2.5.3 Calculating the harvest rate
In this study, the rate of energy acquisition by grazers is quantified using the product of the harvest rate, as described by Holling’s disc equation (a type II functional response), and the energy content of the harvested resources (Brown et al., 2017). The formula for this calculation is given as
\begin{equation} H=\frac{\text{αER}}{(1+\alpha R)}\nonumber \\ \end{equation}
where\(\ \alpha\) represents the probability of encounter, ℎ denotes handling time, R symbolizes resource abundance, and E signifies the energy yield per unit of food. Considering the relatively small size of the grazing plots (2 hectares), it is assumed that each herbivore individual encounters resources with uniform probability. However, total resource availability varies, as the number of sheep units differs across plots (Fig. 2c). Consequently, the resource abundance per plot (\(R_{\text{plot}}\)) is modified to:
\begin{equation} R_{\text{plot}}=\frac{1}{\text{SU}}R\nonumber \\ \end{equation}
Here, E is represented by the crude protein percentage (CP%) of herbage, and resource abundance is indicated by the above-ground biomass (measured in grams). The handling time (ℎ) is quantified through the use of tagged sensors that record foraging time (in seconds). This leads to the revised equation:
\begin{equation} H=\frac{ER_{\text{plot}}}{(1+R_{\text{plot}})}\nonumber \\ \end{equation}