Woody plant encroachment impacts on soil

Plant Soil (2009) 320:153–167
DOI 10.1007/s11104-008-9880-1

REGULAR ARTICLE

Woody plant encroachment impacts on soil carbon
and microbial processes: results from a hierarchical
Bayesian analysis of soil incubation data
Jessica M. Cable & Kiona Ogle & Anna P. Tyler &
Mitchell A. Pavao-Zuckerman & Travis E. Huxman

Received: 23 September 2008 / Accepted: 18 December 2008 / Published online: 15 January 2009
# Springer Science + Business Media B.V. 2009

A. P. Tyler : M. A. Pavao-Zuckerman : T. E. Huxman
Department of Ecology and Evolutionary Biology,
University of Arizona,
Tucson, AZ 85721, USA

soil incubation data and complementary field data to
gain a more mechanistic understanding of soil carbon

turnover; (2) application of the approach to soil
incubation data collected from a semi-arid riparian
grassland experiencing encroachment by nitrogenfixing shrubs (mesquite). Soil was collected from
several depths beneath large-sized shrubs, mediumsized shrubs, grass, and bare ground—the four primary
microsite-types found in this ecosystem. We measured
respiration rates from substrate-induced incubations,
which were accompanied by measurements of soil
microbial biomass, soil carbon, and soil nitrogen. Soils
under large shrubs had higher respiration rates and
support 2.0, 1.9, and 2.6 times greater soil carbon,
microbial biomass, and microbial carbon-use efficiency, respectively, compared to soils in grass microsites.
The effect of large shrubs on these components is most
pronounced near the soil surface where microbial
carbon-use efficiency is high because of enhanced
litter quality. Grass microsites were very similar to bare
ground in many aspects (carbon content, microbial
biomass, etc.). Encroachment of mesquite shrubs into
this semi-arid grassland may enhance carbon and
nutrient cycling and increase the spatial heterogeneity
of soil resource pools and fluxes. The HB approach

allowed us to synthesize diverse data sources to
identify the potential mechanisms of soil carbon and
microbial change associated with shrub encroachment.

T. E. Huxman
Biosphere 2, B2 Earthscience, University of Arizona,
Tucson, AZ 85721, USA

Keywords Decomposition . Respiration . Soil
nitrogen . Sonoran desert . Prosopis velutina

Abstract Belowground processes and associated
plant–microbial interactions play a critical role in
how ecosystems respond to environmental change.
However, the mechanisms and factors controlling
processes such as soil carbon turnover can be difficult
to quantify due to methodological or logistical constraints. Soil incubation experiments have the potential
to greatly improve our understanding of belowground
carbon dynamics, but relating results from laboratorybased incubations to processes measured in the field is
challenging. This study has two goals: (1) development

of a hierarchical Bayesian (HB) model for analyzing

Responsible Editor: Klaus Butterbach-Bahl.
J. M. Cable (*) : K. Ogle
Department of Botany, University of Wyoming,
Laramie, WY 82071, USA
e-mail: jcable1@uwyo.edu
e-mail: cablejm@gmail.com
K. Ogle
Department of Statistics, University of Wyoming,
Laramie, WY 82071, USA

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Introduction
Belowground processes are critical drivers of ecosystem dynamics (Ritz et al. 1994; Wardle 2002), and
thus, they are important for understanding and
predicting whole-ecosystem dynamics. For example,
plant roots and soil microorganisms are key players in
soil and ecosystem carbon cycling (e.g., Schimel et al.

1994; Williams et al. 1998; Wullschleger et al. 1994).
Moreover, microbial decomposition of soil carbon is a
major conduit for the loss of CO2 from the soil to the
atmosphere (Raich and Potter 1995), potentially
contributing to climate change (Houghton et al. 1998;
Raich and Schlesinger 1992). In-turn, microbialmediated soil carbon fluxes are being altered by
climate change, either directly via the impacts of
elevated temperatures and an altered hydrological
cycle (Austin et al. 2004; Kirschbaum 1995; Raich
and Schlesinger 1992; Saleska et al. 1999), or
indirectly through changes in vegetation structure
(Huxman et al. 2004; Raich and Schlesinger 1992;
Waldrop and Firestone 2006). Although important,
belowground processes can be difficult to directly
measure, but unraveling such mechanisms is necessary for building a predictive framework of how
belowground carbon cycling will respond to and
feedback to global change (Hunt and Wall 2002;
Saetre and Stark 2005).
Soil incubations are commonly used to unravel the
mechanisms underlying soil carbon dynamics with

respect to soil respiration or CO2 efflux (e.g., Dutta et
al. 2006; Saetre and Stark 2005; Schuur and Trumbore
2006; Zak and Kling 2006). Generally, soil is collected
in the field and is brought to the lab, treatments are
applied to the soil samples, samples are “incubated” in
controlled conditions, and CO2 efflux is measured.
Incubation treatments may include labile carbon (e.g.,
sugar) substrate additions to determine active microbial
biomass (Fliessbach et al. 1994), microbial diversity
(Lin and Brookes 1999; Schipper et al. 2001), or
variation in microbial substrate use (Hamer and
Marschner 2005). Such incubation experiments have
been implemented to explore microbial responses to
stress or perturbations such as wet–dry cycles
(Fierer et al. 2003), altered nutrients (Thirukkumaran
and Parkinson 2000), and plant species shifts (Saetre
and Stark 2005). Hence, incubation studies are
valuable for elucidating key factors affecting soil
carbon dynamics.

