Quantifying the timescales over which exogenous and endogenous conditions affect soil respiration



  • Understanding how exogenous and endogenous factors and above-ground–below-ground linkages modulate carbon dynamics is difficult because of the influences of antecedent conditions. For example, there are variable lags between above-ground assimilation and below-ground efflux, and the duration of antecedent periods are often arbitrarily assigned. Nonetheless, developing models linking above- and below-ground processes is crucial for estimating current and future carbon dynamics.
  • We collected data on leaf-level photosynthesis (Asat) and soil respiration (Rsoil) in different microhabitats (under shrubs vs under bunchgrasses) in the Sonoran Desert. We evaluated timescales over which endogenous and exogenous factors control Rsoil by analyzing data in the context of a semimechanistic temperature–response model of Rsoil that incorporated effects of antecedent exogenous (soil water) and endogenous (Asat) conditions.
  • For both microhabitats, antecedent soil water and Asat significantly affected Rsoil, but Rsoil under shrubs was more sensitive to Asat than that under bunchgrasses. Photosynthetic rates 1 and 3 d before the Rsoil measurement were most important in determining current-day Rsoil under bunchgrasses and shrubs, respectively, indicating a significant lag effect.
  • Endogenous and exogenous controls are critical drivers of Rsoil, but the relative importance and the timescale over which each factor affects Rsoil depends on above-ground vegetation and ecosystem structure characteristics.


Soil respiration (Rsoil) represents a substantial source of CO2 to the atmosphere, sometimes in excess of 70% of total ecosystem respiratory efflux (Janssens et al., 2001; Law et al., 2001; Barron-Gafford et al., 2011). Rsoil can also be a variable carbon flux, making its quantification important for improving our ability to predict ecosystem carbon dynamics. Of special interest is the influence of biotic (e.g. above-ground plant function) and abiotic (e.g. environmental) drivers on Rsoil. Over the last decade, substantial progress has been made in modeling Rsoil by moving beyond simple temperature response functions (see Lloyd & Taylor, 1994; Davidson et al., 2006, 2012) to developing frameworks and models for water-limited semiarid systems (Huxman et al., 2004; Cable et al., 2008; Lellei-Kovács et al., 2011), including multiple vegetative cover types or soil microhabitats (Cable et al., 2009; Zhang et al., 2009; Jin et al., 2010), and incorporating antecedent environmental effects (Zhou et al., 2011; Cable et al., 2012).

Despite this progress, there are still significant challenges in mechanistically understanding carbon efflux processes in soils. For example, little has been done to explicitly describe how Rsoil is influenced by the combined effects of leaf-level plant physiological activity and antecedent environmental conditions, as has been called for in the literature (Vargas et al., 2011). Such processes are hypothesized to be responsible for current modeling challenges that limit our predictive abilities on fine timescales (Barron-Gafford et al., 2011). Quantifying the effect of endogenous (e.g. physiological processes such as photosynthetic carbon fixation) and exogenous (e.g. environmental features that influence metabolic processes driving carbon utilization) factors has the potential to greatly advance our theory on underlying sensitivities of Rsoil to different global change drivers and may improve our ability to quantify and predict ecosystem carbon balance in natural settings.

Dependence of Rsoil on above-ground plant carbon fixation has been hypothesized as a source of within-day variation in Rsoil (Högberg et al., 2001, 2009; Tang et al., 2005; Baldocchi et al., 2006; Gaumont-Guay et al., 2006; Carbone & Trumbore, 2007; Barron-Gafford et al., 2011; Carbone et al., 2011; Niu et al., 2011). In particular, the hysteretic relationship of Rsoil with temperature may be the result of abiotic forcings (Phillips et al., 2010), but it may also be tied to subdaily lags in recently fixed carbohydrate transport from the leaves to the roots. It has been hypothesized that a stimulation of rhizosphere respiration from late-afternoon root exudation of recent photosynthates induces a higher Rsoil than early-morning rates occurring at a similar temperature (Barron-Gafford et al., 2011). Understanding the physiological dynamics of such a time-lag would be a powerful tool to assist in the prediction of rhizosphere carbon processes. We might expect this antecedent effect to be a function of the type and size of vegetation (e.g. grass, shrub, etc.), wherein large woody plants tend to have longer phloem transport times than herbaceous plants (Carbone & Trumbore, 2007; Vargas et al., 2011). Thus, the vegetative composition of an ecosystem may be important in determining the period over which antecedent (prior) plant carbon gain is important for Rsoil.

Shifts in the distribution of vegetation is a widespread feature of global change, and understanding how these community-level changes affect ecosystem processes has been a goal of modern ecology for some time. For example, many regions of North America have experienced widespread changes in the relationship between grass and shrub life forms (Goodale & Davidson, 2002). In the context of Rsoil, the distribution and dominance of woody plants relative to grasses may determine not only the importance of endogenous and exogenous effects on Rsoil, but also the timescales over which these effects are important for Rsoil. Increased woody plant cover affects canopy structure and influences ecosystem processes as a result of changes in trait composition, such as vertical root distribution (Schenk & Jackson, 2002) and maximum rooting depth (Canadell et al., 1996; Hultine et al., 2006). Such traits are related to plant photosynthetic capacity and plant-specific responses to environmental stress (Potts et al., 2006; Barron-Gafford et al., 2012), both endogenous factors likely to influence below-ground processes such as Rsoil. Additionally, woody plants shade and cool the soil (Martens et al., 2000; McLain et al., 2008; Villegas et al., 2010b), which can extend periods of elevated surface soil moisture as a result of reduced soil evaporation (Scholes & Archer, 2007; Breshears et al., 2009; Villegas et al., 2010a,b). Moisture and temperature are major exogenous drivers of Rsoil, but how they differentially affect extant and antecedent conditions across various microhabitats and their combined influence on Rsoil are poorly understood (Cable et al., 2009; Barron-Gafford et al., 2011).

