Table 1 Fitting results and goodness of fit.

Database & model	Parameters fit	b/a	r²(%)	\({\chi }_{r}^{2}\)	AIC
Mammals (all, N = 637)
B = cM^α	c = 0.0692, α = 0.72		95.2	1.07	−1220
logB = β₀ + β₁logM + β₂(logM)²	β₀ =−2.19, β₁ = 0.54, β₂ = 0.014		96.1	1.01	−1271
B = aM + bM^2/3	a = 0.0016, b = 0.079	49	97.9	1.00	−1264
Polar mammals (N = 14)
B = cM^α	c = 0.1326, α = 0.6928		98.8	0.86	−32.0
B = aM + bM^2/3	a = 0.00085, b = 0.142	167	98.9	0.78	−33.2
Desert mammals (N = 99)
B = cM^α	c = 0.0556, α = 0.7393		96.9	0.94	−233
B = aM + bM^2/3	a = 0.002, b = 0.066	29	97.2	0.93	−244
Polar and Desert mammals (N = 113)
B = cM^α	c = 0.0569, α = 0.7468		96.9	1.02	−233
B = aM + bM^2/3	a = 0.002, b = 0.0706	35	97.0	0.97	−245
Hybrid			98.0	0.90	−277
Plants (N = 89)
B = cM^α	c = 0.0053, α = 0.81		95.7	1.03	−77.5
B = aM + bM^3/4	a = 0.00021, b = 0.0064	30	95.8	1.00	−78.7
B = aM + bM^β	a = 0.00021, b = 0.0064, β = 0.750	30	95.8	1.00	−76.7
Flying Birds (N = 510)
B = cM^α	c = 0.143, α = 0.657		88.4	1.04	−1309
B = aM + bM^2/3	a = 0.0001, b = 0.137	1370	90.9	1.01	−1308
Flightless Birds (all, N = 22)
B = cM^α	c = 0.062, α = 0.744		90.2	0.75	−55.0
B = aM + bM^2/3	a = 0.0014, b = 0.092	66	85.7	0.69	−52.8
Flightless Birds (without outliers, N = 20)
B = cM^α	c = 0.041, α = 0.805		98.6	0.88	−53.5
B = aM + bM^2/3	a = 0.0042, b = 0.062	17	98.7	0.88	−54.5
Insects
B = cM^α	c = 0.007, α = 0.832		60.4	1.04	0.85
B = aM + bM^2/3	a = 0.0046, b = 0.0021	0.46	58.9	1.09	7.00

See Statistical Methods section for details. The first three columns present the different fitting models considered for the different datasets, along with the parameter fits and ratio b/a (when applicable). The following columns display the goodness of fit results: the coefficient of determination r², reduced χ² and Akaike Information Criterion⁶³. In every case, we find that Eq. 2 is statistically compatible with the data and has in several cases better goodness of fit than other fitting models. A model selection approach (based on AIC) suggests that Eq. 2 outperforms a pure power law model with varying exponent for mammals, polar mammals alone, desert mammals alone, polar and desert mammals alone, flightless birds without outliers and plants. Additionally, note that the pure power law fitting model systematically requests different power law exponents for different databases, challenging the validity of the 2/3 or 3/4 laws, whereas in Eq. 2 the exponents are fixed and only prefactors vary.

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