The Island of the Blue Dolphins: Theme Analysis

IndependenceThe majority of this novel focuses on Karana as she learns to survive alone on the island. We witness her development as, through necessity, she adapts to her surroundings as a lone individual and teaches herself to make weapons, for example. 
In so doing, she teaches the readers that it is possible to be self-sufficient and brave and the novel, therefore, encourages the spirit of the American Dream in that this person alone is able to brave the elements and survive many years by hard work and indomitability.
Questioning of gender roles
Her enforced independence and survival also exemplifies how the construction of gender bears no relation to the ability of a man or a woman. It had been a custom in her village that only men could make weapons, and if women did so they would break when required. Now she is alone, she must make weapons and in so doing learns that the custom is a myth and shows the gender division of labor is based on something other than biology. 
This questioning of the division of labor comes earlier when the women are required to perform roles usually allotted to men. Because of the massacre, they are needed to hunt and fish and go on to show that they are as good if not better than their male counterparts. They only return to their usual roles when the remaining men complain of being usurped, and the patriarchal ideology is reinstated. When she is alone, though, the rules of patriarchy (which she has been raised with) begin to diminish.
Relationship between humans and animals
This novel encourages its readers to be aware of the environment and to recognize the havoc that can be wreaked by humans. Captain Orlov and the Aleut hunters epitomize how greed might spill over into carnage as they kill vast numbers of sea otters and go on to kill many of the male islanders. 
Hunting, then, is depicted in a negative light and this is reiterated when Karana reveals later in the novel that she will no longer kill animals unnecessarily as she begins to see the similarities between humans, birds and animals and wants to play no part in destruction.