goal is to survive until she is rescued, but she gradually recognizes her need for companionship, and turning the island into a proper home becomes a goal as well. When she is attacked by wild dogs, she overcomes her cultural fears:

...I wondered what would happen to me if I went against the law of our tribe which forbade the making of weapons by women... Would the four winds blow in from the four directions of the world and smother me? ... I thought about these things for two days and on the third night when the wild dogs returned to the rock, I made up my mind that no matter what befell my I would make the weapons.
(O'Dell, Island of the Blue Dolphins, Google Books)

This survival instinct drives her actions throughout the book, and enables her to hide when a violent rival tribe lands on her island. She remains hidden from all of them except one young girl, with whom she feels a connection; Karana's loneliness allows her to trust the young girl, but her survival instinct keeps her from revealing herself to the rest of the tribe. At the end, she allows herself to be rescued by an American ship, understanding that she needs other people to be happy.

Based in part on a true story, Island of the Blue Dolphins is Scott O'Dell's 1960 novel about a young Indian girl who is marooned on an island and lives there alone for many years.

Karana, the protagonist, is a very pragmatic girl. When she is marooned, she immediately takes charge of the situation, building shelter and searching for food. When her brother Ramo is killed by a pack of wild dogs, she is furious, taking it on herself to kill some of the dogs in revenges; however, she tames the leader of the pack and secures their protection on the island. She adapts to isolation on the island, teaching herself tasks that she would never have learned in her tribe. Karana also feels a great loneliness, and domesticates several animals to fill her sense of community. Finally, on meeting a girl from the rival tribe that attacked her own, Karana realizes that she needs people to survive emotionally, and allows herself to be rescued by a passing American ship.

In Scott O'Dell's Island of the Blue Dolphins, Karanas is a young girl of a tribe that lives on an island they call Ghalas-at (the Island of the Blue Dolphins) with her family, including her brother:

My brother Ramo was only a little boy half my age, which was twelve. He was small for one who had lived so many suns and moons, but quick as a cricket. Also foolish as a cricket when he was excited.

During talks between a Russian captain and members of a Native American tribe called the Aleuts, the leaders of the island—including her father—allow the visitors to hunt in exchange for valuables and iron spearheads. An agreement is reached.

When the hunting is done, the visitors refuse to pay the agreed upon amount and a fight breaks out. Karanas' father is killed, but she and her brother Ramo (and others) survive.

That night was the most terrible time in all the memory of Ghalas-at. When the fateful day had dawned, the tribe numbered forty-two men, counting those who were too old to fight. When night came and the women had carried back to the village those who had died...there remained only fifteen. Of these, seven were old men.

Ultimately, the new leader of Karanas' people decides they must move to another place and he leaves, promising to return. One day a ship sent by this man (Kimki) does arrive, but Ramo forgets something on the island. Rather than leave him there alone, she jumps overboard and they live on the island alone. They have to work hard to eat. They also have to contend with a pack of wild, dangerous dogs.

While we ate beside a small fire I could hear the dogs on the hill not far away, and through the night their howls came to me on the wind.

Before long, Ramo, who is still very young but believes he is capable of doing things he does not have the experience for, leaves the camp alone. He does not return. Karanas searches and finds her brother's body, killed by wild dogs. From now on, she must find her own way.

This is basically Karanas' history. From this moment on, Karanas is responsible for herself. She fights off the dogs and wounds one. Finding it later almost dead, she cares for it and they become friends—she calls it Rontu. It is good for Karanas to have a companion. She makes friends with some other animals on the island, and builds a home for herself. The Aleuts return and Karanas meets a young girl from the tribe who she becomes friends with: Tutok. The girl stays for some time, but eventually the Aleuts leave, taking Tutok with them. Karanas will remain many years on the island. She will lose Rontu, but will adopt one of his litter, training him and naming him Rontu-Aru.

Karanas spends many years alone on the island except for her animal companions. When a ship does arrive some time later, Karanas runs from the man that calls her from the ship's canoe. For two years she thinks about that day and that voice:

Every day of the spring and summer since then, she has gone to the headland and watched—always at dawn and at dusk.

Finally a ship arrives again. Three men find her house, with the smoke of the fire rising into the sky. The man in a grey robe makes a sign similar to the one hanging on his beads at his waist. The men speak to her and she wants to laugh because they make...

...the strangest sounds she has ever heard.

The somehow communicate. Karanas will leave with the men. She takes Rontu-Aru, a pair of caged birds, and days later she collects her things and leaves the island for good.