Social Darwinism was a prominent ideology in 19th century Europe and the United States. It sought to apply a somewhat crude interpretation of Darwin's theory of evolution by natural selection to society. The phrase "survival of the fittest" was actually coined, not by Darwin, but by the English sociologist Herbert Spencer. He put forward the idea that life was a perpetual struggle in which the strongest in society prevailed and the weakest went to the wall. Social Darwinism purported to be not just descriptive, but normative. In other words, it didn't just seek to explain what was happening in society, but to actively endorse it. To Social Darwinists like Spencer in England and William Graham Sumner in the United States, it was only right and proper that the strong should always prevail.
A struggle for survival provides the dramatic center of Strindberg's Miss Julie. On the one hand, Julie is one of society's stronger members, a part of the privileged social elite. Yet at the same time, her status as a woman in a male-dominated society renders her relatively weak in relation to the aristocratic males with whom she's surrounded. As an upper-class woman in late 19th century society, Julie has been placed in an invidious position. She's considered one of society's fittest while at the same time being kept in a state of relative weakness by the mores and conventions of her own social class.
Julie's rebellion against the standards of prevailing gender relations represents an intense struggle of the spirit. But it's a struggle she's ultimately destined to lose. Julie's concerted efforts to defy existing gender roles and expectations ultimately lead to her downfall and ruin. There is a tragic sense of inevitability about all this, a sense that nothing she could ever do would ever be enough to allow her to prevail, to experience the freedom she so desperately desires with all her soul.
And Julie's tragic fate serves as a powerful critique of the Social Darwinist analysis of society. Far from being as natural and scientific as the devotees of Social Darwinism would have us believe, society and its often repressive structures are wholly artificial, constructed by groups of individuals to serve specific ends. That being the case, Social Darwinism stands revealed as a self-serving ideology which, despite its scientific garb, acts to reinforce a specific social order in which the dominant groups (the "fittest") prevail, and those deemed weak, such as Julie, are allowed to go under.