How exogenous and endogenous conditions modulate ecosystem carbon dynamics in the context of mixed vegetation ecosystems is difficult to assess because of the potential, but hidden, role that antecedent conditions may play in driving current fluxes. Therefore, the objectives of this study were as follows: to quantify the response of Rsoil to current and previous temperature, soil water content, and leaf-level carbon gain in a grass–shrub mixed ecosystem; and to determine the critical time periods over which antecedent exogenous (soil water) and endogenous (photosynthesis) factors influence Rsoil rates. We accomplished this by integrating datasets of above-ground plant carbon gain and Rsoil collected at different spatial and temporal resolutions. The datasets were used to inform a simple model of leaf-level photosynthesis, which was coupled to a semimechanistic model of Rsoil. The coupled model performed well across a number of vegetation microhabitat settings and provided us the means to evaluate the relative roles of endogenous and exogenous factors in controlling Rsoil in a semiarid shrubland.

Materials and Methods

Site information

The study site is located in the Santa Rita Experimental Range (31.8214°N, 110.8661°W, elevation: 1116 m a.s.l.) south of Tucson, AZ, USA. The site was historically a grassland, but is now dominated by velvet mesquite (Prosopis velutina Woot.), which covers c. 35% of the c. 2800 m2 study site. Much of the intercanopy space consists of a mosaic of bunchgrasses (predominantly Eragrostis lehmanniana Nees, but also including Digitaria californica Benth and Bouteloua eriopoda). Soils here are a deep sandy loam (Scott et al., 2009), and the mean depth to groundwater at the upland site exceeds 100 m (Barron-Gafford et al., 2013). Mean annual precipitation is 375 mm, with c. 50% falling in July–September as part of the North American monsoon (Fig. 1c).

Figure 1.

(a, b) Time series of light-saturated photosynthesis (Asat) (a) and soil respiration rates (Rsoil) (b). Data are shown for two microhabitats (mesquite, triangles/black line; bunchgrass, circles/gray line) collected across 7 d spanning all seasonal periods, as illustrated by precipitation (black bars) and observed enhanced vegetation index (EVI, squares) (c), which represents the ‘greenness’ of the site. Each point represents the mean (± 1 SE) of 10 individual measurements, although the individual measurements (N = 30 for Asat, N = 144 for Rsoil) were used in the Bayesian analysis. A simple spline curve connects the points in time. Using the individual observations in our analysis was required to estimate the spatial effects and to link the individual measurements to the collar-level covariates.

An eddy covariance tower was installed at the site in 2004 to continuously monitor ecosystem-scale carbon, water, and energy exchange, as well as all associated meteorological variables (Scott et al., 2009). Thirty-minute measurements of soil moisture (CS616, Campbell Scientific, Logan, UT, USA) and soil temperature (T108, Campbell Scientific) were made at 5, 10, and 50 cm depths, under both mesquite and E. lehmanniana bunchgrass microhabitats (Scott et al., 2009). Thirty-minute measurements of incoming photosynthetically active radiation (PAR; LI-190, Li-Cor, Lincoln, NE, USA), air temperature and relative humidity (HMP35D, Vaisala, Helsinki, Finland) were made 8 m above ground.

Manual soil respiration measurements

To evaluate exogenous (soil moisture and temperature) and endogenous (photosynthetic gain) drivers of soil respiration (Rsoil), we measured Rsoil throughout an entire growing season, at nearly biweekly intervals for a total of 27 d of measurement in 2007. Rsoil was measured within P. velutina (hereafter, ‘mesquite’) and E. lehmanniana (‘bunchgrass’) microhabitats using a custom chamber and permanently installed soil collars (diameter = 10.2 cm; depth = 5 cm). As described in Barron-Gafford et al. (2011), collars were installed every 10 m along 50 m transects, whereby we identified the closest P. velutina and E. lehmanniana individual and placed a collar halfway between the base of the plant and the canopy dripline. Transects ran west and south from the eddy covariance tower, yielding a total of 20 collars (five collars per transect × two transects per microhabitat type × two microhabitat types).

To measure Rsoil, we used a 3 l opaque PVC soil chamber connected to a portable CO2 gas analyzer (LI-840, Li-Cor Biosciences) interfaced with a laptop for data collection and storage, as described by Cable et al. (2008) and Barron-Gafford et al. (2011). The accumulation of CO2 in the chamber over time followed a straight line, and we fitted a linear regression of CO2 vs time to obtain the rate of change (slope of line: ppm s−1). We converted the slope of this line to a flux density with volume/area corrections (Pearcy et al., 1990), providing a measurement of Rsoil (μmol CO2 m−2 s−1), as has been described for this measurement system (Cable et al., 2009; Barron-Gafford et al., 2011). Associated with each Rsoil measurement, soil moisture integrated over 0–12 cm was measured in the collar using a handheld water content sensor (HydroSense system, Campbell Scientific Inc.), and soil temperature from 0 to 10 cm was measured using a temperature probe (Temp-100, Oakton Instruments, Vernon Hills, IL, USA). Near-surface air and surface soil temperature were also measured using thermocouples installed within the soil chamber. These measurements were repeated across 14 d, spanning all seasons (DOY 10, 24, 35, 47, 61, 84, 96, 113, 132, 145, 160, 177, 189, 200, 209, 210, 211, 216, 233, 236, 245, 261, 283, 301, 316, 330, 362; Fig. 1b).

