You are kind of off on a few things, but I say the following in deep respect...
The real threat to a farm is not actually with toxic gick in their manure, but rather from their hooves, Foot Rot being the greatest threat. They call it Biosecurity and often farms will have a person wash their
boots with disinfectant, and the cattle trailers that come in to kill this nasty stuff off. With foot rot, the bacteria gets brought onto a farm, and then can last 30 years or more in the soil. It is a tough thing to combat. Maine found this out when the
local fairs stopped having the State Vet check animals before they were put on display for fair-goers. It got so bad that for many years sheep were almost absent from these fairs because we did not want foot rot in our flocks.
There is a ratio of Ram to Ewes, but it is about 30-50, and not 6.
The number of sheep or cattle on a given area is not based upon the animal, but upon "Animal Units." Where I live we have a stocking rate...or land carrying capacity for pastures of 2 animal units per acre. That means it can handle 2000 pounds of live weight animals. It does not matter the animal type. Since a sheep weighs 200 pounds on average, it means I can have 10 sheep per acre. If I have 100 pound lambs, then it can hold 20 lambs per acre. Or 5 adult sheep, and 10 lambs...do you see how the math works out? It means I could have (1) 2000 pound
beef cow, or 400 five pound chickens per acre.
An animal unit is always 1000 pounds, but your area will state how many animal units a region has per acre. We got really good pastures here so it is pretty high, they deserts will have a stocking rate of 10 acres per animal unit.
Just keep in mind, this number is based on set-stocking, and no intensive grazing practices. So with intensive grazing, rotational grazing, or mob grazing, you can bump up the stocking rate some.
All this gets cross referenced to your topic on whether society should be using
wood to make paper. In that I said due to taxes and growth rates of wood, I was making $30 per year, per acre. I also said I was clearing forest to make more farmland. Using the stocking rate mentioned here, you can see why. Since I can have 2000 pounds of any animal type per acre, I can make far more money raising 10 sheep with a
profit of $100 per sheep ($1000 per acre) then I ever could as forest. Farming is way more intensive then just letting
trees grow, BUT the payoff per acre is a lot better too.
I am just trying to explain all this, and how it has to be calculated to make intelligent choices for a farm, I am in no way trying to talk down to you here. I am just trying to explain how stocking rates all work for farm decision making.