Table 2 Output from the nonlinear mixed-effects modelling of N₂O production as an exponential function of experimentally induced decreasing oxygen.

Model	Parameter	Estimate	s.e.	t -value	P value	Random effect	Variance structure	AIC
M1	a	123.94	24.61	5.11	<0.001	Yes	No	746
	b	0.0535	0.010	5.12	<0.001	No
M2	a	120.57	24.17	4.99	<0.001	Yes	Yes	730
	b	0.0514	0.011	4.37	<0.001	No
M3	a	133.44	22.95	5.81	<0.001	Yes	Yes	728^*
	b	0.0732	0.015	4.72	<0.001	Yes
M4	a	137.44	23.09	5.95	<0.001	Yes	No	742
	b	0.0780	0.015	5.05	<0.001	Yes
M5	a	612.62	149.7	4.09	<0.001	Yes	Yes	NA
	b	0.0681	0.009	6.84	<0.001	No

NA, not applicable.
^*M3 had the lowest AIC score but its random intercept (a) and exponent (b) were highly correlated (r=−0.99), which suggested that the model was over parameterized and therefore M2 was taken as the most parsimonious fit to the data.
The goodness of fit for each model to the data was judged using the Akaike Information Criterion (AIC), where a lower value indicates a better fit. M2 and M3 were improved further by the addition of a power variance structure at the level of each of the 12 experiments. Note that M5 was fitted to data calculated assuming a bacterial mode of N₂O production with random isotope pairing of ¹⁴NO and ¹⁵NO using equations (6 and 7) (pN₂O_total′) and, as such, comparison with the other models using AIC is not appropriate. In addition, note the far higher intercept in M5, which manifests as over production of N₂O in Fig. 5b.

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