Ecological Applications, 24(6), 2014, pp. 1421–1433
Ó 2014 by the Ecological Society of America

Spatial patterns of grassland–shrubland state transitions:
a 74-year record on grazed and protected areas
DAWN M. BROWNING,1,2,4 JANET FRANKLIN,3 STEVEN R. ARCHER,2 JEFFREY K. GILLAN,1
1

AND

D. PHILLIP GUERTIN2

USDA-ARS, Jornada Experimental Range, P.O. Box 30003, MSC 3JER, New Mexico State University, Las Cruces,
New Mexico 88003 USA
2
School of Natural Resources and Environment, University of Arizona, Tucson, Arizona 85721 USA
3
School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, Arizona 85287 USA

Abstract. Tree and shrub abundance has increased in many grasslands causing changes in
ecosystem carbon and nitrogen pools that are related to patterns of woody plant distribution.
However, with regard to spatial patterns of shrub proliferation, little is known about how they
are inﬂuenced by grazing or the extent to which they are inﬂuenced by intraspeciﬁc
interactions. We addressed these questions by quantifying changes in the spatial distribution
of Prosopis velutina (mesquite) shrubs over 74 years on grazed and protected grasslands.
Livestock are effective agents of mesquite dispersal and mesquite plants have lateral roots
extending well beyond the canopy. We therefore hypothesized that mesquite distributions
would be random on grazed areas mainly due to cattle dispersion and clustered on protected
areas due to decreased dispersal and interspeciﬁc interference with grasses; and that clustered
or random distributions at early stages of encroachment would give way to regular
distributions as stands matured and density-dependent interactions intensiﬁed. Assessments in
1932, 1948, and 2006 supported the ﬁrst hypothesis, but we found no support for the second.
In fact, clustering intensiﬁed with time on the protected area and the pattern remained random
on the grazed site. Although shrub density increased on both areas between 1932 and 2006, we
saw no progression toward a regular distribution indicative of density-dependent interactions.
We propose that processes related to seed dispersal, grass–shrub seedling interactions, and
hydrological constraints on shrub size interact to determine vegetation structure in grasslandto-shrubland state changes with implications for ecosystem function and management.
Key words; LISA; livestock exclusion; mesquite; Moran’s I; pair correlation function; point pattern
analysis; Prosopis velutina; Ripley’s K; Sonoran Desert; spatial autocorrelation; spatial ecology.

INTRODUCTION
The spatial arrangement and size of plants mediates
ecosystem function in water-limited ecosystems by
inﬂuencing soil erosion and deposition, decomposition,
spread of disturbance, and land use (Ludwig et al. 2005,
de Knegt et al. 2008, Neff et al. 2008). In ecosystems
undergoing state transitions, the reordering of plant
functional groups contributes to major shifts in ecosystem function by eliciting changes in biophysical processes (Ellison et al. 2005) and responses to external
drivers (Scheffer and Carpenter 2003). In grasslands and
savannas undergoing state-transitions caused by woody
plant proliferation (Van Auken 2000, Naito and Cairns
2011), structural changes are dramatic, with signiﬁcant
consequences for ecosystem function (Barger et al. 2011,
Eldridge et al. 2011) and management (Bestelmeyer et al.
2011). Although increases in the abundance of shrubs
and trees have been widely reported, less emphasis has
been placed on how spatial patterns develop on
Manuscript received 30 October 2013; accepted 10 December
2013; ﬁnal version received 13 January 2014. Corresponding
Editor: J. A. Ludwig.
4 E-mail: dbrownin@nmsu.edu

landscapes as new individuals are recruited and existing
plants grow. When woody plants proliferate in grasslands, changes in soil organic carbon and nitrogen pools
are closely tied to patterns of shrub distribution. A
better understanding of spatial patterns accompanying
woody cover change could therefore improve our ability
to predict landscape-scale changes in ecosystem carbon
and nitrogen cycling accompanying changes in vegetation structure, shed light on the relative importance of
the interacting factors driving or constraining shifts in
life-form abundance, and increase our understanding of
feedbacks involved with state transitions and their
thresholds (Peters et al. 2004).
Livestock grazing is the most geographically extensive
form of land use worldwide (Asner et al. 2004) and
heavy grazing by domestic herbivores in the late 1800s
and early- to mid-1900s is a shared history for many of
the world’s arid and semiarid ecosystems (hereafter
drylands; Ash et al. 1997, Holechek et al. 2000). Spatial
patterning of vegetation resulting from livestock grazing
can be substantial (Rietkerk et al. 2000), reﬂecting both
direct and indirect inﬂuences on seed dispersal, seedling
recruitment, gap formation, plant competition, soil
properties, and ﬁre (Archer 1994, Fuhlendorf et al.

