The relation between animal gain and stocking rate: Derivation of the relation from the results of grazing trials

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Abstract
Several models have been proposed in the literature relating gain per animal (Ya) and stocking rate (x) from grazing experiments. Results from an experiment in which tropical pasture species were grazed continuously by beef cattle at a number of stocking rates (Jones, 1974) were used to examine this relation. A simple linear model of the form y = a − bxfitted the data well. Production per hectare (Yh) was related to stocking rate by yh = ax − bx2.Stocking rate for maximum gain per hectare (the optimum stocking rate) on each pasture could be calculated from the linear regression by a/2b.Data from a number of stocking rate experiments in tropical and temperate environments were examined to see if this relation held for a wider range of stocking rates and pasture types. Results were expressed on a common basis by calculating the optimum stocking rate and relating ratios of gain to ratios of stocking rate relative to that at the optimum.For gain per animal, the overall relation obtained: Ya = l·999–0·999x (r = –0·992; P < 0·001; n = 114) did not differ significantly from the expected linear relation: y = 2−x. Linearity was established over the range 0·18–2·0 times the optimum stocking rate. At rates greater than twice the optimum, animal gain was negative. When expressed as gain per hectare (Yh) the quadratic equation Yh = 2x − x2 gave a good fit to the data over this range.It is suggested that, since the relation between production per animal and stocking rate (animals/ha) remains linear over a wide range of stocking rates, two rates of stocking (with replication) may be adequate for grazing experiments and these would not have to span the optimum stocking rate in order to predict gain at the optimum stocking rate.