Plant Soil (2009) 320:153–167

Integrating information from incubation experiments with complimentary field data to learn about
mechanisms operating in a natural setting is challenging. For example, synthesis of incubation data is often
limited to relatively simple analyses (e.g., Hook and
Burke 2000; Robertson et al. 1997) that do not
simultaneously consider all data sources and may
not accurately reveal mechanisms necessary for
understanding carbon dynamics in the field. On the
other hand, the work by Saetre and Stark (2005) is
unique in that they analyze substrate-induced incubation data within the context of a relatively detailed
mass-balance model that couples carbon and nitrogen
transformations. Another class of incubation experiments, which generally do not involve substrate
additions, periodically measure CO2 efflux over
several weeks or months. Generally, the goals of such
experiments are to estimate the size of the initial
carbon pool and the decay coefficients, but not
necessarily microbial biomass or physiological
activity. Functions describing carbon mineralization
kinetics (such as a first-order decay model) are often

fit to incubation data via non-linear regression
routines (Alvarez and Alvarez 2000; Dalias et al.
2001; Grandy and Robertson 2007; Paul et al. 1999).
Although these fitting approaches incorporate a semimechanistic model, the methods are somewhat
unsatisfactory because they do not consider multiple
sources of uncertainty (e.g., random and fixed effects)
or multiple types of data (subsets of data are often
analyzed independent of others).
Thus, although the experimental approaches and
laboratory methods associated with soil incubation
experiments may be quite involved and produce a
wealth of information, data analyses have lagged
behind. Towards bridging this gap, we present an
approach for analyzing soil incubation data obtained
from substrate-induced respiration experiments that is
grounded in a hierarchical Bayesian (HB) modeling
framework (e.g., Clark 2005; Ogle and Barber 2008).
The HB model simultaneously integrates all available
and relevant laboratory and field data to yield
estimates of microbial biomass, soil carbon availability, and microbial activity, facilitating inference about

microbial and substrate controls on soil carbon
cycling. Furthermore, the insight provided by this
HB data-model integration approach may reduce the
need for time-consuming and expensive laboratory
analyses associated with detailed incubation studies.

Plant Soil (2009) 320:153–167

Thus, the goals of this study are two-fold: (1)
present a HB approach for analyzing soil incubation
data and (2) apply the HB approach to an incubation
experiment that explores the effects of woody-plant
encroachment on soil carbon dynamics. Woody plant
expansion into native grasslands is a near-global
phenomenon (Archer et al. 1995; Chapin et al.
1995; Polley et al. 2003), and the resulting shifts in
vegetation structure and composition can alter carbon
inputs and chemical composition, affecting the
decomposability, turnover, and amount of soil carbon
(Hibbard et al. 2001; Jackson et al. 2000). The semiarid riparian system that we are studying in

southeastern Arizona is undergoing encroachment by
a deeply rooted nitrogen fixing shrub (mesquite,
Prosopis velutina) that is causing the accumulation
of highly decomposable leaf litter at the soil surface
and woody root material at depth. In grasslands,
however, relatively decomposable root material may
be deposited more uniformly to depth or concentrated
near the surface (e.g., Jackson et al. 1996; Titlyanova
et al. 1999). The presence of large woody plants
(or shrubs) may modify other factors that affect
decomposition, including microclimate (via canopy
effects on soil temperature and moisture), substrate
availability (via litter inputs), microbial biomass and
community structure, and the efficiency of microbial
carbon consumption (Saetre and Stark 2005). In semiarid ecosystems, both carbon and water availability
limit microbial activity, so vegetation characteristics
that modify these resources are expected to strongly
control soil carbon decomposition (Austin et al. 2004;
Hibbard et al. 2001). Thus, this study aims to
understand how encroachment by mesquite may

affect soil carbon processes in semi-arid ecosystems.
In order to address the two goals of this study, we
combine experimental data and the HB modeling
approach to evaluate the following three hypotheses.
We hypothesize that increased dominance of nitrogen
fixing shrubs in a semi-arid riparian ecosystem will:
(1) elevate soil carbon stocks throughout the soil
profile due to higher productivity compared to
co-occurring grasses, (2) increase microbial biomass
near the soil surface due to inputs of high-quality leaf
litter compared to deep soil that receives low-quality
woody root litter, and (3) enhance microbial substrateuse efficiency due to inputs of more decomposable
litter (high nitrogen content) compared to grasses (low
nitrogen content) and open/bare spaces (low litter

155

inputs). Evaluating these hypotheses will lend insight
into the impacts of woody-plant expansion on soil
carbon dynamics in this semi-arid system.

Materials and methods
Site description
This study was conducted at a medium-dense
mesquite shrubland (e.g., intermediate between a
grassland and closed-canopy woodland in terms of
shrub density) located along the San Pedro River,
southeast of Tucson, Arizona. The site is characterized by sandy-loam soils that are fairly homogenous
to 50 cm (R.L. Scott, personal communication). Mean
annual precipitation is 39 cm, of which approximately
60% falls in the summer (July–September) and about
22% in the winter (December–March) (average from
1971 to 2000 National Climate Data Center; NCDC
2008). Mean annual air temperature is 17°C, and the
maximum occurs in June (33°C) and the minimum in
January (0.6°C) (NCDC 2008). The two dominant
plant species are velvet mesquite (Prosopis velutina)
and giant sacaton bunchgrass (Sporobolis wrightii).
Prior to the summer monsoon, the vegetation cover is
about 50% mesquite, 20% sacaton, 20% other shrub
species, and 10% open space (Scott et al. 2000). The
field portion of this study was conducted in the dry
pre-monsoon season, prior to the growth of ephemeral
herbaceous plants that fill-in bare space. Seasonal
activity and productivity differ between shrubs and
grasses primarily because large mesquite access deep
soil water and sacaton access near-surface soil water
derived from recent rains (Potts et al. 2006; Scott et
al. 2000).
Soil sampling and incubation experiment
In May 2006, we collected soil samples associated
with four different microsites: large mesquite (>2 m
tall), medium mesquite (0.5–2 m tall), sacaton
(hereafter, grass), and bare ground. We examined
two size classes of mesquite because large shrubs may
differentially affect soil carbon compared to small
shrubs due to their ability to access groundwater and
their higher productivity. Pits were excavated (∼0.5 m
deep) near the center of bare spaces and about 0.5 m
from the base of large mesquite, medium mesquite,