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DAWN M. BROWNING ET AL.

2008). Woody plant proliferation in drylands often
occurs against this backdrop of altered patterns in the
soil surface and herbaceous cover. As the size and
density of shrubs increases atop this matrix, so too does
the spatial heterogeneity of soil properties (e.g., Throop
and Archer 2008) and the nature of erosion–ﬁre
feedbacks (Okin et al. 2009, Ravi and D’Odorico
2009), typically culminating in the transition from
grass- to shrub-dominated states that represent major
shifts in ecosystem function (Archer 2010, Eldridge et al.
2011).
Studies on the effects of livestock grazing on
vegetation spatial patterns have largely focused on
herbaceous plants (Adler et al. 2001, Rayburn and
Monaco 2011). Grazing-induced changes in patterns of
species composition, above- and belowground biomass
and the size of non-vegetated gaps can inﬂuence woody
plant seedling emergence and survival (e.g., Jurena and
Archer 2003, Montané et al. 2012) and hence patterns of
shrub distribution (Seifan and Kadmon 2006). Furthermore, grazing may intensify shrub–inter-shrub contrasts
(Allington and Valone 2010). Studies that quantify
spatial patterns, spatially structured population dynamics, and their change (e.g., Condit et al. 2000, Miriti
2007, Rayburn and Monaco 2011) therefore have the
potential to enhance our understanding of livestock
grazing inﬂuences on species interactions and environmental heterogeneity in ways not possible with shortterm, ﬁne-scale experiments.
Woody plant encroachment since the late 1800s/early
1900s has been well documented in desert grasslands of
southeastern Arizona (McClaran 2003). Analysis of
temporal changes in shrub cover revealed two distinct
phases on sandy loam uplands: an active encroachment
phase from 1900 through the 1930s, followed by a
stabilization phase from the 1960s through the present
(Browning et al. 2008). The encroachment phase was
characterized by pronounced net increases in woody
plant cover and transition from a perennial grassdominated state to a mixed savanna state, whereas the
stabilization phase was characterized by oscillations
around a mean of approximately 35% shrub canopy
cover to a shrubland state. A companion study, based
on census data from grazing exclosure plots established
in 1932 and re-mapped in 1948 and 2006, further
revealed that removal of livestock in this historically
grazed system resulted in enhanced shrub recruitment
relative to grazed areas over the 74-year period
(Browning and Archer 2011). With the current study
we sought to utilize spatially explicit records from the
plots established in 1932 to quantify how spatial
patterns of shrub distribution changed with these
changes in shrub cover and abundance and to determine
the extent to which the presence or removal of livestock
may have inﬂuenced those patterns. Although quantifying spatial patterns may not permit clear identiﬁcation
of the process or processes that generate them, it is akin
to the multiple working hypothesis approach (Cham-

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berlin 1965) in that it can provide evidence that is
consistent with certain processes and rule out others
(Perry et al. 2006, Franklin 2010).
OBJECTIVES/HYPOTHESES
Our objectives were to use census data from 1932,
1948 and 2006 for the invasive shrub Prosopis velutina
(velvet mesquite) to compare an area historically grazed
by livestock since the mid-to-late 1800s to that of a
heavily grazed area subsequently protected from livestock since 1932. Our comparisons focused on: spatial
patterns of shrubs; spatial autocorrelation of shrub
density at plant neighborhood and plot scales; and
distances between shrubs (hereafter inter-shrub distances).
In addressing these objectives we tested hypotheses
regarding the effects of livestock removal on patterns
of shrub proliferation across space and time. In the
spatial dimension, we hypothesized that removal of
livestock would result in a greater degree of clustering
in mesquite individuals relative to areas where livestock
grazing has persisted. Although mesquite is dispersed
by both rodents (Glendening 1952) and livestock
(Kneuper et al. 2003), livestock are better vectors of
long-distance seed dispersal and are potentially more
effective in terms of the number of seeds dispersed and
enhancing the probability of successful germination
and establishment (Brown and Archer 1987). Removal
of the livestock seed dispersal vector should therefore
reduce recruitment away from parent plants and
thereby indirectly promote a clustered distribution at
short distances approximating canopy radii. Conversely, livestock promote heterogeneity in vegetation via
grazing and trampling of emergent plants (Huntly
1991, Rayburn and Monaco 2011), so patterns on the
protected area are expected to be clustered relative to
the adjacent grazed site.
Shrub cover in recent decades at this site has
ﬂuctuated around 35% (Browning et al. 2008), a level
that approximates the predicted carrying capacity for
woody vegetation for the mean annual rainfall at this
site (Sankaran et al. 2005). We therefore hypothesized
that in the temporal dimension, shrub distributions in
1948 would become regular (uniformly distributed) by
2006 as mesquite stands developed and matured. This
outcome would be expected if dispersal of mesquite
seeds by rodents and livestock and their subsequent
establishment was clumped or random during the
encroachment phase, with density-dependent interactions (self-thinning) generating a regular distribution
during the stabilization phase as shrub cover approached and reached is maximum potential. In this
scenario, mean inter-shrub distances on grazed and
protected areas would be expected to initially have a
higher variance, followed by a net decrease from 1932 to
1948, then stabilize between 1948 and 2006 and be less
variable.

