Carbon use efficiency (CUE) is a fundamental parameter for ecological models based on the physiology of microorganisms. CUE determines energy and material flows to higher trophic levels, conversion of plant-produced carbon into microbial products and rates of ecosystem carbon storage. Thermodynamic calculations support a maximum CUE value of ~ 0.60 (CUE max). Kinetic and stoichiometric constraints on microbial growth suggest that CUE in multi-resource limited natural systems should approach ~ 0.3 (CUE max/2). However, the mean CUE values reported for aquatic and terrestrial ecosystems differ by twofold (~ 0.26 vs. ~ 0.55) because the methods used to estimate CUE in aquatic and terrestrial systems generally differ and soil estimates are less likely to capture the full maintenance costs of community metabolism given the difficulty of measurements in water-limited environments. Moreover, many simulation models lack adequate representation of energy spilling pathways and stoichiometric constraints on metabolism, which can also lead to overestimates of CUE. We recommend that broad-scale models use a CUE value of 0.30, unless there is evidence for lower values as a result of pervasive nutrient limitations. Ecosystem models operating at finer scales should consider resource composition, stoichiometric constraints and biomass composition, as well as environmental drivers, to predict the CUE of microbial communities.
Most of the net primary production of the biosphere is mineralised through decomposer food webs (Cebrian & Lartigue 2004). The trophic base of these food webs is the production of microbial biomass from the catabolism of detrital organic matter. The efficiency of this conversion, often termed carbon use efficiency (CUE), controls the conversion of plant-produced carbon into microbial products, rates of ecosystem carbon storage, and energy and material flows to higher trophic levels (Six et al. 2006; Miltner et al. 2012).
The terms growth yield, growth efficiency, metabolic efficiency and CUE are variously defined and sometimes used interchangeably. Adding to the confusion, these ratios are estimated using a variety of methods that differ in their capacity to represent the metabolism of microbial communities. These difficulties complicate comparisons between systems and impede the development of predictive models (Manzoni et al. 2012). Herein, we address these issues by considering the thermodynamic, physiological and ecological constraints on microbial growth; the role of multi-resource stoichiometry in regulating the growth of microbial communities; the limitations of existing methodologies for assessing microbial community growth; and the options for representing microbial community growth in ecological models. Our goals are to clarify apparent inconsistencies in the literature, emphasise the commonalities of microbial community metabolism across systems and recommend strategies for representing the CUE of microbial communities in ecological process models.
2. Microbial CUE: Definitions and Controls
The thermodynamics of microbial growth can be measured in multiple currencies. Analyses that calculate growth yields (Y) as cells per mole of adenosine triphosphate (ATP) formed during growth (YATP), yields per substrate electron available for respiration or incorporation into cellular material (Yav e−), and yields per kilocalorie of total energy consumed from the medium by both assimilation and dissimilation (Ykcal) converge on a maximum value of approximately 0.60 (Payne 1970; Payne & Wiebe 1978; Roels 1980; Von Stockar & Marison 1993; Lettau & Kuzyakov 1999).
In ecological studies, growth yields are generally calculated in terms of carbon, rather than energy. In this paper, we refer to growth yields calculated from rates of carbon transformation as CUE, typically (though not always) defined as the ratio of growth (μ) to assimilation, that is, CUE = μ/(μ + R), where R includes any C losses to respiration (Sterner & Elser 2002; Manzoni et al. 2012). Using this definition, CUE is generally greater than zero and limited to a maximum value set by thermodynamic constraints. However, CUE can be negative if some metabolic costs are considered external to the assimilation of carbon leading to μ < 0 (Wang et al. 2012a,b), as when biomass declines because losses through respiration and/or mortality exceed C income. The definition of CUE as growth-to-assimilation ratio is consistent with most ecological models of microbial metabolism, and is thus useful for comparing empirical and modelling studies.
Microbial growth rates, biomass composition and environmental C and nutrient availability vary across systems, but these parameters are interrelated through evolutionary legacies such that growth rate (μ) and CUE can be represented as functions of environmental resource supply in relation to biomass composition (Elser et al. 2003; Gillooly et al. 2005; Frost et al. 2006; DeLong et al. 2010; Doi et al. 2010; Franklin et al. 2011). Thus, CUE is a measure of the energetic and material costs of sustaining an autocatalytic organism in a particular environment. The maximal value of CUE (CUEmax) is fixed by thermodynamic constraints (Roels 1980), but the realised CUE of microbial communities varies with environmental conditions, substrate availability, stoichiometry, and the physiological state and composition of the community (Manzoni et al. 2012).