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and grass. Bare spaces were devoid of surface litter
and pits were excavated at least 1 m away from the
nearest plant. Soil (∼200 g) was collected from each
pit in the following increments (or depths): 0–2, 2–5,
5–10, 10–15, 15–20, 20–30, 30–40, and 40–50 cm,
resulting in 96 soil samples (8 depths×4 microsites×3
replicates). Caliche was present at 50 cm, preventing
deeper pits. Soils were transported from the field in
ice-filled coolers and stored at 4°C until analysis
(within 48 h). Each soil sample was sieved (2 mm) to
remove roots and rocks. Gravimetric water content
(mean ± 1 SD = 1.53 ± 1.01%) and water-holding
capacity (WHC, 28±2.96%) were measured on a
subset of samples.
Each soil sample was divided into a pair of 50 g
sub-samples that were placed in 0.5 pint glass jars.
The soil in paired jars was brought to 50% WHC
(±2%): one with pure deionized (DI) water and the
second with a dextrose–DI water solution (4.2 mg
dextrose/g soil, 30 mg dextrose/mL water) to determine substrate-induced respiration (SIR) (West and
Sparling 1986). The sealed jars were incubated at a
constant temperature of 25°C in the dark. Respiration
(CO2 efflux, μmol CO2 g−1 soil s−1) was measured
with a closed-loop gas-exchange system that pumped
air from the jars through a Li-820 (LiCor Inc.,
Lincoln, NE) and a flow meter (0.5 L/min). Respiration was measured prior to substrate addition (dry
soil) and at 24 and 48 h after water and substrate
addition. Jar lids were removed for 120 s to vent the
high CO2 concentrations, and respiration was subsequently measured for 60 to 120 s.
Soil not used for incubations was processed for
microbial biomass carbon (n=25) and organic carbon,
inorganic carbon, and nitrogen content (n = 91).
Microbial biomass was determined on subsamples
selected to give a representative coverage of the soil
system; subsamples were distributed among the
microsites and depths as follows: bare (0–2, 2–5, 5–
10, 15–20, 40–50 cm), grass (0–2, 2–5, 5–10, 20–30,
30–40 cm), medium mesquite (0–2, 2–5, 10–15, 40–
50 cm), and big mesquite (0–2, 5–10, 15–20, 20–30,
30–40 cm). Field moist soil samples (5 g) were
treated via chloroform fumigation–extraction using
K2SO4 in a soil:extractant ratio of 1:4 (Vance et al.
1987). Microbial carbon in the extracts was determined with a total carbon analyzer (Shimadzu-5000
Kyoto, Japan) and calculated using an extraction
efficiency of 0.38 (Vance et al. 1987). Additional soil

Plant Soil (2009) 320:153–167

samples were ground to a fine powder and inorganic
carbon was measured with a modified pressurecalcimeter method (Sherrod et al. 2002); total carbon
and nitrogen were measured by dry combustion
(NC2100 soil analyzer, CE Elantech, Lakewood,
NJ). Organic carbon was calculated as the difference
between total and inorganic carbon.
Hierarchical Bayesian analysis of incubation data
Here we describe a hierarchical Bayesian (HB)
modeling approach (e.g., Berliner 1996; Clark 2005;
Ogle and Barber 2008; Wikle 2003) for analyzing the
different types of incubation data that we obtained in
this study. The HB method provides a fully consistent
statistical framework for analyzing the diverse data
within the context of a Michaelis–Menten type
process model for microbial respiration. One of the
two goals of this study is to describe the general HB
approach and apply it to data to address the second
goal of this study, which is to elucidate the effects of
different microsites on microbial activity and soil
respiration. The HB model has three components: (1)
the data model that defines the likelihood of the
observed data, (2) the probabilistic process model of
microbial respiration, and (3) the parameter model
that defines the prior distributions for the process
model parameters and variance terms. See Table 1 for
descriptions of all the symbols used in the following
sections.
The data model
The data model combines the data likelihoods for
observed respiration rates, organic carbon contents,
and microbial biomass. First, we work with measured
respiration rates (r) that have units of μmol CO2 g−1
soil s−1. Note that r is positive-valued, its variance
tended to increase with its mean, and Lr=log(r), the
natural logarithm of r, is approximately normally
distributed. Thus, for microsite m (four types), soil
depth d (eight layers), soil pit q (three reps), substrateaddition type s (water or dextrose), and time period t
(24 or 48 h), we assume:


Lrfm;d;q;s;tg
Normal mLrfm;d;q;sg ; t Lr ;
ð1Þ
mLrfm;d;q;sg is the mean or latent log-flux value and τLr
is the precision (1/variance) that describes observation

