Table 1 Comparing fitting models to the prokaryote abundance distribution.

	ΔAIC PL	ΔAIC TPL	ΔAIC LN	ΔAIC Weibull	α	standard error (α)	β	λ
Upper ocean	0.47	0	0.74	0.77	1.57	0.09	1.34	0.000019
Deep ocean	0.03	0	2.01	15	0.89	0.02	0.73	0.000002
Mesocosm C1	23	0	8.44	5.84	0.52	0.02	0.41	0.000106
Mesocosm C2	0	2	2.01	3.00	0.52	0.31	0.52	0
Mesocosm C3	19	0	13	11	0.53	0.02	0.43	0.000088
Mesocosm C4	26	0	8.36	5.57	0.54	0.02	0.42	0.000119
Mesocosm C5	38	0	13	9.49	0.57	0.02	0.38	0.000178
Mesocosm C6	18	0	13	11	0.52	0.02	0.44	0.000080

The delta Akaike Information Criterion (ΔAIC) indicates the most likely fit (value 0 in bold) and the difference to the most likely fit. For the six cases reported, the most likely fit is a distribution with a power-law decay (either pure or truncated). The parameters of a power law distribution P(x) ~x ^{−1− α} are the scaling exponent α; for the truncated power-law P(x) ~ x ^{−1− β} exp(−λx), are the scaling exponent β, and the characteristic abundance λ (λ = 0, for a pure power-law). ΔAIC PL: delta Akaike Information Criterion for power-law distribution fit; ΔAIC TPL: delta Akaike Information Criterion for truncated power-law distribution fit; ΔAIC LN: delta Akaike Information Criterion for log-normal distribution fit; ΔAIC W: delta Akaike Information Criterion for Weibull distribution fit. The standard error of the power-law scaling exponent (α) is also reported. For the upper ocean, the prokaryote abundance distribution shows a double power-law regime. A Maximum Likelihood Estimation for a double power-law model gives P(x) ~ x ^{−1− δ}, with exponent δ = 1.54 for x < 2,313; and P(x) ~x ^{−1− α}, with exponent α = 0.36 for x ≥ 2313 (see Materials and Methods).

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