The dynamics of an animal - vegetation system: Sheep farming

The paper studies the economy and ecology of sheep farming at the farm level in a Nordic context, with a crucial distinction between the outdoors grazing season and the winter indoors feeding season, and where climate conditions fix the length of the grazing season. Two different categories of animals, ewes (adult females) and lambs, and one plant species are included in our ecological model. The farmer is assumed to maximize present-value profit where the revenue is made up income from meat and wool production, and we find that livestock cycles may represent an optimal management policy. We also show that, in a possible steady state with a constant number of animals and constant vegetation quantity, slaughtering either only lambs or only ewes is optimal.