Plant Soil (2009) 320:153–167

157

Table 1 Description of symbols used in the HB model, including units and the type of data or node denoted by each symbol
Symbol

Type Unitsa

Description

t, m, d, q,
s
Lr

NA

NA

Indices for time (t), microsite (m), depth (d), soil pit (q), and treatment addition type (s)

SD

Log respiration rates

μLr

SP

Log(μmol m−2 s−1
layer−1)
Log(μmol m−2 s−1
layer−1)

τLr, τμLr
τC , τB
CLayer
BLayer
μCLayer
μBLayer
C
C*
B
B*
μ×μLr
AC
AB
Bcm
Ccm
λ

SP
SP
SD
SD
LN
LN
SP
SP
SP
SP
SP
LN
SP
SP
SP
LN

g C m−2 layer−1
g M m−2 layer−1
g C m−2 layer−1
g M m−2 layer−1
Unitless
G C m−2
unitless
G M m−2
log(μmol m−2 s−1)
μmol CO2 g C−1 s−1
μmol CO2 g M−1 s−1
% cm−1
% cm−1
unitless

Ac

LN

μmol CO2 g soil−1 s−1

Am

LN

μmol CO2 g soil−1 s−1

Mean or predicted log-respiration value
Precision terms for Lr and μLr
Precision terms for CLayer and BLayer
Observed carbon content
Observed microbial biomass carbon
Mean or latent amount of carbon
Mean or latent amount of carbon
Relative amount of carbon in each soil layer (depth) and microsite
Total amount of carbon in a column of soil in each microsite
Relative amount of microbial biomass in each soil layer and microsite
Total amount of microbial biomass in a column of soil in each microsite
Latent or mean log respiration rate
Substrate-use efficiency of microbes
Base-line microbial metabolic activity
Relative amount of microbial biomass per cm of soil
Relative amount of carbon per cm of soil
Limitation index: relative importance of microbial activity vs. substrate availability
to respiration
Reduced model: respiration rate when substrate is limiting (microbial biomass
unlimiting)
Reduced model: respiration rate when microbes are limiting (amount of substrate
unlimiting)

SD stochastic data, SP stochastic parameter or quantity, LN logical node or described by deterministic function
a

g M is grams of microbial biomass carbon (dry weight) and g C is grams of soil carbon

error. Within each substrate-addition type, there were
no systematic differences between the 24 and 48 h
time periods, so time period is treated as a replicate
and used to estimate τLr.
Respiration is the response variable of interest, and
organic carbon and microbial biomass are covariates
in the Michaelis–Menten model (see Eq. 6). Let
CLayerfm;d;qg and BLayerfm;d;qg denote the observed
amounts of organic carbon (g C·m−2 per layer) and
microbial biomass (g dw·m−2 per layer) from the
fumigation–extractions, respectively; we assume:


CLayerfm;d;qg
Normal mCLayerfm;d g ; t C ;
ð2aÞ


BLayerfm;d;qg
Normal mBLayerfm;d g ; t B ;

ð2bÞ

mCLayerfm;d g and mBLayerfm;dg are the mean or latent
amounts of organic carbon and microbial biomass,

respectively, and the precision parameters τC and τB
describe variability introduced by soil pit random
effects. We further define mCLayerfm;dg and mBLayerfm;d g
as follows:
mCLayerfm;d g ¼ cfm;d g  Cfmg ;

ð3aÞ

mBLayerfm;d g ¼ bfm;d g  Bfmg ;

ð3bÞ

c{m,d} and b{m,d} (both are unitless) are the relative
amounts of carbon or biomass in a given microsite and
P
P
layer such that cfm;dg ¼ bfm;dg ¼ 1, and Cfmg and Bfmg
d
d
are the total amounts of carbon (g C/m2) and biomass
2
(g dw/m ) in an entire 0–50 cm column of soil. The
depth-dependent distribution of carbon and microbes
(c, b) and their total amounts (C*, B*) are quantities
that we wish to estimate.

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Plant Soil (2009) 320:153–167

The process model
Latent respiration, microbial biomass, and organic
carbon are unobservable quantities that are informed
by the data. Latent respiration is described by a
process model that includes process uncertainty,
whereas we implemented an errors-in-variables-type
model (Dellaportas and Stephens 1995) for biomass
and carbon (Eqs. 3a and 3b). We define the process
model for latent respiration mLrfm;d;r;sg as:


mLrfm;d;r;sg
Normal m  mLrfm;d;sg ; t mLr ;

ð4Þ

the mean m  mLrfm;d;sg is described by a Michaelis–
Menten (MM)-type equation, and τμLr is the precision, which describes process error due to, for
example, soil pit random effects that cannot be
captured by the relatively simple MM model (i.e.,
Eq. 5). Such random effects could reflect differences
in microbial community structure, soil texture, or
other soil or microbial properties that were not
measured.
We chose a MM-type model partly because this
fairly simple model lends insight into key parameters
that describe microbial substrate use efficiency and
“inherent” microbial activity. When coupled with the
incubation data within the HB framework, estimates
of these parameters facility inferences about microbial
activity. The general form of the MM model for
respiration (R) as a function of the amount of carbon
substrate (C) and microbial biomass (B) is:
R¼

AC  AB  C  B

AC  C þ AB  B

ð5Þ

AC (μmol CO2·g organic C−1·s−1) describes microbial carbon substrate-use efficiency, and AB (μmol
CO2·g microbial C−1·s−1) is an index of the inherent
microbial activity or metabolism in the absence of
competition for carbon substrate. Note that when the
substrate is saturating (C→ ∞), Eq. 5 reduces to
R=AB·B such that respiration is limited by and
proportional to microbial biomass. We assume that
sugar addition results in substrate saturation, and
applying Eq. 5 gives:
m  mLrfm;d;sg ¼