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METHODS
Study site
The study was conducted on the 21 514-ha Santa Rita
Experimental Range (SRER) 80 km south of Tucson,
Arizona along the western edge of the semi-desert
grassland region of the Sonoran Desert (Brown 1994;
31.813468 N, 110.88758 W). Annual precipitation in the
region is bimodal with a pronounced peak in late
summer (July–September monsoon) and a lesser peak in
winter. Mean annual precipitation (1922–2007) at the
Rodent Station rain gauge situated 0.3 km from our
plots was 354 mm with an average summer (June–
September) precipitation of 207 mm (SD ¼ 73) and an
average winter precipitation (October–May) of 147 mm
(SD ¼ 69). Vegetation on the SRER ranges from Larrea
tridentata desert scrub at the lowest elevations to
Quercus spp. woodlands at the highest.
Mesquite (Prosopis spp.) is a leguminous shrub that
has extensively invaded grasslands in the Southern
Great Plains and southwestern United States. At the
SRER, velvet mesquite (P. velutina) is the dominant
shrub at 990–1200 m elevation and increases in its cover
and density since 1900 have been well documented
(McClaran 2003). Our study focused on a 0.8-ha portion
(200 3 40 m) of a plot established on the SRER by
William McGinnies in 1932 to evaluate herbivore effects
on vegetation on a sandy loam upland ecological site
(National Resource Conservation Service reference no.
R041XC319AZ; Breckenfeld and Robinett 2003) at 1100
m elevation. Soils are classiﬁed as Aridisols (ﬁne, mixed,
superactive, thermic Ustic Paleargids; sandy clay loam
surface texture) in late Pleistocene-age Sasabe-Baboquivari complex with an average maximum clay content of
25% at 23 cm depth (Browning et al. 2008). No ﬁres
have been recorded on this site since the SRER was
established in 1902.
The SRER, representative of many of the grasslands
of the Southwestern United States, was severely
degraded by the turn of the 20th century, the result of
decades of heavy, year-round, unregulated cattle grazing. Cattle were removed shortly after the SRER was
established in 1902 to promote vegetation recovery and
then reintroduced in 1916. Year-round grazing was
practiced from 1916–1972, with stocking rates steadily
decreasing from a maximum of 0.17 animal unit years
per hectare in 1918 (Browning et al. 2008). A rotational
grazing system was implemented in 1972 and maintained
through the time of our study (see Mashiri et al. 2008).
Field data collection
The 74-year record of mesquite stand structure
resulted from three exhaustive ﬁeld census campaigns
conducted on plots established on the SRER by William
McGinnies in 1932. These plots were initially designed
to differentially exclude various combinations of livestock and lagomorphs, but only the livestock exclusion
treatments have been maintained since 1952. The 1932