CUE tends to increase with growth rate because total maintenance costs, included in R, often decrease relative to assimilation (del Giorgio & Cole 1998; Van Bodegom 2007; Robinson 2008). Some CUE estimates exceed thermodynamic maxima for growth yields because the measurements do not capture the full maintenance costs of metabolism, and catabolic and anabolic processes can be temporally displaced (Gommers et al. 1988; Russell & Cook 1995), as discussed in section 'Respiration and growth'. CUE can be relatively high when C availability (i.e. energy) is limiting, which couples catabolic and anabolic metabolism. In contrast, carbon sources that are recalcitrant to decomposition, as the result of stochastic oxidation and condensation reactions in the environment, may reduce CUE by increasing the cost of extracellular and intracellular catabolism (Blagodatskaya & Kuzyakov 2008). Nutrient limitation can also reduce CUE by uncoupling catabolism and anabolism through energy spilling pathways and increased extracellular production of enzymes and polysaccharides (Larsson et al. 1995; Russell & Cook 1995). In addition, environmental variables such as temperature and soil moisture alter microbial metabolism, shifting the balance of μ and R, and thereby CUE (Allison et al. 2010; Manzoni et al. 2012). This variability of CUE with respect to metabolic, environmental and stoichiometric factors is largely neglected in ecosystem models. In the sections that follow, we consider these constraints in a unifying framework that bridges terrestrial and aquatic systems, based on the premise that the metabolic and stoichiometric constraints on microbial metabolism are broadly similar across ecosystems.
3. Microbial Community Metabolism and Stoichiometry
3.1 Respiration and growth
The relationship of CUE to growth and respiration rates is nonlinear. On broad scales, faster biomass-specific growth rates generally increase CUE in a saturating fashion as it approaches the thermodynamic limit (CUEmax). This large-scale pattern masks several confounded factors. For example, productivity may be greater in relatively cold, nutrient-rich water bodies than in warmer oligotrophic ones. As a result, CUE decreases as temperature increases, but the trend can result from declining nutrient availability rather than a different temperature sensitivity for growth and respiration (Lopez-Urrutia & Moran 2007). This example indicates that both environmental constraints and resource supply need to be considered in interpreting CUE patterns and representing CUE in models.
For organisms, communities and ecosystems, the temperature sensitivity of respiration is largely determined by the activation energy of the respiratory electron transport system (~ 0.62 eV) (Brown et al. 2004; Yvon-Durocher et al. 2012). Within this pattern, the ‘apparent’ activation energy for microbial respiration may vary with local conditions because resource supply and other environmental factors affect responses to temperature (e.g. Ågren & Wetterstedt 2007; Wagai et al. 2013). For example, activation energies for the mineralisation of recalcitrant organic matter by microbial communities can be greater than 0.62 eV because more enzymatic steps are needed to transform organic carbon into CO2 (Sierra 2012). Ramirez et al. (2012) reported a value of ~ 0.85 eV for microbial respiration from 28 soils in unamended microcosms maintained for 1 year.
Because CUE represents the ratio of growth to assimilation rates, differences in the temperature sensitivity of these two components causes variations in CUE as a function of temperature. Generally, respiration increases more than growth as a function of temperature, so that CUE tends to decrease with temperature, in both soils and aquatic systems (Rivkin & Legendre 2001; Allison et al. 2010; Wetterstedt & Ågren 2011).
Other environmental drivers such as water availability in soils may also uncouple growth and respiration, causing shifts in CUE. In a short-term water stress event, for example, CUE increases as osmoregulatory solutes and storage compounds are accumulated (Uhlířová et al. 2005; Herron et al. 2009). However, in the long term CUE is reduced by repeated stress events, as the cumulative effects of the C costs for water stress responses become apparent (Tiemann & Billings 2011). Aquatic organisms may experience similar effects in response to fluctuating salinity conditions.
As resource supply or composition shifts, microorganisms, as individuals or communities, respond to changes in resource availability by altering the kinetics of enzyme-mediated assimilation pathways (Button 1993; Narang 1998; Hobbie & Hobbie 2012). Monod models describe enzyme-mediated uptake (I) as a saturating function of substrate or nutrient concentration (C), I = Imax C/(C + Ks), where Imax is the maximum uptake rate and the Ks is the half-saturation constant. In natural systems, the availability of substrates for uptake is generally linked to the activities of extracellular enzymes that deconstruct macromolecules. These activities are represented by Michaelis–Menten models, V = Vmax S/(S + Km), where Vmax is the maximum reaction rate and the Km is the half-saturation constant. Selective pressures to optimise uptake rate in relation to the resource costs of sustaining the uptake system are such that the Monod parameters C, Imax and Ks and the Michaelis–Menten parameters S, Vmax and Km are correlated, with C ≈ Ks and S ≈ Km (Williams 1973; Lobry et al. 1992; Sinsabaugh & Follstad Shah 2010; Hobbie & Hobbie 2012). As a result, equilibrium values of I and V approach Imax/2 and Vmax/2 and the ratio of growth rate (μ) to Ks remains relatively constant. A pulse of substrate that exceeds the concentration to which the community has adapted will result in an increase in uptake, which transiently uncouples catabolism and anabolism. An analogous effect is expected if there is a transient loss of a key substrate. As assays of microbial growth are often conducted over short-time intervals (one-to-few hours), a dynamic system with respect to substrate availability may show considerable variance in μ (and CUE). As the temporal scale expands to ecosystem models, CUE variation will attenuate, approaching the value of a steady-state system.
