4.2 The effect of both EE and HR on FCE
In this study, we employed two indicators to assess the FCE of grazers. Our results demonstrate that FCE increases with harvest rate but decreases with energy costs (Fig. 4). Notably, we defined foraging efficiency as the ratio of harvest rate to energy costs, which significantly enhanced the FCE (Fig. 4). Both harvest and energy expenditure are predictive of FCE. Of these, physical activity can cause the greatest variation in the rate of energy expenditure (Wilson et al., 2018). For instance, foraging has been shown to elevate energy consumption in wapiti and moose by 33% and 28-39%, respectively (Karasov, 1992), while an improved harvest rate has been linked to increased body weight gain (Van der Graaf et al., 2005). In addition, our findings reveal that estimating energy costs provides a more comprehensive prediction of FCE across both groups, as opposed to the harvest rate, which only predicts FCE within each group individually (Fig. 4). This suggests that the harvest rate is not directly proportional to energy consumption, pointing to underlying physiological differences in energy expenditure. Our analysis further clarifies that FCE is more influenced by harvest rate in the lamb group compared to the dry ewe group (Fig. 5), in the case of larger sheep, harvest rate contributes to FCE but is offset by the energy expenditure required, leading to a contrasting conclusion in the lamb group. The interaction effects in lambs neutralize the impact, although they do not eliminate the negative effect (Fig. 5). Energy expenditure during foraging includes step-level feeding strategies (Supplementary Fig. 1) and unique fluctuation patterns (gut throughput rate: foraging-ruminating), akin to those observed such as the tail-beat oscillations of sharks during swaying, the wing-beat cycle of birds, and the push-off by limbs in terrestrial animals (Gleiss et al., 2011).
Although our controlled experiments enabled us to assess the relationship between harvest and energy expenditure across different-sized animals and their impact on FCE, they did not fully capture the optimization of behavioral strategies during the diffusion process (Benoit et al., 2020; Klarevas‐Irby et al., 2021). The grazers may seek more efficient resources to improve their harvest rate or adopt more efficient diffusion strategies, both of which can influence foraging efficiency. Therefore, we hypothesize that grazers in a free-ranging environment may exhibit altered relationships between harvest rate and energy costs, subsequently affecting FCE.

Conclusions

Our study introduces an ecological research framework that links observable foraging behaviors of herbivores to their proficiency in converting resources into energy. The rapid utilization of resources during acquisition is pivotal for optimizing energy conversion efficiency in animals. However, the energy expended in this process inherently restricts the efficiency of resource acquisition. A significant finding of our study is that animals of varying sizes demonstrate distinct differences in energy expenditure and resource acquisition rates. Typically, smaller animals, such as lambs, are more heavily influenced in terms of resource acquisition efficiency, whereas larger animals, like adult sheep, are predominantly affected by energy consumption. This distinction provides a novel approach for inferring the internal physiological states of animals, including foraging behavior and energy transformation, by observing their behavioral patterns. Conclusively, comprehending and forecasting the energy conversion efficiency of terrestrial herbivores is crucial for evaluating their survival and development in ecological habitats. Furthermore, insights into the growth stages of these animals enhance the precision of growth rate assessments.