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and 1948 mapping efforts were conducted using a survey
instrument consisting of a telescopic alidade and plane
table (Glendening 1952). Plant locations on these maps
were digitized into a geographic information system
along with plants mapped in 2006 using a global
positioning system (GPS) to achieve ,0.5 m horizontal
accuracy. The geo-coding process for 1932 and 1948
maps yielded positional accuracy similar to that derived
from the 2006 GPS campaign (additional details can be
found in Browning and Archer 2011). The 2006 ﬁeld
effort encompassed a 100 3 40 m area accessible to
lagomorphs and livestock since 1916 (hereafter, grazed
area) and an adjacent area of equal size protected from
livestock since 1932 (hereafter, protected area).
Analyses of spatial pattern on grazed and protected areas
Point pattern methods based on locations of individuals and area methods based on continuous distributions were used to quantify spatial structure. These
combined approaches characterize patterns at multiple
spatial scales (Fortin and Dale 2005) and can reveal
patterns not discernible from one or the other (e.g.,
Barot et al. 1999). Hypothesized changes in mesquite
spatial patterns were evaluated against a null model of
complete spatial randomness (CSR) that describes a
pattern generated by a spatial Poisson process with a
constant ﬁrst-order intensity (k) over the study region
(Fortin et al. 2002). We implemented CSR as the null
hypothesis assuming process stationarity, wherein the
effects of the presence or absence of livestock on the
establishment and arrangement of mesquite plants does
not change over time. In other words, neither the
removal of livestock nor the stage of shrub encroachment would alter patterns of mesquite distributions. If
mesquite density is spatially non-stationary, the ability
to distinguish whether spatial patterns (i.e., clustering)
are due to ﬁrst- or second-order interactions is
confounded (Wiegand and Moloney 2004). While null
models accounting for heterogeneity exist, parameterizing appropriate alternatives to CSR (i.e., choosing
cluster size for a Poisson cluster process or k for a
heterogeneous Poisson process) is problematic due to a
lack of independent data. Local spatial statistics are
unaffected by non-stationarity and were also examined.
The point and area statistics used in this study can
detect clustering or positive spatial autocorrelation
(values signiﬁcantly greater than expected under CSR),
regular (uniform) patterns, or negative spatial autocorrelation (values signiﬁcantly less than expected under
CSR). Point pattern distributions were based on nearest
neighbor distances and all inter-point (plant–plant)
distances. Local and global area-based analyses were
used to quantify livestock removal effects on spatial
autocorrelation and patchiness in mesquite density.
Analysis of mesquite spatial patterns in 1932, the year
when fences were constructed and livestock were
removed from the protected area, were performed using
all plants regardless of whether they occurred inside or

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DAWN M. BROWNING ET AL.

outside of the exclosure. Subsequent analyses for 1932,
1948, and 2006 were conducted for protected and grazed
plots separately to permit comparisons across time.
Second-order point pattern analysis and spatial
autocorrelation methods (e.g., statistics of spatial
variance) were used to determine if mesquite plants on
the protected area exhibited a higher degree of clustering
and patchiness than those on the grazed area; and at
what distances differences in the degree of clustering
occurred. The point pattern analyses quantiﬁed the
proportion of possible pairs of points (individual plants)
in Euclidean space whose members were within a certain
distance from one another. We implemented the
commonly-reported linearized version of Ripley’s K
L(r) (Ripley 1976) and the pair correlation function g(r)
(Stoyan and Stoyan 1994) using the spatstat package in
R version 1.22-1 (Baddeley and Turner 2005). Ripley’s
isotropic edge correction for rectangular study areas was
applied in both cases. This procedure rotates the point
pattern to estimate the point intensity outside the study
area (Ripley 1991). L(r) and g(r) were calculated using
1.0 m lags up to 20.0 m (one half distance of shortest
plot dimension).
Ripley’s K focuses on a point and counts the number
of other points around it within a speciﬁed radius;
counts are cumulative in that sequential distances
encompass all points included in the shorter lags. The
Ripley’s K calculations were made for each point in the
study area to obtain a global statistic. The number of
points within the speciﬁed radius was then compared to
the number of points expected based on a stationary
CSR Poisson process. In this study, Ripley’s K is
reported as L(r)  r for easier interpretation where zero
is the theoretical value or expected number of points at a
speciﬁed radius. A L(r)  r . 0 means there are more
points than would be expected. A L(r)  r , 0 means
there are fewer than expected.
To examine point patterns at a given distance, we
calculated the pair correlation function, g(r) (Stoyan and
Stoyan 1994), which depicts patterns based on nested
rings rather than the circles used to calculate the
cumulative L(r)  r metric. The g(r) looks at a
neighborhood of points surrounding the speciﬁed radius
and gives greater weight to points near the radius and
less weight to points further away. In this type of
weighting, known as an Epanečnikov kernel, points
lying outside the bandwidth are not considered in the
calculation at that radius. We used a bandwidth of 0.5
m, which approximates one-half of the distance between
1-m steps, to insure rings collectively covered the sample
space. Using the ‘‘envelope’’ command in spatstat, we
simulated 999 realizations of a pattern of CSR resulting
from a homogeneous Poisson process. The simulated
points had the same intensity (i.e., point density) as the
observed points. The g(r) and L(r)  r metrics were
calculated at each step for all 999 simulations. High and
low values of the envelopes were the maximum and
minimum statistic values at a given lag. We present the