The need to allocate cellular resources to optimise the acquisition of multiple essential nutrients imposes additional limits on microbial growth and growth efficiency (Chen & Christensen 1985; Zinn et al. 2004; Cherif & Loreau 2007; Danger et al. 2008; Franklin et al. 2011). Sinsabaugh & Follstad Shah (2012) proposed a community growth model that incorporates the co-limiting effects of multiple resource acquisition:
where Si and KSi are, respectively, the concentration and half-saturation constant of resource i. The premise of the model is that the acquisition of multiple resources by a microbial community is neither wholly independent nor fully integrated across the constituent populations. Because nutrient assimilation is a saturating function, growth increases sublinearly with environmental nutrient concentration, approaching an asymptote (μmax) that represents the maximum capacity of a cell. At the community scale, biomass increases may allow growth to continue rising until pressed by another limit. CUE may increase with growth rate, if fixed maintenance and respiratory costs per unit biomass decline as a fraction of energy and material income. Alternatively, growth limitation caused by limited availability of an essential non-carbon element may decouple growth from respiration, decreasing CUE.
The elemental C, N and P composition of microbial biomass varies narrowly relative to environmental variation in C, N and P availability. The mean C : N ratios for microbial biomass in soils, plankton and aquatic ecosystems are 8.6, 6.6 and 8.3 respectively; C : P ratios are more variable with means of 60, 106 and 166 (Cleveland & Liptzin 2007; Sterner et al. 2008; Manzoni et al. 2010; Sistla & Schimel 2012). Variation within and across systems is about twofold for C : N and threefold for C : P (Sardens et al. 2012). These stoichiometric requirements for biomass production force microbial communities to adapt their foraging strategies to the available substrates, which affects rates of growth and respiration.
In stoichiometric theory, nutrient-limited growth occurs when the availability of an essential element (E) relative to carbon (C : E) falls below the critical ratio or threshold element ratio (TER) required for optimum growth. The relationship between TERC : E and CUE is commonly defined by
where AE is the assimilation efficiency of element E and BC : E is the C : E ratio of biomass (Frost et al. 2006; Manzoni & Porporato 2009). This definition is typically adopted in litter and soil biogeochemical models with the assumption that AE = 1 (Bosatta & Staaf 1982). In contrast, Doi et al. (2010) define TERC : E as
where GEmaxE and GEmaxC are maximum growth efficiencies with respect to C and E. These definitions highlight a confusing issue in the literature regarding the interpretation of TER. Studies of ectothermic animals focus on variation in assimilation efficiency, which is calculated as a fraction of ingestion, and biomass composition as the principal determinants of TER because CUE is relatively constant. For osmotrophic microbial communities, assimilation efficiency is a problematic concept, given that ingestion and assimilation are not distinct processes, and CUE can vary considerably, implying that TER has a similar variance.
Moreover, AE may also vary with the physical structure of the environment. In soils, for example, pore-scale spatial heterogeneities in substrate availability and stoichiometry may cause transfer of nutrients between microbial populations in different patches. At larger scales, that is, soil core, these transfers may manifest as lower nutrient assimilation efficiency (AE < 1) (Manzoni et al. 2008).
Traditionally, the TERC : N for terrestrial microbial communities is considered something close to a constant with a value of 20–25, based on empirical studies that measure the critical transition in organic matter decomposition from net N immobilisation to net N mineralisation (Berg & McClaugherty 2003). However, these studies focused on the mineralisation of plant residues with relatively low C : N ratios. An expanded analysis that includes litter types with C : N ratios ranging from 10 to 1000 (i.e. including conifer litter and wood) suggests that TERC : N does scale with the initial litter C : N ratio, implying that CUE decreases with increasing litter C : N (Fig. 1b). This analysis is based on the assumptions that the CUE and microbial composition are constant through time, and that BC : N does not depend on substrate quality. As a result, a single value of TER is obtained for each substrate type. A more recent study including variability in BC : N and thus TER, however, shows similar (albeit weaker) patterns (Ågren et al. 2013).
It is important to emphasise that the scaling of TERC : E and C : E is sublinear, implying (1) that AN (eqn (2)) may not be a constant and (2) changes in CUE do not fully compensate for the stoichiometric imbalance between litter and decomposer biomass. This gap leads to N immobilisation when litter C : N ratio is high. In other terms, CUE can be greater than predicted by the bulk C : N ratio of the litter either because nutrients are translocated from the surrounding environment (net immobilisation) or opportunistic microorganisms are selectively targeting low C : E substrates within the litter matrix (Allison 2005; Bastian et al. 2009). Nonetheless, as litter decomposition progresses N immobilisation and community CUE generally increase, and TER declines until the critical value 20–25 is reached. What remains unclear is whether microbial community CUE continues to increase (and TERC : N decrease) as the C : N ratio of soil organic matter moves below the N immobilisation-mineralisation threshold. If TERC : N does not decrease, CUE is expected to decline as C increasingly becomes the limiting resource. Complicating this issue is the increasing recalcitrance of the residual organic matter to decomposition, which is associated with slower microbial growth, and presumably lower CUE.
