Table 1 Statistical output of models exploring the key drivers of metabolic rate.

Model	Parameter	Value	SE	t value	p value
(a) With plasticity	I₀	−11.03	0.1558	−70.80	<0.001
	ln(M)	0.6307	0.0461	13.70	<0.001
	T_A	0.7217	0.0319	22.61	<0.001
	T_C	−0.1709	0.0647	−2.641	0.008
	ln(M):T_C	−0.0741	0.0205	−3.619	<0.001
	T_A:T_C	0.1124	0.0230	4.881	<0.001
(b) Without plasticity	I₀	−11.00	0.1595	−68.96	<0.001
	ln(M)	0.6518	0.0481	13.54	<0.001
	T_A	0.7015	0.0282	24.88	<0.001

The estimated coefficients (value) for size- and temperature-dependence parameters are shown with standard errors (SE), t values, and p values, obtained from linear mixed-effects models fitted to metabolic rate data on 44 invertebrate populations from nine streams of different temperature (Fig. 1). In both models, log metabolic rate [ln(I) in J h⁻¹] was the dependent variable and the random effects structure included a random intercept for species identity and random slopes for each of the main effects. (a) The most parsimonious model included an intercept [ln(I₀)], main effects of log body mass [ln(M) in mg], acute temperature exposure [T_A in K], and chronic temperature exposure [T_C in K], and interactive effects of T_C on ln(M) and T_A. (b) An alternative model without metabolic plasticity contains only an intercept and main effects for ln(M) and T_A, in line with the general MTE prediction of a universal size-scaling and activation energy (but with ΔAIC > 31 (see Supplementary Table 7), indicating significantly weaker explanatory power than the model with metabolic plasticity.

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