2.6 Statistical analysis
In this study, we employed Ridge Regression to explore the connections
between HR, EE, and FCE, addressing the multicollinearity issue evident
between HR and EE. Ridge Regression, chosen for its L2 regularization,
effectively manages predictor intercorrelations in our small sample size
with multicollinearity. A key methodological step was determining the
optimal regularization strength (alpha) through cross-validation using
RidgeCV. This algorithm automatically tunes alpha, searching
logarithmically scaled alpha values to minimize Mean Squared Error
(MSE). To ensure model robustness, we conducted a sensitivity analysis,
focusing on variations in Root Mean Squared Error (RMSE) across
different alpha values, indicating model stability under varying
regularization levels. The final Ridge Regression models for the Lamb
and Dry Ewe datasets were refined using alpha values from
cross-validation. Model performance was evaluated based on RMSE, which
measures the standard deviation of prediction errors. Our analyses
utilized Python’s scientific computing libraries: Pandas for data
manipulation, Scikit-learn for machine learning modeling and
cross-validation, and Matplotlib for visualizations.
Results
The HR and EE show a negative corrected relationship in lamb group
(Y = -3E-06X + 1.3112; R² = 0.6613; p <
0.001; Fig. 3) and dry ewe group (Y = -1E-06X + 1.5233; R²
= 0.8539; p < 0.001; Fig. 3).
The FCE was negatively correlated with EE
across all studied herbivores
(Y = -7E-07X + 0.4145; R² = 0.8098; p <
0.001; Fig. 4a), and negatively correlated with EE in dry ewe group
(Y = -4E-07X + 0.2963; R² = 0.7152; p <
0.001; Fig. 4a), there was no significant association relationship in
lamb group. The FCE positively correlated with harvest rate in the lamb
group (Y = 0.2266X + 0.0906; R² = 0.4214; p< 0.001; Fig. 4b) and in the dry ewe group (Y =
0.3349X - 0.1943; R² = 0.8376; p < 0.00; Fig.
4b).
Using the ridge regression model, we found that FCE was more positively
affected by the HR than negatively affected by energy expenditure, and
the interaction effects show slightly negative effects on FCE in the
lamb group (Fig. 5a). In the dry ewe group, we found that FCE more
negatively affected by energy expenditure than positively affected by
the harvest rate, and the interaction effects show slightly negative
effect but more than that in lamb group (Fig. 5b)
Discussion
Grazing or wild herbivores meet their physiological requirements for
growth and survival by rapidly harvesting resources (Mysterud, 2006;
Stigter and Van Langevelde, 2004), which serve as substrates for
digestible and utilizable energy (Kamra et al., 2012; Van Soest, 1996).
Our study extended beyond merely assessing the behavioral rate of
resource acquisition to also include an evaluation of the functional
costs associated with the foraging process. Typically, the home range
within which animals acquire resources is limited by their energy
expenditure (Fagan et al., 2013). By restricting the diffusion process
using experimental exclusion plots, grazers effectively minimized energy
losses associated with searching for food. Consequently, our focus
shifted to examining the influence of individual behavioral
characteristics on resource acquisition and corresponding energy
expenditures, specifically in terms of the feed conversion efficiency.
Most vertebrates possess a digestive storage organ like the stomach or
crop to balance rapid food intake with slower energy utilization,
indicating that energy food harvest from their environment at a much
faster rate than they can process and utilize it (Speakman and Król,
2010).