Leaf-level measurements of photosynthetic activity

Light-saturated photosynthetic CO2 assimilation (Asat) was measured on five P. velutina and five E. lehmanniana individuals at the site using a portable gas-exchange system (LI-6400; Li-Cor), which allows the user to create a stable microenvironment that mimics ambient conditions outside the cuvette (LI-6400 manual; Li-Cor Biosciences, 2013). Within each species, individual plants were of similar size and located along the Rsoil transects described earlier. As described by Barron-Gafford et al. (2012), Asat measurements were made mid-morning to midday (10:00–13:00 h local time) at a constant irradiance of 1500 μmol m−2 s−1, as delivered by the LI-6400 red-blue light source (LI-6400-02b). Once clamped into the chamber, the leaf was acclimated to a CO2 setpoint of 375 ppm, while exposed to ambient temperature and relative humidity at a constant flow rate of 500 μmol s−1. Leaves placed into the cuvette were allowed to acclimate and stabilize for a minimum of 10 min before gas exchange measurements. All measures were conducted on intact leaves on the southern side of the plant, midway up the canopy. Asat measurements were repeated during multiple periods throughout the growing season (pre-monsoon, during the monsoon, and post-monsoon) to capture a spectrum of physiological activity, across a range of temperature, precipitation, and soil moisture conditions. Conducting measurements across this range of states was critical to capturing phenological patterns of plant and soil activity. In total, Asat was measured on seven individual days in 2007 (DOY 176, 193, 215, 232, 259, 275, 282) for a total of 70 measurements (Fig. 1a).

Data analysis framework

We combined our measurements of Rsoil, Asat, and associated environmental drivers to infer endogenous (Asat) and exogenous influences on Rsoil. We achieved this by way of a Bayesian modeling framework (Wikle, 2003; Clark, 2005; Clark & Gelfand, 2006; Xie & Carlin, 2006) that integrates these datasets that are misaligned in space and time, propagates uncertainty in Asat to Rsoil, and yields estimates and associated uncertainties for parameters describing endogenous and exogenous influences on Rsoil. Our Bayesian framework comprised three primary components: a data model that describes the likelihoods of the observed Asat and Rsoil; a process model that includes a simple linear model for Asat and a nonlinear model for Rsoil that incorporates spatial and temporal random effects; and a parameter model that specifies prior distributions for process model parameters and all variance terms. Together, these components were used to generate posterior distributions of parameters that modulate rates and responses of Asat and Rsoil. That is, the parameters describe the effects of current environmental conditions, past environmental conditions, and the linkages between above-ground carbon gain and below-ground carbon efflux.

Data and process models for Asat and Rsoil

For the data models, we assumed that each Asat observation is normally distributed with mean μAsat and a variance that we estimated. Thus, for observation i (i = 1, 2,…, 70) and microhabitat m (mesquite or bunchgrass) associated with i, the process model for μAsat is given by the linear regression:

display math(Eqn 1)

where Tair max, VPDmax, SWC, μAsat represent the daily maximum air temperature (°C), maximum vapor pressure deficit (kPa), and soil water content at 5 cm (v/v) on each measurement day, respectively. Previous analyses suggest that near-surface soil moisture (5 cm) is an appropriate correlate for seasonal dynamics of photosynthetic function within this well drained, sandy soil (Barron-Gafford et al., 2012). The main effects of these environmental drivers are captured by c2, c3, and c4; all c parameters vary by m to allow for microhabitat differences in the sensitivity to each environmental driver. Using these parameter estimates and the environmental data from the site's eddy covariance station, we generated daily estimates or predictions of Asat, which we refer to as Apred. Therefore, Apred associated with each day of year d (d = 1, 2,…, 365) and microhabitat m (mesquite or bunchgrass) is given by:

display math(Eqn 2)

where Tair max, VPDmax, and SWC were computed from the eddy covariance station data. To account for the development of seasonal vegetation cover, we rescaled the mean growing season Asat (i.e. as given by Eqn 1 for μAsat,) by the MODIS enhanced vegetation index (EVI) estimated for the site for 2007 (Scott et al., 2009) to obtain Apred. It is important to note that this simple model for predicting photosynthesis is not meant to replace more mechanistic, higher-order models of photosynthesis (sensu Farquhar et al., 1980; von Caemmerer, 2000) or develop a model of plant function that is more specific to this system. Rather, efforts were focused on linking above-ground uptake and below-ground processes, and the models described in Eqns 1 and 2 yield an appropriate estimate of that photosynthetic uptake.

Next, we assumed that each observation of loge(Rsoil) is normally distributed with mean μLR (natural log scale) and a variance that we estimated (Cable et al., 2008, 2011). The process model for μLR is based on an Arrhenius-type function described by Lloyd & Taylor (1994) that was modified by Cable et al. (2008) to incorporate collar random effects (ε). For each observation i (i = 1, 2,…, 144) and collar c (c = 1, 2,…20 collars) associated with i:

display math(Eqn 3)

where LRb is the natural log of Rb, the ‘base’ Rsoil at 25°C (298.15 K). We use 25°C because the annually averaged soil temperature across the two microhabitats was 25.1°C, and this is a standard reference temperature against which to compare with other studies (Cable et al., 2011). EO (Kelvin) is a temperature sensitivity parameter that is somewhat analogous to an energy of activation term, TO (Kelvin) is another temperature sensitivity parameter, and T is soil temperature (°C; 0–10 cm). We allowed TO to vary by m to account for inherent differences in the temperature sensitivity of Rsoil between microhabitats.

