Relative growth rates and the grazing optimization hypothesis

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Abstract
A mathematical analysis of the changes in plant relative growth rates necessary to increase aboveground production following grazing was conducted. The equation derived gives an isoline where production of a grazed and ungrazed plant will be the same. The equation has four variables (mean shoot relative growth rate, change in relative growth rate after grazing, grazing intensity, and recovery time) and may be analyzed graphically in a number of ways. Under certain conditions, small increases in shoot relative growth rate following grazing will lead to increased aboveground production. Under other conditions, very large increases in relative growth rate after grazing can occur without production being increased over that of ungrazed plants. Plants growing at nearly their maximum potential relative growth rate have little opportunity to respond positively to grazing and potentially can sustain less grazing than plants with growth rates far below maximum. Plants with high relative growth rates at the time of grazing require large increases in growth rate while slow growing plants require only small increases. High grazing intensities are least likely to increase production and high grazing frequencies require greater responses than infrequent grazing events.