Answer by Rory Young:
Generally, the older the female in the herd the more dominant she will be.
Adult males on the other hand live on their own or form small temporary groups. Among the males the bigger the male is the more dominant he will be.
Elephants never stop growing although the growth does taper off dramatically after 25yo in males and 20yo in females. Therefore the older the male is the more dominant he will be too usually.
However, a bull in "musth", which is when a male elephant goes into season, will temporarily be more dominant than all other elephants, male or female.
Being in a herd is necessary for the females in order to protect the young. The downside however is that this makes getting enough food more difficult. It is of course easier to find enough food for one individual than a herd. For this reason the females are obliged to remain in herds whilst the males can wander off and feed themselves more easily in a usually less nomadic manner.
For the herds of females to find enough quantity of food and, especially importantly, to get the necessary variety of nutrients that they need, the females have to travel long distances to different locations for different foods. This necessitates a lot of acquired knowledge which is of course improved on over the years. This makes the older females more knowledgeable and more valuable and more dominant.