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L(r)  r metric to enable direct comparisons with values
reported in other studies and the g(r) metric to permit
interpretations at discrete distances.
Global Moran’s I (Moran 1950) and a local indicator
of spatial autocorrelation (LISA; Anselin 1995) were
used to quantify spatial autocorrelation of mesquite
across grazing treatments and time. We used 5 3 5 m
cells to characterize spatial heterogeneity in mesquite
density (number of shrubs per cell) because smaller sizes
would approximate the information conveyed in point
pattern analysis, and because this cell size approximated
the mean size of mesquite canopies when shrubs were
mapped in 1932. Global and local indicators of spatial
autocorrelation were calculated using GeoDa software
version 0.9.5-i (Anselin et al. 2006) for grazed and
protected areas. Moran’s I ranges from 1.0 signifying
dissimilarity between adjacent values to 1.0 signifying
similarity between adjacent values; the expected value
for a random (null) pattern is zero. We quantiﬁed
nearest neighbor correlations (single lag) between each 5
3 5 m cell and its eight neighbors. Signiﬁcant deviations
from random patterns of association relative to the
mean density were determined using 999 random
permutations of Moran’s I for grazing and year
comparisons at a ¼ 0.05.
Local spatial statistics estimate the pattern for each
sample location and are useful when the assumption of
stationarity (a spatially homogeneous pattern-generating process) may be violated (Getis and Ord 1992). We
decomposed the global index of spatial association
(Moran’s I ) into contributions from local neighborhoods using a LISA (Anselin 1995). A target (t) cell with
a high mesquite density surrounded by neighboring (n)
cells of similarly high mesquite density (high(t)–high(n))
could result from short-range seed dispersal (e.g.,
majority of seeds falling near parent plant), facilitation,
or favorable microsite conditions. Conversely, negative
spatial associations (high(t)–low(n) and low(t)–high(n))
could reﬂect competition for light or soil moisture or
allelopathy (Fortin and Gurevitch 2001).
Spatial patterns and stage of shrub encroachment
The hypothesis that the mean and variance of intershrub distances would decrease with shrub stand
development was evaluated using two distance metrics:
the average distance between individual mesquite plants
and their nearest neighbor (NN) and the average
distance between random locations and the nearest
mesquite plant (empty space [ES] function; Baddeley
2010). The ES function is a metric for estimating the
degree of inﬁlling, whereas the NN metric is more
sensitive to clustering of plants based on the single
nearest neighbor (Baddeley 2010). NN statistics were
calculated in ArcGIS version 10.0 using the Near
function (Environmental Science Research Institute
2004).We tested for differences in mean NN distances
using analysis of variance (ANOVA) between years by
grazing treatment and between treatments by year.

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Residuals for mean NN distances mildly violated the
normality assumption; analysis of natural log-transformed data did not affect the conclusions. Multiple
comparisons were conducted using Tukey’s studentized
range tests.
The ES function was calculated using a 200 3 40 m
raster layer with 1.0-m pixels. The 1.0-m pixel size
coincided with the sampling interval (or lag distance)
for point pattern metrics. The mean distance to the
nearest mesquite plant for 4000 pixels in the grazed and
protected areas was calculated for each date using the
Euclidean Distance tool in ArcGIS. The scale-dependent nature of the ES function prohibited use of
ANOVA.
RESULTS
Spatial pattern on grazed and protected areas
Mesquite plants in 1932 were not clustered on either
the grazed area or the area slated for livestock removal
(Fig. 1A). The null hypothesis of CSR could not be
rejected for either spatial metric at any lag distance on
either the grazed or protected areas when the study was
initiated (Fig. 1A, B). Mesquite plants on the protected
area in 1948 were clustered at short (1 and 2 m) and
intermediate (8 m) distances (Fig. 1C). Conversely,
mesquite plants on the grazed area in 1948 were
randomly distributed at all distances. Clustering of
mesquite on the protected area in 2006 was even more
pronounced and evident at all distances between 1 and
12 m (Fig. 1D), with peak clustering occurred at 1–2 m.
In contrast, there was no evidence of signiﬁcant
clustering on the grazed area at any distance.
At the time plots were established in 1932, mesquite
densities were not spatially autocorrelated relative to
what would be expected under CSR for the area
designated for continued grazing (Moran’s I ¼ 0.047,
P ¼ 0.104). In contrast, mesquite densities were weakly,
but positively autocorrelated on the area designated for
livestock removal (Moran’s I ¼ 0.082, P ¼ 0.026; Fig.
2A). The lack of spatial autocorrelation in mesquite
density on the grazed area was consistent across time,
whereas patterns in mesquite density on the protected
area become increasingly positively autocorrelated (2006
Moran’s I ¼ 0.261, P ¼ 0.001; Fig. 2A–C). The slope of
the line (i.e., Moran’s I value) remained ﬂat for the
grazed area, but progressively increased on the protected
area owing to the development of high-density focal cells
surrounded by high-density neighboring cells.
Spatial patterns of local differences in neighbor
associations between grazed and protected areas are
further illustrated in Fig. 3. Positive associations (lowdensity focal cells surrounded by low-density neighboring cells [designated ‘‘low–low’’] and high-density focal
cells surrounded by high-density neighboring cells
[designated ‘‘high–high’’]) were present on the area
slated for livestock and lagomorph exclusion, but were
not evident on the area designated for continued
livestock grazing. By 1948, additional areas of locally