Importantly, we extended the original Lloyd & Taylor function by modeling LRb and EO as functions of antecedent and current conditions similar to Cable et al. (2008). The model for LRb incorporates the influence not only of environmental conditions (SWC and temperature) but also of photosynthetic activity (Asat), essentially linking above- and below-ground carbon dynamics within a singular model of Rsoil. In fact, Asat is just a proxy for many plant attributes – such as the general metabolic state of the plant, the actual amount of fixed carbon, nitrogen status, etc. – but here we use this measure of maximum carbon assimilation potential to indicate peak capacity for each growth form, for each phenological point in time. The model for LRb for observation i associated with microhabitat m is:

display math(Eqn 4)

where AntApred is the antecedent leaf-level, predicted saturated photosynthesis, which is linked to Apred in Eqn 2; and SWC, AntApred SWC and AntSWC, α1 are current and antecedent soil water contents, respectively. The α1 parameter represents the base rate under average soil water content (i.e. at mean centered SWC = 0 and AntSWC = 0) at a reference temperature of 25°C and in the absence of above-ground carbon inputs (AntApred = 0). The endogenous effect of AntApred is given by α2, and the exogenous effects of AntSWC, SWC, and their interaction are captured by α3, α4, and α5, respectively. All α parameters vary by m to allow for potential microhabitat differences in sensitivities to each driver. We employ a model for EO{i} that is identical to Eqn 4, but with its own set of parameters β1, β2, …, β5 instead of α1, α2, …, α5.

Lloyd & Taylor (1994) suggest that EO and TO are relatively conserved across many ecosystem types, so we used semi-informative normal priors for TO and the ‘base’ EO value (i.e. β1 = EO at mean centered SWC = 0 and AntSWC = 0 and at AntApred = 0). We chose normal priors for TO and β1, with the prior means given by the Lloyd & Taylor estimates of TO and EO (227.13 and 308.56 K, respectively), as described in Cable et al. (2008, 2012). TO was also restricted between 1 and 285 K, where 285 K was just below the minimum value of T measured throughout the study. We assigned standard, noninformative priors to all remaining parameters (i.e. c, α, β, and all variance terms).

Equations 1-4 describe our ‘final model’ which we compared with three alternative formulations (the Asat model was the same in all four models). The first, which we refer to as the current effects model’, modifies the models for LRb and EO by only expressing these quantities as functions of current endogenous and exogenous conditions (i.e. α3 = α5 = β3 = β5 = 0 and AntApred{d,m} is replaced with Apred{d,m}, Eqn 4). Thus, Rsoil is linked to the current soil water and current photosynthesis (i.e. Apred on the day of the Rsoil measurement), and it is does not depend on antecedent soil water. The second, which we refer to as the ‘day random effects model’, builds from the current effects model by including temporal random effects (γ) such that Eqn 3 was modified to include the addition of γ{t}, where t is the measurement day index (t = 1, 2, …, 27). The third, which we refer to as the exogenous model’, retains the original Eqn 3, but it assumes that LRb and EO are uncoupled from endogenous, above-ground carbon gain (i.e. α2 = β2 = 0, Eqn 4). Comparison of the four models allowed us to quantify: the amount of variation in Rsoil that is captured by temporal effects that do not provide direct insight into the underlying factors governing Rsoil (compare the current effects model with the day random effects model); how much of the variation captured by the temporal random effects is explained by exogenous antecedent drivers (compare the exogenous model with the day random effects model); and how much is explained by endogenous and exogenous antecedent drivers (compare the final model with the day random effects model).

Quantifying the antecedent drivers

Historically, when incorporating antecedent conditions, one predetermines the duration of the ‘antecedent period’ arbitrarily (e.g. 10 d, 2 wk, etc.) and whether or not d/wk into the past carry an equal or declining degree of influence. For example, one may define antecedent soil water as the mean SWC over the past 10 d (i.e. soil water on each day has equal influence). We take a different approach, which allows the data on Rsoil to inform not only the process parameters in Eqns 3 and 4, but also the parameters describing the actual antecedent variables. In our model for Rsoil, we work with SWC and predicted maximum photosynthesis (Apred) on a daily timescale, and we defined their associated antecedent values as weighted averages of their past daily values, where the weights are unknown quantities.

Thus, we defined a stochastic model for the antecedent conditions that are relevant to the mechanistic model for Rsoil. For variable X (X = Apred or SWC), and for day of year d, collar c, and microhabitat m associated with observation i in the Rsoil dataset, the antecedent value of X is:

display math(Eqn 5)

where k is day into the past (k = 0 (‘today’), 1 (‘yesterday’), 2, …, Ndays). Note that the weight, wX, quantifies the relative importance of variable X occurring k d ago for current Rsoil, and we used different weights for Apred and SWC. For AntApred, we summed from k = 0 to k = Ndays such that the current day's Apred value is included; for AntSWC, we summed from k = 1 to k = Ndays, as the current SWC is directly incorporated into the model for Rsoil via the LRb and EO models (see Eqn 4). For each microhabitat, we assigned a noninformative Dirichlet before their vector of weights, which forces each wX to be between 0 and 1 and for all weights to sum to 1 across the antecedent period of Ndays within each microhabitat type. Exploratory analyses that varied the value for Ndays suggested that Ndays = 4 is appropriate in this study. If AntX has a significant effect on Rsoil – that is, the corresponding α (or β) parameter in Eqn 4 is significantly different from zero – then the wX values inform us about the relative importance of SWC or Apred conditions experienced on different days into the past; notably high values of a particular wX would indicate important lag times. We computed the correlations between the posterior (Markov chain Monte Carlo (MCMC)) samples for each pair of parameters. The posterior results for the correlations between the covariate effects (e.g. α or a values and β or b values) in the Rsoil and Asat model are provided in the Supporting Information (Table S1)). These results indicate that some of these effects are relatively highly correlated (e.g. a[3] and a[4], b[3] and b[4], a[4] and b[4]), but this correlation is accounted for within the Bayesian model, and it did not cause issues with convergence of mixing of the MCMC chains.