The Doi et al. (2010) formulation, which defines TER as the element ratio corresponding to maximum growth efficiencies (eqn (3)), circumvents the problem of defining assimilation efficiency for osmotrophs. The ratio GEmaxN/GEmaxC appears to have a narrow range of variation with a mean value of approximately 1.4 (Herron et al. 2009; Jones et al. 2009; Doi et al. 2010; Zeglin et al. 2012). If so, eqn (3) predicts that TERC : N is directly proportional to BC : N, rather than a function of CUE as represented in eqn (2). As a result, the TERC : N values predicted by eqn (3) vary more narrowly than those predicted by eqn (2). The Doi et al. (2010) formulation more closely approximates traditional ecological conceptions of the role of nutrient availability in regulating microbial community metabolism. From this perspective, maximal growth efficiency is predicted when the environmental availabilities of all essential elements are at their TER, or when nutrient concentrations are great enough to saturate available uptake capacity, conditions that are rare in natural environments.
While TER values are useful indicators of relative nutrient limitation, CUE can be more directly modelled as a function of nutrient and substrate availabilities. To evaluate the relationship between CUE and substrate C : E, Manzoni et al. (2010) developed a model describing remaining C and N during litter decomposition. The model explicitly accounts for CUE (e in their notation) and can be used to estimate the value of CUE through nonlinear fitting of the C and N data. The estimated CUE, averaged over the course of decomposition, declined with increasing initial litter C : N and C : P ratios (Fig. 1a), providing a scaling relationship linking substrate stoichiometry to CUE. This declining pattern also leads to increasing TER values as the C : N and C : P of the litter widens. For litter with an initial C : N ratio of 50–70 (global averages for initial litter C : N and C : P ratios are 57 and 1217 on a mass basis, McGroddy et al. 2004), the CUE for decomposition is predicted to be about half the maximum CUE achieved with high-nutrient substrates, approximately 0.3 (Fig. 1a).
Sinsabaugh & Follstad Shah (2012) presented a stoichiometric model that relates ecoenzymatic activities (EEA), biomass composition and environmental nutrient concentrations to the CUE of heterotrophic microbial communities.
where CUE max is set at 0.60; SC : N = BC : N/LC :N ·1/EEAC : N and SC : P = BC : P/LC : P·1/EEAC : P; LC : N and LC : P are the elemental C : N and C : P ratios of labile organic matter; KC : N and KC : P are half-saturation constants; EEAC : N = BG/(LAP + NAG); EEAC : P = BG/AP where BG, AP, NAG and LAP are the potential activities of β-1,4-glucosidase, acid (alkaline) phosphatase, β-1,4-N-acetylglucosaminidase and leucine aminopeptidase respectively. These indicator enzymes generate assimilable nutrients from the principal organic sources of C, N and P (β-linked glucans, protein and aminopolysaccharides, and phosphoesters respectively). AP and AN are assimilation efficiencies for P and N. BC : P and BC : N are the elemental C : P and C : N ratios of microbial biomass. The parameters SC : N and SC : P are scalar measures of resource availability for microbial growth based on the composition of available organic matter and the relative distribution of EEA. The model is a saturating function that predicts community CUE as a geometric mean of N and P supply relative to C. Using global EEA data sets, the model yields similar estimates of mean CUE for terrestrial soils, freshwater sediments and plankton (0.29, 0.27, 0.28, respectively, approximately CUEmax/2) even though relative nutrient availabilities, EEA and biomass composition vary across these systems (Sinsabaugh & Follstad Shah 2012).
Assuming for simplicity that only N limits decomposition, eqn (4) can be reduced to CUE/CUEmax = (1 + KC : N·EEAC : N·LC : N/BC : N)−1. Fitting this simplified expression to the CUE measured in soils and estimated from the stoichiometric model by Manzoni et al. (2010) yields a numerical value for the term KC : N·EEAC : N/BC : N = 0.0155 (solid line in Fig. 1), which corresponds to a CUE/CUEmax value of 0.82 for soils and litter. Using the mean soil values for these parameters given by Sinsabaugh & Follstad Shah (2012), KC : N = 0.5, EEAC : N = 1.434, BC : N = 8.6, their predicted value for CUE/CUEmax is 0.46. The latter estimate implies that the mean value of AN for soils (eqn (2)) is approximately 0.5, rather than the generally assumed value of 1. This lower estimate may be reasonable for soils considering the net mineralisation of N and the competition for mineral nitrogen by plants and dissimilatory microbial processes. If AN decreases as the C : N ratio of organic matter narrows, then TERC : N is less variable than eqn (2) otherwise predicts, bringing the formulations of TERC : N in eqns (2), (3) into congruity. Indeed, the equations yield similar values for the mean TERC : N of soils (14.3 for eqn (2), 12.1 for eqn (3)), assuming mean BC : N = 8.6, AN = 0.5, CUE = 0.3, and GEmaxE/GEmaxC = 1.4. These TERC : N estimates approximate the mean C : N ratio of soil organic matter (14.3 ± 0.5 SE, Cleveland & Liptzin 2007).
