Farm animals have a lifecycle just like humans. They get born, mature into adults, have children and die of old-age. But in contrary to humans they procreate asexually. A single animal in a pasture is enough to start a livestock industry (when it is still young enough).
Of all animals, chicken have the highest rate of growth. They more than double their number each year. But they also have the lowest yield of food per butchered animal: a mere 6 units.
Cattle and sheep procreate much slower. Sheep double about every 30 months, cattle slightly lower with every 36. But butchering a cow or sheep yields a whole 200 units of food, enough to feed two citizens for a year.