8


A
A mC
m;d g mBLayer fm;d g
>
< log A Cfm;dgmCB LayerfþA
B mBLayer fm;d g
C fm;d g
Layer fm;d g
>
:

log AB  mBLayerfm;dg




if s ¼ water
if s ¼ sugar

ð6Þ

Note that mCLayerfm;d g and mBLayerfm;d g are given in
Eq. 3, and that Eq. 6 explicitly links the different data
sources via their associated latent processes.
One might expect AB to be affected by the
composition of the microbial community, but because
these data were unavailable and since all samples
were collected in close proximity, we assume that AB
is independent of microsite or soil depth. We tested
this assumption with the model and found no differences in AB across microsite and depth. On the other
hand, we expect that AC will depend on the quality
and chemical composition of the available substrate,
and we assume that AC is related to the nitrogen
content (%N) of the organic matter such that:


ACfm;d g ¼ a þ b  Nfm;d g  aveN ;

ð7Þ

where α is the value of AC when nitrogen content is
equal to aveN (the average %N measured in this
study; aveN=0.053%), and β describes the sensitivity
of AC to changes in %N.
The parameter model
Ultimately, we want to estimate the unobserved
quantities c, b, C*, B*, AB, and AC (i.e., α and β)
and the precision terms τLr, τC, τB, and τμLr, and we
specify prior distributions for these quantities. (The
HB model will also estimate missing data—for
example, we were unable to measure microbial
biomass for all depth by microsite combinations,
and the associated missing data model is given by
Eq. 2b.) We assign independent, non-informative



(diffuse)normal
 priors to log(AB), α, β, log Cfmg ,
and log Bfmg . We assume Dirichlet priors for the
depth-dependent distributions of carbon substrate,
c{m,.}, and microbial biomass, b{m,.}, where the {m,.}
refers to all depths such that c{m,.} and b{m,.} are
vectors that vary by microsite. The Dirichlet prior
constrains the proportions (i.e., c{m,d} and b{m,d}) to
be between 0 and 1 and, within a microsite, the
proportions sum to one across all depths. We assume
a non-informative Dirichlet prior that is equivalent to
a uniform prior in the one-dimensional case. Finally,
we assume independent, diffuse gamma priors for the
precision parameters (i.e., τLr, τC, τB, and τμLr).
We also estimated several quantities that are
deterministic functions of the above parameters. We
divided c{m,d} and b{m,d} by soil layer thickness

Plant Soil (2009) 320:153–167

159

(dL, cm) to obtain the relative amounts of soil carbon
(ccm, %/cm) and microbial biomass (bcm, %/cm),
allowing for direct comparisons of ccm and bcm
between layers and microsites. We also computed the
average microbial carbon-use efficiency associate with
each microsite as a weighted average of AC{m,d} with
weights given by c{m,d}:
AveACfmg ¼

Nd
X

cfm;dg  ACfm;dg :

ð8Þ

d¼1

To explore the relative importance of microbial
activity and carbon substrate availability to heterotrophic soil respiration, we calculated a “limitation”
index (λ):
!
AB  Bfmg
lfmg ¼
ð9Þ
AveAC fmg  Cfmg
If λ= 1, microbial activity and carbon substrate
availability are equally limiting (or controlling)
respiration; if λ>1, substrate is most limiting and if
λ40 cm)

under big mesquite (mean±1 SE=0.088±0.030%;
0–55 cm), followed by medium mesquite, grass, and
bare microsites (0.040± 0.004, 0.046±0.004, and
0.033±0.001%, respectively). Soil nitrogen was highest in the surface layer (0.275±0.041%; across all
microsites) compared to deeper layers.
The HB model successfully captured the observed
patterns in soil respiration, soil organic carbon, and
microbial biomass. For example, regressions of
observed vs. predicted log respiration (i.e., Lr vs.
μ ×μLr, Eq. 6), organic carbon (i.e., CLayer vs.
μCLayer, Eq. 2a), and microbial biomass (i.e., BLayer
vs. μBLayer, Eq. 2b) indicate that the full model
successfully fit the observed data (Fig. 2). The full
HB model accounted for 94%, 96%, and 61% of the

