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Cattle trampling of endangered plants, certain animal species, and ground nests may be a management concern on rangeland. Researchers need theoretical models of trampling loss to assist in design of studies and interpretation of results. Managers can use such models to assist in grazing management decisions. We present null (random background) models for predicting probability of trampling loss, explore the effects of failure of assumptions underlying these models, and develop alternative models for dealing with nonrandom grazing and nonrandom placement of vulnerable objects. The null models predict that if time-based stocking rate (head-days ha-1) is held constant and 1 pasture is grazed under several rotation schedules (a study design used to simulate rotational grazing), or if 1 pasture is divided into n paddocks through which 1 herd rotates, the probability of trampling is operationally constant. This qualitative prediction holds when grazing is nonindependent and nonrandom, competing risks exist, and objects subject to trampling are dispersed nonrandomly. Quantitative predictions of the null models do not hold under nonrandom grazing, which is expected to reduce probability of trampling. Researchers can use predictions of the models as a priori hypotheses. If empirical results deviate from the predictions, then researchers should search for the underlying cause-effect mechanisms. For management, the models indicate that trampling varies with livestock density and time grazed but is independent of herd rotation.

A Theoretical Basis for Study and Management of Trampling by Cattle