Pecking order is the phenomenon that dominating individual usually eat first. It is commonly observed in animals. In animals, it is often due to the fact that the strong individual won the fights for eating first, or is able to win those fights in future.
This is what I used to learn: "a pecking order is about access to resources decided before the access as the result of a competition, not just straight competition". For example, the order of food-feeding in bird is sometimes decided by brightness of feathers, without any direct competition (fight) for the food.
However, many other sources equate pecking order with dominance hierarchy, or the metabolic evolutionary pressure, namingly some individuals have an evolutionary advantage over others, making them more fit to survive .
For example, bacteria can has dominance hierarchy (a.k.a pecking order). Supporting literature include this.
See also history of "pecking order", pecking order of plants, and another article on dominance hierarchy.
I am not sure if my understanding is correct and if this viewpoint is universally accepted -- is there a consensus on the definition of pecking order?