Plant Soil (2009) 320:153–167

variation in observed (log) soil respiration, microbial
biomass, and organic carbon (Fig. 2).
To evaluate the full versus reduced model, we
compare parameters shared by both models (c, b and
λ). We consider two quantities significantly different
if the 95% credible interval (CI)—the interval defined
by the 2.5th and 97.5th percentiles—for each quantity
does not contain the other quantity’s posterior mean.
For example, the full model and reduced model
yielded similar estimates for λ, c, and b as the 95%
CIs obtained from the full model contained the
associated parameter’s posterior mean for the reduced
model (Fig. 3a–c). The full model resulted in slightly
more precise estimates for these parameters, which is
reflected in the narrower CIs; the mean widths of the
95%CIs for the full vs. reduced models were: 0.14 vs.
0.14 (c), 0.11 vs. 0.15 (b), and 6.1 vs. 6.9 (λ).
Now we focus on parameters unique to the full
model, and posterior results for a subset of parameters
are given in Table 2. The posterior distributions of
ccm (% C/cm) and bcm (% dw/cm) show that both
organic carbon content and microbial biomass were
most concentrated near the surface and declined with
depth (Fig. 4a,b). The strongest depth-dependent
decline occurred under big mesquite; conversely,
microbes and carbon were more uniformly distributed
with depth in bare soil. Differences in the posterior
estimates of total carbon content and total microbial
biomass were greatest between non-mesquite microsites (grass, bare; low C* and B*) and mesquite
microsites (big and medium shrubs; high C* and B*)
(Table 2). In general, soils in bare areas have the
lowest C* and B* while soils under big mesquite had
the highest C* and B* (Table 2). Despite strong
microsite differences in C* and B*, microbial biomass
per unit of carbon (i.e., B*/C*) was similar across
microsites (Fig. 4c).
Depth averaged microbial carbon substrate-use
efficiency (AveAC) was lowest for bare soil, intermediate for grass and medium mesquite microsites, and
highest for big mesquite microsites (Fig. 5a, Table 2).
Depth-varying microbial carbon-use efficiency (AC)
was positively correlated with soil N content (β>0,
Table 2, Fig. 5b). Over the range of N contents
measured in this study, the posterior mean for
AC increased from ca. 0.01 (N=0.02%) to 0.19 μmol·g
C−1·s−1 (N=0.28%) (Fig. 5b). Pronounced depthdependent variation in soil N under big mesquite led
to a strong depth-dependent decline in AC (Fig. 5c). In

Plant Soil (2009) 320:153–167

161

this system, carbon substrate availability rather than
microbial activity appears to be the dominant controller of respiration (λ>1) (Fig. 6). Substrate availability
is most limiting in medium mesquite and bare
microsites ðl ffi 10:6Þ and least limiting under big
mesquite ðl ffi 3:5Þ (Fig. 6).

Discussion
Woody plant encroachment and soil carbon turnover

Fig. 2 Evaluation of model goodness-of-fit by comparing log
of observed (measured) and model-predicted (a) respiration
rates, (b) microbial biomass, and (c) organic carbon. For a,
solid circles are respiration rates associated with pure water
addition and open circles are rates associated with sugar–water
addition. The dotted lines are the 1:1 lines, and solid lines are
the least squares regression fits with the following coefficients:
a water addition: Logð yÞ ¼ 0:09 þ 0:99  Logð xÞ; R2 ¼
0:94, s ugar–water addition: Logð yÞ ¼ 0:37 þ 0:84
Logð xÞ; R2 ¼ 0:96, b Logð yÞ ¼ 1:2 þ 1:3  Logð xÞ; R2 ¼
0:48, c Logð yÞ ¼ 1:6 þ 0:68  Logð xÞ; R2 ¼ 0:61

We used a hierarchical Bayesian (HB) modeling
approach to bridge lab and field studies within a
unified statistical framework, with the goal of gaining
mechanistic insight into soil carbon–microbial interactions. This framework was used with soil incubation
data to explore how encroachment of a nitrogen-fixing
shrub (mesquite, Prosopis velutina) into a semi-arid
riparian grassland may be affecting soil carbon
cycling, and we evaluated three hypotheses related
to this question. In support of Hypothesis #1, total
organic carbon under mesquite (big and medium
shrubs) was 1.8 and 1.5 times greater than total
carbon under bare and grass microsites, respectively
(C*, Table 2). Big mesquite shrubs also resulted
in 2.2 times greater accumulation of organic carbon in
surface layers (0–2 cm) compared to bare, grass, and
medium mesquite (Fig. 4b). In support of Hypothesis
#2, microbial biomass was 1.9 and 2.3 times greater
under mesquite (big and medium shrubs) compared to
grass and bare microsites, respectively (B*, Table 2).
Similar to the soil carbon patterns, big mesquite
appear to enhance the relative amount of microbes by
nearly threefold in surface layers compared to grass
and bare microsites (Fig. 4a). In support of Hypothesis #3, microbes associated with big mesquite had
approximately threefold greater carbon substrate-use
efficiency than the other three microsites (Fig. 5a).
Woody plant encroachment into other arid and
semi-arid grasslands has led to changes in soil carbon
stocks (Jackson et al. 2002) that are consistent with
our observations. While Jackson, Banner, Jobbagy et
al. (2002) did not observe a significant or consistent
effect of shrub encroachment on the depth distribution
of carbon in the top 100 cm, we found that big
mesquite facilitate accumulation of carbon and
microbial biomass in the near-surface layers
(Fig. 4a,b). The large shrubs in this ecosystem access

162

Plant Soil (2009) 320:153–167
20

Table 2 Posterior means and 95% credible intervals (2.5th and
97.5th percentiles) and units for a subset of the HB model
parameters. Mesq. refers to mesquite

a

15

λ

Parameter
10

τLr
τμLr
τC ×105
τB
AB
α
β

5
Full Model
Reduced Model

0

Bare

Grass M. Mesq. B. Mesq.

Relative amount of microbes (b)
Reduced Model

Microsite
0.25

b

0.20

0.15
Bare
Grass
M. Mesquite
B. Mesquite

0.10

0.05
0.05

0.10

0.15

0.20

0.25

Relative amount of carbon (c)
Reduced Model

Relative amount of microbes (b)- Full Model
0.30

c

AveAC
Bare
Grass
Med. Mesq.
Big. Mesq.
B*
Bare
Grass
Med. Mesq.
Big. Mesq.
C*
Bare
Grass
Med. Mesq.
Big. Mesq.

