ecological modelling 211 ( 2 0 0 8 ) 182–190 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/ecolmodel Heterotrophic soil respiration—Comparison of different models describing its temperature dependence Mikko Tuomi a,b,* , Pekka Vanhala a , Kristiina Karhu a , Hannu Fritze c , Jari Liski a a Finnish Environment Institute, Mechelininkatu 34a, P.O. Box 140, 00251 Helsinki, Finland b University of Helsinki, Department of Mathematics and Statistics, Gustaf H ¨ allstr ¨ omin katu 2b, P.O. Box 68, Helsinki, Finland c Finnish Forest Research Institute, Vantaa Research Center, P.O. Box 18, 01301 Vantaa, Finland article info Article history: Received 22 May 2007 Received in revised form 31 August 2007 Accepted 7 September 2007 Published on line 22 October 2007 Keywords: Heterotrophic respiration Markov chain Monte Carlo Probabilistic model comparison abstract Several models are used to describe the temperature dependence of heterotrophic soil respi- ration. Six such models are examined here in detail against incubation measurements from different sources. These models are compared using common sums of squared residuals, Bayesian model probabilities and Markov chain Monte Carlo (McMC) samplings of model parameter spaces. The McMC samples were calculated to study the probability distribu- tions of model parameters in detail. We show that the temperature dependence can be described best using a Gaussian model. The often-used Q 10 value as well as four other com- monly used models either produce poor fittings or parameter distributions too correlated to be considered useful. © 2006 Elsevier B.V. All rights reserved. 1. Introduction Quantifying the temperature dependence of heterotrophic soil respiration is a problem commonly occurring during study of the cycling of carbon and other organic matter-related ele- ments in terrestrial ecosystems. Mathematical formulations of this dependence are used to analyse and compare measure- ments (e.g. Lloyd and Taylor, 1994; Fang and Moncrieff, 2001). They are also needed to describe this process for larger sim- ulation models (e.g. Parton et al., 1987; Jenkinson, 1990; Liski et al., 2005). For both these purposes, a widely applicable and reliable formulation would be necessary. A simple exponential function is perhaps the most com- monly used formulation for the temperature dependence of heterotrophic soil respiration. This function implies that the magnitude of temperature sensitivity is independent of tem- perature in proportional terms. However, the temperature sensitivity of decomposition is known to decrease with higher ∗ Corresponding author. E-mail addresses: mikko.tuomi@ymparisto.fi, mikko.tuomi@utu.fi (M. Tuomi). temperatures (Kirschbaum, 1995; Tjoelker et al., 2001). There are more complicated equations, e.g. the Arrhenius equation and its derivatives, that account for this feature (Lloyd and Taylor, 1994, and references therein). The Arrhenius equa- tion has, in addition, solid theoretical bases for describing the reactions of single chemical compounds. However, these bases may not be valid for the decomposition of soil organic matter, which is a product of numerous chemical, physical and biological processes (Davidson and Janssens, 2006). Many other functions have also been introduced but consensus is still lacking on the best model, or even a small group of the best models, for describing the temperature dependence of soil organic matter decomposition. One reason for the missing consensus on appropriate temperature-dependence models may be differences in the data used to develop and test the models. Another reason may lie in the inadequate mathematical analyses conducted and the criteria employed in evaluating the models. Goodness of 0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2007.09.003