Model implementation and model comparison

The four Rsoil model formulations were implemented in the Bayesian statistical software package OpenBUGS (Lunn et al., 2009). For all models, we ran three parallel MCMC chains for 110 000 iterations; we discarded the first 10 000 (burn-in) samples and thinned every 50th iteration to reduce both storage requirements and within-chain autocorrelation. This yielded an independent sample of 6000 values for each parameter from the joint posterior distribution (Brooks & Gelman, 1998; Gelman, 2003). We used the built-in Brooks–Gelman–Rubin diagnostic tool to evaluate convergence of the chains to the posterior distribution (Gelman, 2004). For each parameter of interest, we present its posterior mean and central 95% credible interval (CI). Regression model coefficients (e.g. c2c4, α2α5, β2β 5; see Eqns 1 and 4) whose 95% CI contains 0 are generally deemed nonsignificant. This criterion that the CIs don't contain 0 is equivalent to a ‘classical two-sided’ test, whereas the Bayesian P-values we report in are equivalent to a ‘one-sided’ test. Thus, in the rare case where the 95% CI only slightly contains 0 (i.e. 0 is very close to one of the interval end-points), the Bayesian P-value is likely to indicate that this parameter is significantly different from 0. In such cases, where the CI and P-value may not ‘agree perfectly’, we utilize the P-value, as the Bayesian approach is generally more conservative in terms of revealing significant effects, and such ‘marginal’ cases may still imply important biological significance.

We used two different model indices to compare the four aforementioned models of Rsoil. We conducted regressions of observed vs predicted Rsoil (on the log scale) to visually and quantitatively evaluate model fit and bias, where the predicted values are the posterior means for μLR in Eqn 3. We also computed the deviance information criterion (DIC; Spiegelhalter et al., 2002) for each model. DIC is a model comparison statistic that accounts for model fit while also penalizing for model complexity, which is represented as the effective number of parameter (pD). In a nonhierarchical model, pD should be approximately equal to the countable number of parameters, but it is often less than the countable number in a hierarchical model. A lower DIC indicates a better model, and a difference of 10 or more between DIC values indicates strong support for the best model (Spiegelhalter et al., 2002).


Exogenous controls on leaf-level photosynthesis

In an attempt to better describe previously unexplained temporal variation in Rsoil (Cable et al., 2008), we incorporated the antecedent effects of light-saturated photosynthesis (Asat) and SWC (AntSWC) to provide a mechanistic link between Rsoil and above- and below-ground controls. Thus, three of the four Rsoil models that we evaluated were linked to Asat, although only the final model incorporated the effects of antecedent Asat. Independent of the Rsoil model, the Asat model performed exceptionally well for both mesquite and bunchgrass (r2 = 0.94 and 0.99, respectively; Fig. 2), and measured and predicted Asat values were well within range of those reported in the literature for these or similar species (Wan & Sosebee, 1990; De Soyza et al., 1996; Potts et al., 2008; Hamerlynck et al., 2010; Barron-Gafford et al., 2012, 2013). Given the covariance among the three parameters examined, we found that adding the singular term of maximum air temperature (Tair max) did not have a significant effect on Asat in mesquite (95% CI for c2 from Eqn 1 contained zero); however, Tair max did have a significant positive influence on Asat in bunchgrasses (Fig. 3a). Furthermore, increases in VPD (VPDmax) were positively correlated with Asat rates in both species (c3 > 0; see Eqn 1), but the influence was nearly five times greater in bunchgrasses (Fig. 3b). Increases in SWC did not significantly influence Asat in mesquite microhabitats (95% CI for c4, Eqn 1, contained zero), but positively affected Asat in bunchgrass microhabitats (c4 > 0), illustrating a greater sensitivity of photosynthesis to changes in shallow water availability within the bunchgrass (Fig. 3c).

Figure 2.

Comparison of observed vs predicted light-saturated photosynthesis (Asat). Data are shown for two microhabitats (mesquite, triangles; bunchgrass, circles) collected across 7 d spanning all seasonal periods; predicted values are the posterior means for μAsat in Eqn 1 The diagonal dotted line is the 1 : 1 line.

Figure 3.

The posterior means and 95% credible intervals (CIs) for the parameters (effects) in the model for light-saturated photosynthesis (Asat) (see Eqn 1). Results are shown for the effects associated with: (a) air temperature (c2); (b) vapor pressure deficit (VPD; c3), and (c) current soil water content effect (SWC; c4). Estimates are shown for two microhabitats (mesquite, triangles; bunchgrass, circles); CIs that overlap the dashed horizontal line at zero indicate the lack of an effect.

