A number of nonlinear models have recently been
proposed for simulating soil carbon decomposition. Their
predictions of soil carbon responses to fresh litter input and
warming differ significantly from conventional linear models.
Using both stability analysis and numerical simulations,
we showed that two of those nonlinear models (a two-pool
model and a three-pool model) exhibit damped oscillatory responses
to small perturbations. Stability analysis showed the
frequency of oscillation is proportional to q
ε−1 − 1

Ks/Vs
in the two-pool model, and to q
ε−1 − 1

Kl/Vl
in the threepool
model, where ε is microbial growth efficiency, Ks and
Kl are the half saturation constants of soil and litter carbon,
respectively, and Vs and Vl are the maximal rates of carbon
decomposition per unit of microbial biomass for soil and litter
carbon, respectively. For both models, the oscillation has
a period of between 5 and 15 years depending on other parameter
values, and has smaller amplitude at soil temperatures
between 0 and 15 ◦C. In addition, the equilibrium pool
sizes of litter or soil carbon are insensitive to carbon inputs in
the nonlinear model, but are proportional to carbon input in
the conventional linear model. Under warming, the microbial
biomass and litter carbon pools simulated by the nonlinear
models can increase or decrease, depending whether ε varies
with temperature. In contrast, the conventional linear models
always simulate a decrease in both microbial and litter carbon
pools with warming. Based on the evidence available,
we concluded that the oscillatory behavior and insensitivity
of soil carbon to carbon input are notable features in these
nonlinear models that are somewhat unrealistic. We recommend
that a better model for capturing the soil carbon dynamics
over decadal to centennial timescales would combine
the sensitivity of the conventional models to carbon influx
with the flexible response to warming of the nonlinear model.