First off, this phrase, 'survival of the fittest' was coined by Herbert Spencer only after reading 'On The Origin Of Species' (it doesn't appear in Species until the fifth edition where it was used as a subtitle as a metaphor for 'differential preservation of organisms that are better adapted to survive to reproduction in changing environments'). Charles Darwin wrote:
It is not the strongest of the species that survives, nor the most intelligent, but the ones most responsive to change.
And here he is really talking about populations, and not individuals. Because it is not the individuals that 'evolve' through their life (generally speaking, there are things such as horizontal gene transfer in bacteria) but rather populations evolve through the genetic variations that occur in each generation and the resulting differential reproduction that occurs.
If you actually look at evolution you see a profound interconnectedness of all things. A human being simply could not live without a vast network of supporting organisms and also things like water, sunlight, and so forth. And those things wouldn't exist without the physics that produces some kind of chemistry in which computational processes can be expressed.
Not to mention our common ancestry with all living things, bacteria and bees and flies and humans all share this history and sometimes the scars. Our eukaryotic cells show evidence of a symbiosis formed between at least three, originally independent, organisms - without which human beings couldn't exist (energy demands, etc). Everywhere we look in nature we see cooperation, symbiosis, interdependence, altruism - why? because they work to the benefit of the organisms.
Nature is a profoundly beautiful dance. Yes, nature is also brutal in some ways, but we Homo sapiens are the only known organisms that have a sufficiently powerful organ of thought where we can compute possible futures and select among them in a way that just might eventually allow us to extricate our future-selves from that cycle.
As man advances in civilization, and small tribes are united into larger communities, the simplest reason would tell each individual that he ought to extend his social instincts and sympathies to all members of the same nation, though personally unknown to him. This point being once reached, there is only an artificial barrier to prevent his sympathies extending to the men of all nations and races. ~Charles Darwin
This is the message of Evolution, we are all connected and we share a common ancestry with ALL life here on Earth...