A simpler model of CUE can be constructed by assuming that all the carbon taken up by microbes that cannot be used for growth at a given BC : N due to limited N availability is mineralised through overflow respiration (Moorhead et al. 2012; Manzoni & Porporato 2009; Schimel & Weintraub 2003). Assuming AN = 1 and neglecting maintenance respiration, CUE is equal to CUEmax when LC : N < ANBC : N/CUEmax (~ 14.3 for BC : N = 8.6, CUEmax = 0.6, AN = 1) and equal to ANBC : N/LC : N when LC : N > ANBC : N/CUEmax:
where LC : N is the substrate C : N ratio as in eqn (4). If, for example, AN is 0.5 as eqn (4) implies, eqn (5) predicts that CUE at LC : N = 14.3 (the mean C : N ratio of SOM) equals CUEmax/2 with CUE = CUEmax at LC : N < 7.1. If AN remains constant at 1.0, CUEmax/2 occurs at LC : N ~ 28, which approximately corresponds to the ecological transition from net N immobilisation to net N mineralisation. This minimal model does not consider net immobilisation of mineral N as a mechanism to compensate for large substrate C : N ratios, which increase the sensitivity of CUE to changes in organic matter C : N. Because it neglects N immobilisation, this minimal model underestimates CUE when BC : N is assumed equal to a reasonable value of 10 for litter (note the bias in the dashed line in Fig. 1a). Nevertheless, it predicts that CUE is inversely related to LC : N when the C : N ratio is wide, consistent with empirical data. Fitting eqn (5) to the estimated CUE (dashed line Fig. 1) yields a value for the term ANBC : N (the only fitting parameter) near 15. If TERC : N is also approximately 15, then CUE by soil microbial communities should approach CUEmax, which is consistent with empirical estimates. If TERC : N is 28, then the CUE of soil microbial communities approximates CUEmax/2.
All three stoichiometric models (eqns (2), (4) and (5)) highlight the key problem of resolving the relationship between AN, TERC : N and CUE. If AN for soil microbial communities averages 0.5, as eqn (4) predicts based on EEA, then the mean CUE for soils is approximately CUEmax/2, consistent with predictions and measurements for aquatic ecosystems. If AN = 1, then the mean CUE of soil microbial communities approaches CUEmax, consistent with measurements for soil ecosystems. In the next section, we argue that the apparent discrepancy between model predictions and experimental measurements is likely the result of differences in the methodologies used to estimate CUE in aquatic and terrestrial ecosystems, rather than a fundamental difference in microbial community metabolism.
4. Measuring the CUE of Microbial Communities
For aquatic ecosystems, the CUE predictions of stoichiometric models are consistent with empirical estimates. del Giorgio & Cole (1998) compiled data on bacterial metabolism in aquatic environments. For rivers, oceans, lakes and estuaries, mean CUE ranged from 0.22 to 0.32. Bacterial respiration (R) increased sublinearly with production (standardised major axis regression: R = 3.42 μ0.61, units = μgC l−1 h−1). A more recent analysis by Robinson (2008) yielded R = 3.69 μ0.58 (μgC l−1 h−1, ordinary least squares regression). Consequently, CUE generally increases with production, approaching an asymptote of approximately 0.50, with a global average of 0.26 (~ CUEmax/2) (del Giorgio & Cole 1998).
A more recent compilation by Manzoni et al. (2012) reported mean CUE values of 0.20–0.30 for lacustrine, estuarine, coastal and riverine systems, as well as microbial cultures. The mean CUE for mid-ocean bacterioplankton was 0.12; similar values were calculated by del Giorgio & Cole (1998) and Robinson (2008). Presumably, the low CUE of marine bacterioplankton reflects the low availability of essential nutrients and labile carbon.
For terrestrial ecosystems, the average microbial CUE for litter decomposition is approximately 0.3 (CUEmax/2, Fig. 1). The mean measured CUE for soil microbial communities is 0.55 (Fig. 1, see also Manzoni et al. 2012), a value that approaches the thermodynamic limits of metabolic efficiency. This value is at odds with the lower CUE prediction of 0.29 from eqn (4), but consistent with the prediction of eqn (5), assuming AN = 1. This twofold discrepancy in CUE estimates impedes development of simulation models for soil processes that incorporate microbial community growth. We argue that the resolution of this issue lies in considering the methodological limitations inherent to measurements of microbial community growth.
There are several methods for estimating CUE. For cultures, direct measurements of mass balance can be made. In natural systems, measurements typically rely on quantifying the transformation of labelled compounds. In aquatic ecosystems, bacterial growth rates are most commonly estimated by measuring rates of biosynthesis using 3H-thymidine (TdR) incorporation into DNA or 3H-leucine (Leu) incorporation into protein (Bell 1993; Findlay 1993; Kirchman 1993). Following a short incubation (~ 1 h), unincorporated label is rinsed away, samples are digested in trichloroacetic acid, and the nucleic acid or protein fractions are isolated for radioisotopic analysis. Production rates expressed in units of carbon are calculated using conversion factors determined from mass-balance calibrations; estimated values for these conversion factors vary about threefold (Kirchman & Ducklow 1993). Concurrent measurements of 3H-TdR and 3H-Leu incorporation show that rates of DNA and protein biosynthesis may differ by up to tenfold. Fungal growth rates can be measured similarly by quantifying 14C-acetate incorporation into ergosterol (Newell & Fallon 1991). To calculate CUE as μ/(μ + R), these production assays must be accompanied by respiration measurements as either oxygen consumption or carbon dioxide production. Because respiration measurements are generally not as sensitive as the production assays, measurements are often made over longer time intervals, which may introduce additional variation into CUE estimates.