Exogenous and endogenous controls on Rsoil

The day random effects model fit the Rsoil data well for both microhabitats (r2 = 0.94 for both mesquite and bunchgrass; r2 = 0.99 when lumped), and observed vs predicted points fell tightly around the 1 : 1 line (Fig. 4a). Much of this goodness-of-fit, however, was the result of the explicit incorporation of the temporal (γ) random effects into Eqn 3 The current effects model, which did not include the γ effects, notably reduced model fit and increased model bias (r2 = 0.55 and 0.65 for mesquite and bunchgrass, respectively, and points do not consistently fall around the 1 : 1 line; Fig. 4b). That is, the poorer performance of the current effects model is attributed to greater variation among average predicted Rsoil rates and substantial overestimation of low fluxes (bias). Accounting for AntSWC within our exogenous model increased goodness-of-fit by 19 and 13% for mesquite and bunchgrass, respectively (Fig. 4c). Inclusion of AntApred and AntSWC into the final model of Rsoil, however, resulted in a more substantial increase in model fit relative to the current effects model, for both mesquite (r2 = 0.89; 29% increase) and bunchgrass (r2 = 0.89; 25% increase; Fig. 4d). This greatest improvement in performance suggests that the final model is capturing potential mechanisms that explain the majority of the temporal random effects associated with the day random effects model. The DIC, however, suggests that the random effects model performed the best (lowest DIC; Table 1), but this model also had the highest number of effective parameters (pD; Table 1). Ultimately, the final model was the optimal choice because of the balance between model performance (second lowest DIC), the number of effective parameters (second lowest pD), and the amount of mechanistic insight provided (comparatively high).

Table 1. Model comparison indices, including the deviance information criterion (DIC), the number of effective parameters (pD, a component of DIC), and coefficients of determination (r2) obtained from a traditional regression of the observed vs predicted Rsoil values
Soil respiration modelDIC pD Observed vs predicted r2
Day random effects model118.935.30.9390.935
Current effects model323.526.20.6860.709
Exogenous model248.020.30.8160.797
Final model187.422.70.8780.891
Figure 4.

Comparison of observed vs predicted natural log (loge) of soil respiration rates (Rsoil) from four different models for Rsoil: (a) the day random effects model is based on the model described in Cable et al. (2008), which incorporated the effects of current soil temperature, current soil water content, spatial (collar) and temporal (day of measurement) random effects, but also includes the effect of current photosynthesis (Apred); (b) the current effects model is similar to the day random effects model but lacks the temporal random effects; (c) the exogenous model includes exogenous effects related to current and antecedent previous soil moisture status (AntSWC) but excludes the endogenous effect of Asat; and (d) the final model includes antecedent exogenous and endogenous factors, linking above-ground productivity and below-ground efflux by including AntApred and AntSWC effects. The predicted values are the posterior means for μLR (mean of logeR) in Eqn 3. The gray and black lines are the regression lines for each microhabitat type; the diagonal dotted line is the 1 : 1 line.

Thus, we focus on the results from the final model to evaluate the influence of antecedent factors. Antecedent drivers can affect Rsoil by influencing the base rate (LRb, Eqns 3 and 4) and/or the temperature sensitivity (EO, Eqn 3). We found that higher LRb is correlated with higher AntApred in both microhabitats (Fig. 5a; < 0.0001 for both microhabitats, Table 2). Importantly, the posterior mean for α2 was nearly fourfold higher in mesquite than in bunchgrass microhabitats, indicating significantly greater sensitivity of LRb to AntApred under mesquite (i.e. 95% CIs for each α2 do not contain the posterior mean of the other microhabitat's α2). AntSWC positively influenced LRb in bunchgrass microhabitats (α3 > 0, Fig. 5b; = 0.0018, Table 2), but current-day SWC did not directly influence LRb (Fig. 5c; 95% CI for α4 contained zero for both microhabitats). Additionally, we detected a significant negative interaction of current-day SWC by AntSWC on LRb, such that the strongest positive effect of AntSWC occurred when current conditions were relatively dry (Fig. 5d; α5 < 0 for both microhabitats; = 0.0092 and 0.0052 for mesquite and bunchgrass, respectively, Table 2). Thus, during prolonged moist periods (i.e. past and current SWC are relatively high), LRb is relatively insensitive to changes in water availability.

Table 2. Bayesian one-sided P-values indicating the significance or relative importance of each exogenous and endogenous variable included in the final model; effects are ranked in order of significance (or importance) for each microhabitat within the base rate (LRb) and temperature sensitivity (EO) models
Log base rate (LRb) modelTemperature sensitivity (EO) model
  1. AntApred, antecedent leaf-level, predicted saturated photosynthesis; SWC, soil water content; AntSWC, antecedent SWC.

Mesquite α 2 AntApred< 0.0001 β 2 AntApred0.0007
α 5 AntSWC × SWC0.0092 β 5 AntSWC × SWC0.0022
α 4 SWC0.1195 β 3 AntSWC0.0713
α 3 AntSWC0.2237 β 4 SWC0.1842
Bunchgrass α 2 AntApred< 0.0001 β 5 AntSWC × SWC< 0.0001
α 3 AntSWC0.0018 β 2 AntApred0.0260
α 5 AntSWC × SWC0.0052 β 4 SWC0.0298
α 4 SWC0.3022 β 3 AntSWC0.1903
Figure 5.

Posterior means and 95% credible intervals (CIs) for the parameters (effects) in the model for the log-scale base rate (LRb (a–d); Eqn 4) and the temperature sensitivity (EO; same as Eqn 4, but with parameters indicated by β values instead of α values) (e–h) associated with the final model of Rsoil. (a, e) The antecedent light-saturated photosynthesis (AntApred) effect on LRb and EO (α2 and β2, respectively); (b) the antecedent soil water content (AntSWC) effect (α3 and β3, respectively); (c) the current-day soil water content (SWC) effect (α4 and β4, respectively); and (d) the AntSWC × current SWC effect (α5 and β5, respectively). Results are shown for two microhabitats: mesquite, triangles; bunchgrass, circles.

