How does Austen explore the theme of nature versus nurture?

Austen made her central characters sets of siblings who have opposing characteristics and even opposing educations. This choice permits her to explore the ideas of human nature and environmental nurturing, as put forth by John Locke and Jean-Jacques Rousseau.
Both Locke and Rousseau built their theories of education on the relationship between the forces that shape individuals, such as family, education, sociocultural environment, and the natural propensities of personality, intellect and temperament. Locke emphasized the importance of nurture, while Rousseau depended on nature.
John Locke:
"The well educating of their children is so much the duty and concern of parents, and the welfare and prosperity of the nation so much depends on [education], that I would have everyone lay it seriously to heart ... [to promote] the easiest, shortest, and likeliest [means of education] to produce virtuous, useful, and able men in their distinct callings."
Jean-Jacques Rouseau:
"Everything is good as it comes from the hands of the Maker of the world but degenerates once it gets into the hands of man."
These sets of siblings represent different positions in the nature versus nurture discussion.
Elinor and Marianne represent the nature side of the discussion.
Lucy Steele and elder sister Anne represent both faulty nature and faulty nurture.
Edward and Robert represent the nurture side of the discussion.
Charlotte Palmer and sister Lady Middleton, like Lucy and Anne, represent both nurture and nature, illustrating flawed, although not faulty, nurture and opposite natures.
Throughout the story, Marianne's nature is pitted against Elinor's. Marianne criticizes Elinor for not being in raptures in her praises for Edward. Marianne is unable to understand how Elinor can control her grief over the loss of their father and the later loss of Norland. Though nurtured in the same environment, with a mother whose nature matched Marianne's, their natures are very different.
Lucy and Anne both have faulty natures: Lucy is manipulative and grasping while Anne is silly and foolish. They also suffer from faulty nurturing: The narrator makes a point of saying that Lucy did not have the benefit of an education that might have turned her mind to a more prosperous direction: "her powers had received no aid from education: she was ignorant and illiterate...." The same lack of education is more apparent in Anne's mentality.
Both Edward and Robert make a case for Edward's personal deficiencies being caused by inadequate nurturing in his education. Robert posits that had Edward received a public instead of private education like he himself did, Edward would fully equipped to take his place in politics [private education at the home of a private tutor; public education in one of the elite schools, like Eton].
Charlotte and Lady Middleton have natures that are as unlike as possible. Both have natural flaws in their natures: Lady Middleton is vain and shallow while Charlotte is affectionate and giddy. Though Mrs. Jennings attempted to provide good nurturing at home and in their educations, her resources, personal and financial, were limited thus the nurturing provided was limited, thus flawed.
There are also trios of siblings:
Edward, Robert and their sister Fanny (Ferrars) Dashwood.
Elinor, Marianne and their younger sister Margaret.
We engage but little with Margaret but are told that while she tends towards Marianne's romanticism, she has not the sense of her older sisters, thus does not present as bright a prospect for adulthood as her sisters do. Margaret reinforces the nature side of the discussion, which is best represented in Elinor and Marianne.
Margaret, the other sister, was a good-humored, well-disposed girl; but as she had already imbibed a good deal of Marianne's romance, without having much of her sense, she did not, at thirteen, bid fair to equal her sisters at a more advanced period of life.
Another example is the trio of Edward, Robert and Fanny. Mrs. Ferrars, representing a consistent (assuming she treated her children about the same) nurturing environment, is the mother of a humble, self-diffident man; a proud, vain, arrogant man, who is nonetheless gregarious; and an arrogant, selfish, cold-hearted woman. With this trio, the influence of nurture--whether a negative or a positive one--is shown to be inadequate to superseding the forces of nature. We see that in a consistent home environment, Mrs. Ferrars raises one child who is humble, one who is gregarious (although vain) and one who is also cold-hearted. Austen makes her exploration of this theme, a recurring one for her, more complex because she introduces the influence of educational environment into the discussion: Edward was educated with a private tutor, Robert at a public school, and Fanny at home and possibly also, although we are not told so, at a school like the one Austen herself attended for a time.
Austen's conclusion seems to be that strong natures can withstand the impact of nurturing influences when they are detrimental, but individuals with weaker natures will yield to the strongest, most compelling influence that nurtures and that the strongest external influences are often, if not generally, of a negative sort. Thus our conclusion must be that Austen sides with Locke over and against Rousseau: She agrees that nurturing of the best sort, as in education, is required to shape individuals, men and women, into wise, thinking, moral citizens who make right choices for their lives and the lives of those they influence.