I keep around 90 ewes as well as ~35 chickens for 12 years now.
The thing is that being around livestock the deal is that the female is the viable unit. No one says they keep sheep (unless they have just a few). Those who are in the business of producing livestock refer to the number of heifers or ewes or cows. The males are just extra trouble and are generally made into meat. One ram per 40 ewes is all that one needs. I don't know the bull/cow ration, but not too many either. 98% of the males born are sold to be made into meat (unless one is raising sheep for wool and then the castrated males are valuable- as they do not fight or give birth [creating a break in the wool] along with horses where geldings are considered superior to mares). With chickens, too many roosters hurt the hens. Maybe 1 rooster to 8-12 hens is OK, but no more.
So, my feeling is that Engels got it wrong. I think that the domestication of livestock led to something more complex than patriarchy. I think that when prehumans and wolves co evolved to become humans and dogs that the social system of the wolves were adopted by the humans. This system has as it's head the alpha female with her mate and then the others in the group under them with the females equal to or slightly superior to the males. Other predators exhibit these types of social systems and some herbivores, such as horses do as well. It is the lead mare that is in charge of the herd, not the stallion as is the hollywood myth.
I wonder if it was the horror of the knowledge that the primary use for males of most all domesticated animals was for meat production that contributed to the overreaction that I see patriarchy to be.
On a farm it is all too clear what happens to most male animals, and I think about the fairly tales - Hansel and Grettel ....the fattening of the little boy to be made into meat....somehow captures the discomfort of feeding the domestic livestock up so that they can be eaten. It is not easy for anyone to do, killing and eating animals that one lives with and often are fond of. In fact it is so awful that it is my theory that this is why we came up with religions at all. To have some way to comfort ourselves about this practice which seems very much like cannibalism, actually.
I have read that as civilization developed into the city/state model that ideas of spiritual beings began to change and of course this follows the religions going from a Goddess to many gods and goddesses to one male God......so that time period well after initial domestication of livestock is when this social change (patriarchy) took root.
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