1425

high (dark red) and low (dark blue) shrub densities
(relative to random) had developed on both the grazed
and protected area, but were much more common and
pronounced in the protected area. The areas of relatively
high and low shrub density on the protected area
persisted to 2006, and in most cases, expanded in size to
magnify the spatial contrasts in shrub distributions on
grazed and protected areas. To illustrate linkages
between global and local measures of association, two
5 3 5 m subplots that deviated from mean density most
strongly on the protected plot are circled in Fig. 2 and
denoted by stars in Fig. 3.
Spatial patterns and stage of shrub encroachment
The shift toward regularity in mesquite plant distributions hypothesized to occur with stand development
was not observed. In fact, the non-cumulative point
pattern metric g(r) demonstrated an increasingly clustered distribution on the protected area from 1932 to
2006 (Fig. 1). Mean mesquite NN distances were
consistently lower on the protected area relative to the
grazed area in all years (Table 1; 1932 P ¼ 0.014, 1948 P
¼ 0.003, and 2006 P ¼ 0.001). Mean NN distances
decreased signiﬁcantly from 1932 to 1948 on both areas.
NN distances then stabilized on the grazed area between
1948 and 2006, but continued to decrease on the
protected area. Variance associated with NN distances,
as indicated by coefﬁcients of variation (CV), remained
virtually constant from 1932 to 1948 on both grazed and
protected areas then declined slightly on both areas from
1948 to 2006.
The mean ES metric (mean distance from a given
point to the nearest mesquite plant) also declined on the
two areas over time, more so on the protected area than
on the grazed area, and in 1948 and 2006 their rank
order was reversed (Table 1; Fig. 4). Empty space
distances continued to decline on both areas from 1948
to 2006, but more so for the protected area.
DISCUSSION
There is active debate regarding the factors contributing to the destabilization of the balance between
woody and herbaceous life-forms that has occurred in
recent decades to favor trees and shrubs over grasses in
many semi-arid and arid regions (Scholes and Archer
1997, Archer 2010). The majority of studies have
focused on tree–grass or shrub–grass interactions and
the extent to which these contrasting life-forms may
partition soil, water, or nutrient resources in time (e.g.,
phenology) or space (e.g., contrasting root systems)
and how climate and disturbance might alter these
interactions. Few have looked at spatial patterns. What
is lacking is an understanding of how interactions
between woody plants might inﬂuence patterns of
increasing density when interactions with herbaceous
vegetation are disrupted and the extent to which
density-dependent interactions might limit their maximum potential cover or biomass. Spatial pattern

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FIG. 1. Univariate point pattern metrics (insets, linearized version of Ripley’s K [L(r)  r] and pair correlation function [g(r)])
derived from mesquite locations mapped in 1932, 1948, and 2006. Metrics (black lines) were calculated at 1.0 m intervals up to 20
m. The simulation envelope (gray shading) depicts the upper and lower limits from 999 Monte Carlo simulations. A black line
outside the gray shaded envelope indicates clustering (line above) or over-dispersion (line below) than expected due to chance at a
given distance. Within the simulation envelope, the metric does not differ from that expected at random.