Estimating microbial growth rates in soils is more difficult. The medium is a heterogeneous mix of organic and mineral particles of diverse composition, size and aggregation. Pore volume is generally not water saturated and the kinetics of nutrient consumption are conflated with the kinetics of sorption and diffusion (Resat et al. 2012). The 3H-TdR, 3H-Leu and 14C-acetate production assays are not widely used for soils for methodological reasons, but there are protocols available (Rousk & Bååth 2011). Applying these assays, the turnover rates (μ/B) for bacterial and fungal biomass in soils are similar to those for aquatic ecosystems (Su et al. 2007; Rousk & Bååth 2011). More commonly, growth rates in soils are estimated from the rate of incorporation of labelled labile carbon substrates into biomass, rather than as rates of community biosynthesis. However, short-term incorporation of labelled substrates into biomass is not necessarily a measure for growth, but rather an estimate of community uptake rate. In addition, most approaches to measure soil CUE quantify respiration in terms of the labelled substrate and therefore do not capture maintenance and growth respiration, leading to an overestimate of CUE. Consequently, this approach may be better described as measure of instantaneous substrate use efficiency than a community CUE. Conceptually, these values may be more closely related to the A terms in eqns (4), (5), than to CUE. If considered as such, eqns (4), (5) predict that CUE for soil microbial communities is similar to that of aquatic ecosystems.
Other limitations of this approach that tend to inflate CUE have been extensively discussed (e.g. del Giorgio & Cole 1998; Frey et al. 2001; Herron et al. 2009). To summarise, most CUE estimates for soil are based on short-term incubations during which microbial uptake rates (and eventually biomass growth) are stimulated by relatively large substrate additions, yielding high apparent CUE. Over time, the initial CUE associated with a labile substrate pulse declines as energy generation and maintenance processes progress (Ladd et al. 1992; Hart et al. 1994; Ziegler et al. 2005). Such a decline is illustrated in Fig. 2 using the soil biogeochemical model developed by Schimel & Weintraub (2003).
The root of the pulse problem is the difficulty of determining the size of bioavailable substrate pools. Microbial communities exhibit multiphasic kinetics. Empirical estimates of the kinetic parameters Km, Ks, Vmax, μ increase as substrate concentrations increase. When ‘tracers’ are added in quantities that exceed ambient bioavailable substrate concentration, the rates are not representative of in situ metabolism. In a review of amino acid cycling in planktonic and soil systems, Hobbie & Hobbie (2012) conclude that uptake of labelled amino acids in soils does not follow Michaelis–Menten kinetics. They attribute this finding in part to the use of substrate concentrations well in excess of ambient bioavailable concentrations, which may be well below extractable concentrations. They also note that nutrient delivery in soils tends to follow a pulse pattern tied to environmental fluctuations such as wet-dry and freeze-thaw cycles. These dynamics generate large stocks of microbial biomass with a high latent capacity to rapidly consume and store nutrient pulses (e.g. Boot et al. 2013). These difficulties are compounded if CUE is calculated using the rate of respiration of the labelled substrate because the respiratory rate of individual compounds is typically a function of the length of their catabolic pathway (Hobbie & Hobbie 2012). For example, Herron et al. (2009) used vapour phase additions of 13C-acetic acid and 15N-ammonia to measure CUE in relation to soil water content. The uptake and respiration of label were relatively insensitive to soil water content, except for very dry soils, but total soil respiration rate increased steadily with soil water content.
This observation highlights another issue: the consumption and fate of a single labile substrate may not reflect microbial community metabolism in toto, because (1) simple substrates can be consumed without preliminary solubilisation or depolymerisation steps (Shen & Bartha 1996); (2) consumption of a particular substrate may be restricted to a subset of the microbial community; and (3) fast-growing opportunist organisms may have higher CUE than slow-growing decomposers adapted to low substrate concentration (Shen & Bartha 1996). For example, Stursova et al. (2012) studied the incorporation of 13C-cellulose into the microbial biomass of litter and soil from a Picea abies forest over a 20 day period. Cellulose decomposition in the fungal-dominated litter was ten times faster than rates in soil but 13C accumulated largely in bacteria. In bacterial-dominated mineral soil, 13C accumulated largely in fungi. Stable isotope probing of community DNA showed that only 10–20% of the taxa present accumulated carbon from cellulolysis. Fungi tend to have wider C : N : P ratios than bacteria and larger C demands (Keiblinger et al. 2010). As a consequence, increasing substrate C : nutrient ratios might result in increased CUE in fungal communities, but decreased CUE in bacterial-dominated ones (Keiblinger et al. 2010).
