Selfishness Overload

The Selfish Gene by Richard Dawkins begins by explaining its purpose, which is to expose how selfishness of genes rules in evolution. Although it states that "altruistic" individuals do exist, it also exposes that in the end, their actions are always done for the good of the species and therefore, are selfish. But although it talks about selfishness and the survival of a species, I wonder if there is selfishness among different kinds of groups inside the same species, much like human conflict today. Not only are we selfish in reference to other species, exploiting anything that may serve useful towards us, but we are also selfish between ourselves. Very few people ever become altruistic and "sacrifice themselves for the good of the species". This is the best example that perhaps we are the most selfish species, the most selfish gene of all. Based on Darwin´s ideas, this means that our species will be the last to die, because we are the strongest of all. We will destroy everything in our path to get there, and indeed we are living up to that responsibility. But perhaps, because we do not care generally about others in our species, we will only care about personal survival. If so, perhaps we will only destroy ourselves until the last, strongest individual of all is left standing. Maybe being the strongest is not the best thing of all, because we are so blinded with our greed that we forget that occasional good is not a bad thing. If we don´t slow things down just a little bit, our own selfishness could backfire.