We found that lower EO is also correlated with higher AntApred in both microhabitats (Fig. 5e; = 0.0007 and 0.0260 for mesquite and bunchgrass microhabitats, respectively; Table 2). Changes in AntSWC positively influenced EO within the mesquite (= 0.0713) but not within bunchgrass microhabitats (= 0.1903, Table 2; Fig. 5f). On the contrary, increases in current SWC reduced EO in the bunchgrass microhabitat (= 0.0298), but had no effect in the mesquite microhabitat (= 0.1842, Table 2; Fig. 5g). There was a significant negative interaction effect of current-day SWC by AntSWC for both microhabitats (Fig. 5h; = 0.0022 and < 0.0001 for mesquite and bunchgrass, respectively) such that the sensitivity of Rsoil to changes in soil temperature was reduced when soil moisture had been relatively constant and/or high. Conversely, EO increased in response to increased moisture availability (i.e. increase in current SWC) if past conditions were relatively dry, as would occur immediately after a sizeable rain event that broke a dry spell.

Characteristics of the antecedent endogenous and exogenous drivers

The noninformative Dirichlet prior that we assigned to the microhabitat-specific weight vectors (wX, Eqn 5) for AntApred in the final model gave equal weight to each day over a 5 d antecedent period (prior mean = 1/5 for each daily wX), with relatively high uncertainty (i.e. wide 95% prior predictive CIs; Fig. 6). The field data notably refined the estimates of wX defining antecedent photosynthesis (AntApred) in the mesquite microhabitat; that is, the posterior means for each daily wX generally differed from the prior mean, and the posterior 95% CIs were much narrower than the prior CIs (Fig. 6a). A clear lag response to Asat emerged such that Asat rates 3 d before the Rsoil measurement were most important in determining current-day Rsoil under mesquite (Fig. 6a). Within the bunchgrass microhabitats, the posterior 95% CIs were wider than those for mesquite, and the means for each wX did not differ notably from the prior means for days 0 or 2–5. Still, a shorter, 1 d lag time is likely, indicating that Asat rates the day before the Rsoil measurement were most important in determining current-day Rsoil under bunchgrasses (Fig. 6b).

Figure 6.

Posterior means and 95% credible intervals (CIs) for the weights (wX, Eqn 5) associated with the definition of antecedent light-saturated photosynthesis (AntApred) within mesquite (a, triangles) and bunchgrass (b, circles) microhabitats. The weights from the noninformative Dirichlet prior (gray squares, with 95% CIs) are provided for comparison with the posterior results.

Similar analyses of the exogenous factors such as AntSWC indicate that SWC conditions associated with the day before the Rsoil measurement were most important in determining current-day Rsoil within both microhabitats, although this 1 d lag was more pronounced under bunchgrasses (Fig. 7a,b). Within the bunchgrass microhabitat, the posterior means for the AntSWC weights were lower than the prior means for days 2–4, and the posterior 95% CIs were about two-thirds narrower than the prior CIs within both microhabitats. Given the aforementioned significant effects of current SWC, AntSWC, and their interaction, this indicates that the current (SWC) and previous day's soil moisture conditions (AntSWC with high value of wX for k = 1; Eqn 5) are the most important soil moisture-related variables for predicting Rsoil in both microhabitats. Soil moisture patterns further into the past (k > 1, Eqn 5) appear to be relatively unimportant for predicting current Rsoil.

Figure 7.

Posterior means and 95% credible intervals (CIs) for the weights (wX, Eqn 5) associated with the calculation of antecedent soil water content (AntSWC) within mesquite (a, triangles) and bunchgrass (b, circles) microhabitats. The weights from the noninformative Dirichlet prior (grey squares, with 95% CIs) are provided for comparison with the posterior results.


Given projected concomitant changes in regional climate and vegetative cover (Seager et al., 2007), it is increasingly necessary to improve predictive capacities of models that link environmentally driven and biologically mediated processes, such as soil carbon cycling and ecosystem–atmosphere exchange dynamics (Davidson et al., 2006). Here, we developed a simple model for estimating soil respiration (Rsoil) across different microhabitat types that provides an insight into the relative influence of endogenous (e.g. above-ground carbon dynamics via photosynthesis) and exogenous (e.g. temperature and soil moisture) controls on soil respiration, while also improving our understanding of their antecedent influences. While this study was conducted within a semiarid environment, it is important to keep in mind the generality of the drivers considered in this study (air temperature, VPD, and SWC). Additionally, semiarid ecosystems make effective model systems for evaluating interactions that characterize terrestrial ecosystem dynamics globally given: that 41% of the earth's terrestrial surface comprises drylands and that this number is predicted to grow as a result of climate change (Feng & Fu, 2013); and that the majority of the terrestrial biosphere is water-limited at some point during the year (Jenerette et al., 2012). Application of this model examining above-ground–below-ground linkages yielded four key results.

First, both endogenous and exogenous controls are critical drivers of variation in Rsoil, but the relative importance of these two types of driver depends on characteristics tied to vegetation structure. For example, there was a positive effect of prior photosynthesis rates on base rates of Rsoil, and Rsoil was greatest during periods of peak above-ground carbon uptake, regardless of microhabitat type (Fig. 5). The temperature sensitivity of Rsoil (EO), however, was reduced by antecedent photosynthesis rates within both microhabitats. This finding might suggest that in periods of greater carbon input into the soils, limitations of temperature on the energy of activation of Rsoil are less constraining. Alternatively, because plant exudates are more labile than most other substrates and EO varies with substrate, the negative relationship between antecedent photosynthesis and EO could reflect the higher amounts of labile soil carbon (sensu Davidson & Janssens, 2006). The temperature sensitivity of Rsoil was also reduced by wetter current soil conditions in bunchgrass microhabitats, but was not affected by current or antecedent soil moisture in mesquite microhabitats. Recent studies have also found a stronger connectivity between Rsoil and patterns of soil moisture under bunchgrasses than under mesquite shrubs, where rates of efflux are less sensitive to wetting cycles (Barron-Gafford et al., 2011). Moreover, every parameter in the Asat model was significantly different between microhabitat types (Fig. 3), such that the physiological responses of the deep-rooted mesquites were only minimally sensitive to changes in temperature and surface soil moisture compared with the bunchgrasses. Thus, although the plant-level physiological responses differ between these two species (Fig. 3), the Rsoil responses among the microhabitat types are less different (Fig. 5), probably because Rsoil represents a mixture of autotrophic and heterotrophic contributions (Cable et al., 2008), and the heterotrophic responses may be similar across microhabitat types.