Collectively, these problems suggest that CUE measurements in soil are inflated relative to those for aquatic ecosystems because the most widely used methodologies do not adequately represent microbial community growth and its associated maintenance costs, given the difficulties imposed by discontinuous water availability. Given the general correspondence between biosynthesis measurements and the predictions of metabolic and stoichiometric theories in other systems, we propose that these models are applicable to microbial community metabolism in soils as well and should be the basis for calibrating simulation models.
5. CUE Representation in Microbial Process Models
The CUE of microbial communities is a major driver of C dynamics and C sequestration potential in simulation models. One example is the widely used CENTURY model (Parton et al. 1988), which describes the dynamics of organic matter decomposition and stabilisation into soil organic matter pools in relation to climatic variables and soil characteristics. Figure 3 illustrates the sensitivity of the mean residence time of soil C from the CENTURY model as the efficiency of C transfer among pools (conceptually similar to CUE) is altered from its baseline value. Decreasing CUE from the default value of 0.55 decreases the mean residence time of soil C, implying less C sequestration. Clearly, not all soil models are structured like CENTURY, and changing mass loss rates together with CUE may buffer the sensitivity illustrated in Fig. 3. For example, Allison et al. (2010) showed that the interplay between increased decay rates and decreasing CUE as temperature increased may favour C storage. Nevertheless, these modelling exercises show that accurate estimates of CUE in soils, and elsewhere, are critical for grounding simulation models that use microbial metabolism to drive carbon dynamics.
Most models that include an explicit microbial pool usually include only the C costs associated with the production of biomass (Manzoni et al. 2012). Fewer also include a basic maintenance cost (e.g. Schimel & Weintraub 2003; Parnas 1975). These growth and maintenance costs are not easy to separate experimentally, but are convenient to model separately. Typically, a fixed fraction of standing biomass defines maintenance respiration (Rm) (e.g. Manzoni & Porporato 2009) and fractions of the leftover C-uptake in excess of this maintenance cost are allocated to a respiration component accompanying biosynthesis (growth-respiration, Rg) and biomass production (μ). Thus most models effectively define CUE as the ratio of μ/(μ + Rg) whereas in the broader literature, CUE is often (implicitly) considered the ratio of μ/(μ + Rg + Rm). These differing conceptions add confusion about CUE values generated by models. For comparison purposes, values of Rm from simulations should be included in estimates of CUE, which can add considerable variation to these estimates.
Variations in model estimates of CUE directly result from separating respiration into the two components, Rg and Rm. First, consistent with empirical data, CUE increases with growth rate (μ) if Rm remains a fixed fraction of biomass while μ becomes a larger component of the ratio μ/(μ + Rg + Rm). Second, CUE will vary with the composition of the substrate consumed because the ratio of μ/(μ + Rg) varies among substrates. Finally, CUE may also vary with temperature if Rg and Rm differ in their temperature sensitivities (Allison et al. 2010; Dijkstra et al. 2011; Wetterstedt & Ågren 2011). Consequently, many variations in CUE can emerge from simple model formulations.
Wang et al. (2012a,b) recently linked maintenance respiration (Rm) to C-uptake rate, rather than holding it at a constant fraction of standing biomass. Although this alternative approach did not have a large impact on the overall model behaviour unless the microbial community was C-limited, it raises questions about other factors affecting Rm. For example, if enzyme production is constitutive and has priority over Rm as claimed by Schimel & Weintraub (2003), then the relationship between Rm and Rg is not as simple as most models assume. In fact, Van Bodegom (2007) summarised eight non-growth components for microbial maintenance. Regardless of how many respiratory terms are included in decomposition models, any model that has at least one that is independent of carbon uptake has the potential to generate a negative CUE when carbon uptake is insufficient to meet maintenance demand.
More complex decomposition models separate respiration into as many as four components (Manzoni et al. 2012). Schimel & Weintraub (2003) and Moorhead et al. (2012) explicitly allocate (1) Rm, (2) Rg for both biomass and enzymes, separately, and (3) ‘overflow metabolism’ (Ro), which represents excess carbon released from litter under N-limitation. They define Rm and Rg, as described above, but calculate Ro by comparing the C : N ratios of substrates consumed with the C : N ratio of biomass and assuming that the excess carbon is respired. Equation (5) uses this approach. Changes in maintenance respiration or enzyme investment may thus alter CUE, as illustrated in Fig. 4, where steady-state CUE is shown as a function of both substrate C : N ratio and the maintenance respiration coefficient. Increasing maintenance respiration decreases CUE for any substrate C : N, but at high C : N ratios overflow respiration also contributes to the decline.
In most biogeochemical models, respiration is linked to microbial C balance, but not to the N balance, thus missing stoichiometric feedbacks on CUE, which are particularly important in the case of litter decomposition. Overflow respiration, represented as a consequence of C : N stoichiometry (e.g. Russell & Cook 1995), is seldom included in decomposition models (Manzoni & Porporato 2009).