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74-YEAR SPATIAL PATTERNS OF TRANSITION

1427

analyses and experimental removal studies have explored woody plant spacing to assess competition
between woody plants and the results are equivocal
(reviewed by Sea and Hanan [2011]). With this study we
sought to infer the intensity of intraspeciﬁc shrub–
shrub interactions from quantitative analyses of spatial
associations over decadal timescales and how these
might be mediated by the removal of livestock.
Spatially explicit historical census records are uncommon and tend to be collected at a relatively small spatial
extent (Miriti et al. 1998, Bowers et al. 2004). To gauge
whether our results represent larger surrounding landscapes, we were limited to estimates of shrub cover. We
quantiﬁed changes in shrub cover using time series aerial
photography (1936, 1971, 1996, 2005) of three additional livestock exclosures on the SRER and the grazed
areas surrounding them. Shrub cover on these adjacent
sites generally, with comparable soils, tracked those
reported for plots in Browning and Archer (2011) and
expanded herein, with cover values on the protected
areas being consistently higher than those on the grazed
areas (data not shown). Additionally, 1932 and 1948
ﬁeld estimates of plant size and density within the 0.4 ha
grazed and protected areas in this study were within the
range of values reported by Glendening (1952) for two
1.8 ha plots (see Fig. 2; Browning and Archer 2011).
Thus, there is reason to believe that shrub dynamics
reported herein are indicative of changes occurring over
a broader area.
Contrasting spatial patterns on grazed
and protected areas
Mesquite plants on the protected site were somewhat
more aggregated than those on the grazed site when
livestock were excluded in 1932. These subtle initial
differences in spatial autocorrelation may reﬂect
chance or local variation in subsurface soil properties
known to occur on these landscapes (Breckenfeld and
Robinett 2003). Although soils on both areas were
classiﬁed similarly, soils are mapped as ‘‘complexes’’
and inclusions have been estimated to constitute 10–
15% of each soil complex (Breckenfeld and Robinett
1997). Third-order soil surveys are generally based on
minimal distributed sampling. A detailed, spatially
explicit sampling of sub-surface soil properties within
the two areas would clarify these competing interpretations.
We hypothesized that the presence of livestock would
promote random patterns of mesquite distribution,
whereas their removal would promote clustering. The
evidence supported this hypothesis. Mesquite density
increased on both the grazed and protected site, but
spatial autocorrelation and the development of highdensity patches intensiﬁed with time on the protected
area through the development of clusters at short
distances and subsequent inﬁlling, but did not deviate
from random on the grazed area (Figs. 1–3). If
independent data had been available to parameterize

FIG. 2. Global Moran’s I (inset values) and scatter plot of
the standardized density of mesquite plants within 5 3 5 m focal
cells in relation to that of its eight neighboring cells on grazed
(ﬁlled circles, dashed regression lines) and protected (open
triangles, solid lines) plots in (A) 1932, (B) 1948, and (C) 2006.
Moran’s I ranges from 1.0, signifying dissimilarity between
adjacent values, to 1.0, signifying similarity between adjacent
values; the expected value for a random (null) pattern is zero.
Density designations represent focal cells–surrounding cells
(e.g., ‘‘high–high’’ denotes a high-density focal cell surrounded
by high-density neighboring cells). Data for 1932 represent
conditions present when livestock exclosures were constructed.
P values are based upon 999 randomizations. To illustrate
linkages between global and local measures of association, two
cells that deviated from mean density most strongly are
identiﬁed in panels (B) and (C) with circles and in Fig. 3 with
stars.

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DAWN M. BROWNING ET AL.

Ecological Applications
Vol. 24, No. 6

FIG. 3. Local indicator of spatial association (LISA) cluster maps and associated global Moran’s I values for mesquite plant
density within 320 5 3 5 m cells (dotted lines). Mesquite density designations (high and low as per Fig. 2) represent focal cells–
surrounding cells. White cells indicate associations are not signiﬁcantly different from random. P values are based upon 999 Monte
Carlo simulations. The top panel uses all data to depict density patterns in 1932 when exclosures were constructed. The remaining
panels use treatment-speciﬁc density data. Cells with strongest deviations from mean density are denoted with black stars (see also
circled points in Fig. 2). Animal proﬁles indicate livestock and lagomorph presence. Symbols in a red circle with a line through it
indicate livestock and lagomorph exclusion.

a heterogeneous null model, we may have been less
likely to detect signiﬁcant clustering on the protected
site. However, the pattern differences between the
grazed and protected areas, and their maintenance and
intensiﬁcation over time, were supported by multiple
lines of evidence (global and local, point and area
statistics).
The promotion of random mesquite distributions by
livestock ostensibly reﬂects a combination of factors.
Cattle are well known for their ability to disperse large
numbers of viable seeds away from parent plants and

thus provide numerous opportunities for recruitment
across a landscape (Brown and Archer 1987). In
addition, widespread grazing by livestock may uniformly reduce herbaceous interference, thereby providing more sites suitable for shrub seedling establishment
(e.g., Seifan and Kadmon 2006). Conversely, the
clustering of mesquite plants observed on the area
protected from livestock presumably reﬂects fewer
opportunities for recruitment away from parent plants
owing to dual constraints imposed by limited seed
dispersal and an herbaceous matrix comprising more