Units

μmol CO2
μmol CO2
μmol CO2
%N−1
μmol CO2

Mean (95%CI)

g soil−1 s−1
g C−1 s−1
g C−1 s−1

9.52
4.33
2.73
6.18
150
0.032
0.712

(7.66, 11.5)
(3.09, 5.91)
(1.81, 38.9)
(1.87, 16.0)
(103, 238)
(0.025, 0.040)
(0.371, 1.08)

0.017
0.026
0.021
0.067

(0.014,
(0.021,
(0.017,
(0.044,

2.81
3.37
6.19
6.51

(1.64,
(1.88,
(3.76,
(3.72,

2,122
2,561
3,272
4,176

(1,596,
(2,043,
(2,720,
(3,552,

g C−1 s−1
0.022)a
0.031)b
0.026)ab
0.095)c

g M m−2
4.07)a
5.11)a
8.70)b
9.12)b

g C m−2
2,650)a
3,112)a
3,850)b
4,803)c

Statistically significant differences are denoted by different
letters (i.e., posterior means are not contained within another’s
95%CI)

0.25
0.20
0.15
0.10
0.05
0.00
0.00

0.05

0.10

0.15

0.20

0.25

0.30

Relative amount of carbon (c)- Full Model

Fig. 3 For bare, grass, medium mesquite, and big mesquite
microsites, full and reduced model comparisons of a posterior
means and 95% credible intervals for λ (grey error bars for the
reduced model), and posterior means for the relative amounts of
b microbial biomass (b) and c organic carbon (c) in each soil
layer or depth (each point is a depth for each microsite). The
dotted line in b and c is the 1:1 line

deep water (Scott et al. 2000), resulting in potentially
more aboveground production and carbon accumulation in the soil surface compared to the shrubs studied
by Jackson et al. (2002). Despite the proliferation of

microbes beneath big mesquite, the amount of
microbial biomass relative to carbon content (B*/C*)
was similar across microsites (Fig. 4c). This suggests
that the amount of carbon, regardless of the quality of
this carbon, constrains the amount of microbial
biomass across microsites; however, the carbon-use
efficiency of these microbes does depend on carbon
(or substrate) quality.
In our system, microbial respiration was controlled
by carbon availability to a lesser extent under big
mesquite compared to the other microsites (Fig. 6).
This was expected because big mesquite microsites
have an extensive litter layer (>7.6 cm deep, data not
shown), high surface soil carbon content, and
nitrogen-rich litter compared to bare soil, grass
microsites, and the lesser-developed medium mesquite microsites. Because Prosopis velutina is a
nitrogen-fixer, soil beneath the big shrubs supported

Plant Soil (2009) 320:153–167
20

163

a.

Bare
Grass
Medium Mesquite
Big Mesquite

18

% Microbes cm-1

16
14
12
10
8
6
4
2
0

b.

% Carbon substrate cm-1

12
10
8
6
4
2
0
0-2

2-5

5-10

10-15 15-20 20-30 30-40

> 40

Depth (cm)
3.0

a

c.

B*/C* (g M.g C-1) x 103

2.5

a
a

a

Bare

Grass

2.0
1.5
1.0
0.5
0.0
M. Mesq.

B. Mesq.

Microsite

Fig. 4 Posterior means and 95% credible intervals (CIs) for the
relative density of a microbes (bcm, %/cm) and b carbon
substrate (ccm, %/cm) across the eight soil depths within each
of the four microsites; and c the ratio of microbes to carbon
substrate, i.e., B*/C* (g dw/g C) across the four microsites. CIs
that do not contain posterior means for other microsites or
depths and/or different letters indicate that means are significantly different

microbes with high carbon substrate-use efficiency
(Fig. 5a), particularly near the surface (Fig. 5c). This
suggests that soil carbon was of higher quality (e.g.,
higher N) compared to bare, grass, and medium
mesquite microsites (low N=low decomposability,

Ball 1997; Fierer et al. 2006). In fact, carbon
substrate-use efficiency was positively correlated with
substrate quality as described by the nitrogen content
of the bulk soil (Fig. 5b). Thus, high respiration rates
in the soil surface beneath big mesquite are attributed
to large, labile carbon stocks and high nitrogen
contents that facilitate the relatively rapid decomposition of high quality litter.
Conversely, bare and grass microsites are devoid of
surface litter, thereby limiting carbon inputs to surface
layers. Low decomposability of soil carbon (low N) in
these microsites resulted in low microbial abundance
and reduced carbon substrate-use efficiency. Although
grass and bare microsites are functionally similar in
terms of litter inputs and microbial activity, at the
ecosystem level grasses may not be equivalent to bare
ground because they support a root system and dense
canopies with high production rates (Potts et al.
2006). Medium mesquite were functionally similar
to big mesquite in that they had similar amounts of
soil microbial biomass and soil carbon (Table 2), but
they were functionally similar to grass and bare soil in
terms of their microbial carbon-use efficiencies
(Fig. 5a). The latter was somewhat surprising since
the chemical composition of soil organic matter
formed from the litter from both medium and large
shrubs was expected to differ from that of grass litter.
As shrubs grow larger, however, the soil beneath their
canopies changes whereby all of the following tend to
increase: soil carbon stocks, microbial biomass,
substrate-use efficiency, and soil respiration.
However, it appears that microbial biomass responds
most rapidly to shrub encroachment, followed by soil
carbon, then microbial substrate-use efficiency. Thus,
our results suggest that there appears to be a lag in
soil carbon processes associated with the conversion
of grassland to mesquite shrubland.
The hierarchical Bayesian modeling approach
The HB modeling approach that we employed
allowed us to synthesize experimental and observational data related to soil carbon–microbe interactions.
Although we applied this approach to short-term,
substrate-induced incubation data, it could be applied
to long-term incubation studies for understanding
mineralization kinetics (Alvarez and Alvarez 2000;
Dalias et al. 2001; Grandy and Robertson 2007; Paul
et al. 1999); more generally, it can be used to