Alternatively, when C-uptake is in excess of the stoichiometric requirements, some models include an excretion mechanism that transfers these products into a soluble pool that may not be immediately used by microorganisms (Hunt et al. 1983; Hadas et al. 1998). Similarly, if the uptake kinetics of the soluble pool are modelled separately from the hydrolysis of insoluble substrates then the two processes are partly decoupled. Spatially explicit models that include diffusion of enzyme, substrate and/or degradation products are a good example (Vetter et al. 1998; Allison 2005; Allison et al. 2010; Resat et al. 2012). These modelling approaches could affect estimates of CUE based on the mass balance of substrate, microbial and respiratory carbon flows. C and N investment in enzymes is also rarely considered (e.g. Runyan & D'Odorico 2012; Franklin et al. 2011; Schimel & Weintraub 2003), despite its potential role in the overall microbial C balance and stoichiometry.
Phosphorus dynamics are largely neglected in soil biogeochemical models (Manzoni & Porporato 2009), with a few exceptions (e.g. Hunt et al. 1983; Parton et al. 1988; Runyan & D'Odorico 2012). Resource allocation to P acquisition leads to reductions in CUE just as N-limitation. Because the C : N and C : P ratios of plant litter and soil organic matter are generally correlated (Cleveland & Liptzin 2007; Manzoni et al. 2010), decreasing CUE as nutrient availability decreases might be the result of co-limitation by both elements. In highly weathered low latitude soils, P availability is considered the primary limitation on microbial growth (Waring et al. 2013). The stoichiometric model proposed by Sinsabaugh & Follstad Shah (2012) (eqn (4)) represents N and P interaction by calculating CUE as a geometric mean of relative N and P availabilities. In this model, the need to allocate resources to acquisition of multiple resources both reduces and buffers CUE.
Another source of variation in model estimates of CUE is biomass stoichiometry, which may vary as a result of changing community composition, for example, the ratio of fungi: bacteria, or through changes in cellular metabolism, for example, production of storage compounds. In addition, the growth rate hypothesis states that growth rates are correlated with the density of P-rich ribosomes (Sterner & Elser 2002), suggesting that biomass P : C ratio may vary with growth rate. As biomass carbon:element ratios increase, so would the apparent CUE, thereby buffering the relationships between litter and microbial stoichiometry and CUE. Such relationships are intrinsic to stoichiometric models (eqns (2), (3) and (4)) and empirical studies show that biomass C : P ratio varies much more than biomass C : N ratio (Cleveland & Liptzin 2007; Doi et al. 2010; Franklin et al. 2011; Sardens et al. 2012). A similar effect may result from transient accumulation of osmolytes during drought, which increase microbial C : N ratio and hence the apparent CUE (Uhlířová et al. 2005; Herron et al. 2009). Incorporating greater stoichiometric flexibility into simulation models should lead to more realistic, and more buffered, CUE values.
In conclusion, most modelling assumptions are at least partly constrained by the stoichiometric relationships between biomass composition and detrital chemistry, thereby allowing CUE to vary. However, few empirical studies have sufficient resolution to provide a clear set of model assumptions needed to generate predictions of CUE with a high level of confidence, especially in terrestrial systems.
6. Conclusions and Recommendations
CUE is an ambiguous term. Even its simplest definition, as the ratio of microbial biomass production to material uptake from available substrates, entrains much uncertainty as a result of differences in the temporal and spatial resolution of the estimates and the metabolic and taxonomic characteristics of the microbial community. As an emergent property of the system, CUE is unlikely to be constant either within or between systems. It is responsive to differences in state and driving variables, yet constrained by multiple biochemical and biophysical limits on metabolism. We argue based on theoretical considerations and the preponderance of empirical observations that CUE over a wide range of field conditions converges on ~ 0.30 or about half the thermodynamic maximum of ~ 0.60 for microbial growth. For the reasons explained herein, we propose that many of the reported values of apparent CUE for terrestrial ecosystems are inflated and should not be used as a fixed parameter or target for simulation models.
We recommend that estimates of CUE within modelling frameworks reflect the relevant characteristics of the study system and goals. For example, broad spatial scale models operating at yearly or longer time steps could use a constant value for CUE of 0.30 unless there is evidence for lower values as a result of pervasive nutrient limitations. Models operating on finer time scales (days to seasons) should consider the effects of changing resource composition, multi-resource stoichiometric constraints, and microbial community physiology, as well as environmental drivers. Operationally, such models could either calculate CUE as a function of nutrient availability (e.g. Eliasson & Ågren 2011), or incorporate stoichiometric models (e.g. eqns (4), (5), as in Moorhead et al. 2012; Schimel & Weintraub 2003 and Touratier et al. 1999) to predict CUE responses as a function of other modelled quantities and processes.
S.M. acknowledges the support of the Agriculture and Food Research Initiative from the USDA National Institute of Food and Agriculture (2011-67003-30222), and the National Science Foundation (DEB-1145875 ⁄ 1145649). D.L.M. and R.L.S. acknowledge support from the NSF Ecosystem Sciences programme (DEB-0918718). A.R. acknowledges the support of the Austrian Science Fund (FWF- I 370-B17).
This study was a collaborative effort; all authors made substantial contributions to the review of literature, synthesis of ideas and development of the article.