Secondly, the time-period over which endogenous drivers are most important for Rsoil – that is, the antecedent effect of Asat – is tied to vegetative structure and composition (Fig. 6). Under bunchgrasses, we found weak evidence for single-day lag in the time between the plant carbon uptake and the associated soil microhabitat Rsoil. Conversely, in mesquite microhabitats, we detected a more significant and longer lag-period, such that photosynthesis rates 3 d previously were the most influential in driving current-day rates of Rsoil (Fig. 6a). This lag period aligns with the expected amount of time that would elapse between leaf-level CO2 assimilation by shrubs, transport of the photosynthate products to the roots, and subsequent efflux of the metabolized products from nearby soils. For example, similar carbon transport lag mtimes in shrubs and trees have been demonstrated based on eddy covariance data (Tang et al., 2005), isotopic labeling techniques (Carbone & Trumbore, 2007), estimates of stomatal conductance and photosynthetic carbon isotope discrimination (Bowling et al., 2002), substrate supply and Rsoil transfer models throughout canopy expansion (P. Y. Oikawa et al., unpublished) and wavelet analysis of the synchronicity of canopy photosynthesis and Rsoil fluxes (Vargas et al., 2011).

Thirdly, the importance of antecedent exogenous drivers and the time-period over which they influence Rsoil are also tied to vegetative structure and composition (Fig. 7). Differential rooting behavior is, again, likely to underlie dissimilarities in the influence of exogenous environmental controls, such as soil water effects on Rsoil. Deep-rooted shrubs such as mesquite are able to access subsurface water at depths beyond the reach of the more shallow-rooted bunchgrasses (De Deyn et al., 2008; Scott et al., 2006; Williams et al., 2006). Thus, bunchgrasses are more reliant on shallow soil water, which reflects recent precipitation inputs, yielding a relatively short antecedent period of influence. Furthermore, patterns of root exudation are driven by above- and below-ground plant activity associated with photosynthesis and nutrient uptake, respectively (Bardgett et al., 2005). Given that the phenology of productivity by the deep-rooted shrubs is comparatively less coupled to precipitation (Scott et al., 2006), so too are patterns of Rsoil within these microhabitats. These findings underscore how a transformation in ecosystem structure (e.g. woody plant expansion) across semiarid regions will probably lead to a change in their functioning in terms of processes important to climate feedbacks, such as the magnitude and timing of ecosystem carbon fluxes (Goodale & Davidson, 2002).

Finally, in order to forecast ecosystem carbon balance under current and future climate regimes, we need a reliable means of estimating the dominant carbon fluxes, and our modeling approach highlights important components that should be considered. Recent models have been fairly successful at capturing the variability in observed Rsoil rates, especially in semiarid, pulse-driven systems (Cable et al., 2008, 2009, 2012; Chatterjee & Jenerette, 2011; Lellei-Kovács et al., 2011). Some of these improvements have stemmed from a better quantification of microhabitat-specific sensitivities to abiotic drivers or the relative importance of moisture at different depths within the soil profile. However, a notable amount of variation in Rsoil has been attributed to random, unexplainable temporal and/or spatial effects (e.g. Cable et al., 2008). We showed that the inclusion of antecedent photosynthesis and soil water effects into a model of Rsoil greatly improved model performance, and these antecedent effects accounted for most of the variation previously captured by the temporal random effects. The importance of incorporating endogenous influences into models of Rsoil is not surprising, given that several recent studies have highlighted the potential importance of photosynthetic inputs for understanding the magnitude of Rsoil (Tang et al., 2005; Kuzyakov & Gavrichkova, 2010; Mencuccini & Holtta, 2010; Vargas et al., 2011).

As noted by Davidson et al. (2006) and Gaumont-Guay et al. (2006), we need to move beyond simple correlations between Rsoil and temperature to better quantify the primary driving effects of temperature, soil water, and carbon substrate supply on Rsoil. Given that we now have > 500 eddy covariance sites worldwide recording environmental forcing variables (http://daac.ornl.gov/FLUXNET/fluxnet.shtml) and that the regional climate modeling community is prepared to integrate growth-form and spatially explicit models of Rsoil (Collins et al., 2008; Shen et al., 2008; Zhang et al., 2009), we are poised to make significant advances in forecasting soil and ecosystem carbon balance through mechanistic models of above-ground–below-ground linkages (Luo et al., 2011). In this regard, this work illustrates the importance of the inclusion of a substrate supply-like term (antecedent photosynthesis) within a simple model of Rsoil that involves important environmental features, thereby improving soil CO2 efflux estimates for semiarid systems. Such integration of biological and physical features in developing predictive capacity in ecology has been an important grand challenge.


This work was supported by the Philecology Foundation of Fort Worth, Texas, a Department of Energy National Institute for Climate Change Research awarded to K.O., a National Science Foundation award (DEB-0414680) to T.H. and R.S., the University of Arizona Water, Environmental and Energy Solutions program through the Technology and Research Initiative Fund, and the Center for Environmental Biology at the University of California, Irvine.