Linear mixed models describing heat loss through the bill as a percent of heat of heat lost through all body surfaces (percent Qbill).

Individual is a random effect and square root of activity is a fixed effect in each model. Models with ΔAICc Table S4).所有模型均将个体设为随机效应（random effect），并将活性的平方根设为固定效应（fixed effect）；含ΔAICc值的模型详见附表S4。