Constraint sets of the three scenarios.

Productive performance constraint imposes that productive performance P(u,T) stays over a minimal productive performance Pb (the minimal annual number of grazing days per hectare associated with a grazing strategy u). Cattle feeding requirement constraint imposes that cattle demand q.u(t) is always lower than the available biomass B*(t). Cattle density constraint is an upper threshold u# on cattle density u(t) during the nesting month. A habitat quality constraint imposes grass height to remain within a minimal hb and maximal h# grass heights during chick rearing. Population size constraint imposes that populations size N(t) stays over a minimum population size Nb throughout time.