| Summary: | Assessing the carrying capacity is of primary importance in arid rangelands. This becomes even more important during droughts, when rangelands exhibit non-equilibrium dynamics, and the dynamics of livestock conditions and forage resource are decoupled. Carrying capacity is usually conceived as an equilibrium concept, that is, the consumer density that can co-exist in long-term equilibrium with the resource. As one of the first, here we address the concept of carrying capacity in systems, where there is no feedback between consumer and resource in a limited period of time. To this end, we developed an individual-based model describing the basic characteristics of a rangeland during a drought. The model represents a rangeland composed by a single water point and forage distributed all around, with livestock units moving from water to forage and vice versa, for eating and drinking. For each livestock unit we implemented an energy balance and we accounted for the gut-filling effect (i.e. only a limited amount of forage can be ingested per unit time). Our results showed that there is a temporal threshold above which livestock begin to experience energy deficit and burn fat reserves. We demonstrated that such a temporal threshold increases with the number of animals and decreases with the rangeland conditions (amount of forage). The temporal threshold corresponded to the time livestock take to consume all the forage within a certain distance from water, so that the livestock can return to water for drinking without spending more energy than they gain within a day. In this study, we highlight the importance of a time threshold in the assessment of carrying capacity in non-equilibrium conditions. Considering this time threshold could explain contrasting observations about the influence of livestock number on livestock conditions. In case of private rangelands, the herd size should be chosen so that the spatial threshold equals (or exceeds) the length of the drought.
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