Average Ac (µmol CO2 .g C-1.s-1)

164

Plant Soil (2009) 320:153–167

0.09

b

a

0.08
0.07
0.06
0.05
0.04
a

0.03

a

a
0.02
0.01
0.00
Bare

Grass

M. Mesq.

B. Mesq.

Microsite

Ac (µmol CO2 .g C-1.s-1)

0.30

b

0.25

0.20

0.15

0.10

0.05

0.00
0.04

0.08

0.12

0.16

0.20

0.24

0.28

% Soil nitrogen
0.30

Ac (µmol CO2 .g C-1.s-1)

c

Bare
Grass
Medium Mesquite
Big Mesquite

0.25

0.20

0.15

synthesize data from microcosm studies. Although we
worked with a specific dataset and particular process
model, the HB approach is highly flexible and can
accommodate different types of data, experimental
designs, sampling protocols, and process models
(Ogle 2008). Traditional methods for analyzing
incubation data generally do not use the data to their
fullest potential and tend to misrepresent uncertainty,
which will impact subsequent inferences. Further,
multiple datasets are often analyzed in a piece-wise
fashion rather than in a single analysis that explicitly
accounts for multiple sources of uncertainty. The HB
approach presented here overcomes these issues by
employing a probabilistic framework that links semimechanistic process models with diverse sources of
data that inform processes of interest (e.g., in this
study, microbial decomposition of soil carbon).
Although our study produced a fairly rich dataset,
other studies may be limited in the types of data
available. For example, measurements of microbial
biomass can be time consuming and expensive,
prohibiting the collection of such data. We note,
however, that the reduced model (e.g., Eq. 10 and
associated text) is appropriate for incubation experiments that only measure respiration rates. Compared
to the full model, the reduced model produced similar
estimates of the relative amounts of microbial
biomass and organic carbon (b and c), soil respiration,
and the importance of microbial activity vs. substrate
availability to soil respiration (λ). This suggests that

0.10

0.05

0.00
0-2

2-5

5-10

10-15 15-20 20-30 30-40

> 40

Depth (cm)

Fig. 5 Posterior estimates of microbial carbon-use efficiency
(AC), where a shows posterior means and 95% credible
intervals for substrate-use efficiency averaged across depth for
each microsite (i.e., AveAC) (statistical differences denoted by
different letters); b shows the predicted relationship between AC
and bulk soil nitrogen content (%), plotted for soil N values that
span the N contents measured in this study, where the middle
line is the posterior mean, the upper and lower curves define the
95%CI, and the symbols (circles) indicate the predicted AC
values associated with the measured N values; and c shows the
posterior means and 95%CIs for AC by soil depth and microsite

Fig. 6 Posterior means and 95% credible intervals for the
limitation index (λ, see Eq. 9), which describes the primary
controller of respiration (microbes or carbon). Statistical differences in the means are denoted by different letters

Plant Soil (2009) 320:153–167

carbon and microbial biomass are not critical to
measure when the goal is to estimate b, c, and λ.
However, if the goal is to estimate microbial
metabolic parameters (AC and AB) and/or the total
amount of carbon or microbes (C* and B*), then
organic carbon and microbial biomass data must be
collected and used with the full model described
herein.
The full model was very successful at predicting
respiration, but it was comparatively less successful at
predicting microbial biomass and organic carbon
(Fig. 2b,c). There are at least two potential explanations for this result. First, latent respiration rates
were mostly informed by two data sources (water and
sugar–water incubation flux data), but estimated total
carbon and total biomass were primarily informed by
one source each (measured organic carbon and
microbial biomass carbon, respectively). Further, the
biomass dataset was small compared to the carbon
and respiration data, and data for some depths were
missing across all microsites. Second, the respiration
data and Michaelis–Menten model inform us
about relatively fast processes related to highly
mineralizable soil carbon and metabolically active
micro-organisms. Conversely, the soil carbon data
integrate over disparate temporal and spatial scales
associated with, for example, labile and recalcitrant
carbon pools, and the biomass data may not accurately describe micro-organisms that are active at the
time of incubation. However, the data-sensitivity
analysis that compares the reduced and full models
suggests that including soil carbon data improves
parameter estimates and reduces uncertainty in predicted soil carbon. In summary, the HB approach can
easily accommodate different types and amounts of
data that can be analyzed within the context of a
process model, facilitating inferences about key
parameters and processes related to, for example, soil
carbon cycling.
Acknowledgements We thank Dr. David Williams and Dr.
Russell Scott for the access to field sites and intellectual
contributions; Greg Barron-Gafford, Ben Collins, Kevin “the
Red” Gilliam, and Amelia Hazard for the field assistance; and
Mary Kay Amistadi and Jon Chorover, School of Natural
Resources, University of Arizona for the TOC analysis of
microbial biomass samples. We acknowledge funding from
SAHRA (Sustainability of Semi-Arid Hydrology and Riparian
Areas) under the STC program of NSF, and NSF awards to
TEH, Jake F. Weltzin, and David G. Williams. The experi-

165
ments herein comply with the current laws of the USA. The
statistical analysis was partly supported by a DOE NICCR
grant (K.O., T.H.).

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