In Animal Farm, dominance and power shape the farm community by making a two tiered system comprised of those who have power and those who lack it.
Old Major's primary objection toward human beings stems from roots of power and dominance. Old Major believes that humans exploit animals. In the opening chapter, the animals embrace his message. Old Major directly states that the animals suffer because human beings are in power and that their dominance shapes the farm community:
...the whole of the produce of our labour is stolen from us by human beings. There, comrades, is the answer to all our problems. It is summed up in a single word — Man. Man is the only real enemy we have. Remove Man from the scene, and the root cause of hunger and overwork is abolished for ever.
Interestingly enough, once the revolution takes place, the pigs essentially copy the humans. Desire for dominance shapes how the pigs view power. Napoleon is more interested in consolidating his power than anything else. He uses Squealer to justify pig leadership and seeks to expel or purge dissenting voices. Napoleon is able to broker deals with others farms to make himself and the other pigs wealthy and powerful at the cost of the other animals' labor.
As a result, power and dominance once again shape the farm community. As a result of the leadership of both the pigs and humans, the farm is divided into distinct levels of insiders, those who wield political power, and outsiders, those who lack it.