September 2014

74-YEAR SPATIAL PATTERNS OF TRANSITION

1429

TABLE 1. Mesquite plant population metrics, spatial statistics, and empty space distance for mesquite plant locations within 100 3
40 m areas grazed by or protected from livestock since 1932.
Density (no. plants/ha)
Year
1932
1948
2006

Grazed
172.5
317.5
442.5

Protected
202.5
602.5
960.0

Canopy area (m2)
Grazed
A,a

4.0 (0.70)
2.6A,b (0.69)
2.4A,b (0.54)

Nearest neighbor (m)

Protected
B,a

3.0 (0.70)
2.0B,b (0.70)
1.6B,c (0.63)

Grazed
4.0 (0.55)
3.1 (0.57)
2.6 (0.59)

Protected
4.6 (0.72)
2.3 (0.66)
1.8 (0.61)

Empty space (m)
Grazed
A

7.0 (1.3)
6.0A (1.0)
3.8A (0.6)

Protected
4.7A (3.0)
3.6B (0.7)
2.5B (0.2)

Notes: Mesquite plant population metrics are density and canopy area. Values for canopy area are means with SE in parentheses.
Spatial statistics are distance to nearest neighbor (NN, mesquite-to-mesquite) and its coefﬁcient of variation in parentheses (CV ¼
SD/mean), and empty space distance (distance from the center of a given 1.0 3 1.0 m cell to nearest mesquite plant and its CV in
parentheses). Signiﬁcant differences (a ¼ 0.05) across treatments are denoted with capital letters; differences between years are
denoted with lower case letters (means that share a letter are not signiﬁcantly different). See Fig. 4 for patterns of empty space
distribution.

competitive plants and hence a restricted subset of
locations for shrub seedling establishment. These
contrasting scenarios point to the need for a better
understanding of seed dispersal and grass–shrub

seedling interactions and the integration of these
competing perspectives into a framework for predicting
the effects of alternative livestock management practices on the shrub encroachment process.

FIG. 4. Maps depicting the distance in meters from a given 1.0-m pixel (8000 total pixels) to the nearest mesquite plant in 1932,
1948, and 2006. Maximum distances (upper right of each panel) are for the entire area; see Table 1 for mean distances on grazed vs.
protected areas. Livestock were excluded from the right half of the area starting in 1932. Prior to that time, the entire area had been
heavily and continuously grazed.

1430

Ecological Applications
Vol. 24, No. 6

DAWN M. BROWNING ET AL.

Spatial patterns and stage of shrub encroachment
Nearest neighbor and second-order spatial statistics
have been used to demonstrate regular patterns among
woody plants and infer intraspeciﬁc competition (e.g.,
Smith and Goodman 1986, Getzin et al. 2006, Meyer et
al. 2008). We hypothesized that the distribution of
mesquite would become increasingly regular as mesquite
stands transitioned from the encroachment phase to the
stabilization phase. Mesquite density increased substantially on both the grazed and protected site throughout
the 74-yr period (Table 1) and mesquite associations in
the protected area exhibited a higher degree of
patchiness with spatial associations both higher and
lower than expected, yielding pockets of high and low
mesquite density (Fig. 3). Thus, there should have been
ample opportunity for density-dependent interactions to
promote a regular spatial distribution, particularly on
the protected site where densities were substantially
higher. However, we saw no evidence that shrub
recruitment was leveling off and no evidence of a
progression toward a regular distribution that might
indicate self-thinning or intraspeciﬁc density-dependent
interactions. To the contrary, spatial aggregation on the
protected area became more pronounced through 1948
and 2006.
There are several lines of evidence suggesting shrub–
shrub interactions should intensify as shrub abundance
increases. Field studies in desert systems have long noted
both clumped and regular patterns of shrub distribution
and the occurrence of overlapping root systems, and
from this have inferred that distributions shift from
clumped to regular as shrubs grow and stands develop
(e.g., Phillips and MacMahon 1987, Wiegand et al.
2005). These inferences have been supported, at least
partially, by neighbor removal experiments (Fonteyn
and Mahall 1981, Manning and Barbour 1988, Ansley et
al. 1998) and time-series aerial photos showing declines
in rates of shrub cover increase with increasing shrub
cover (Fensham et al. 2005) and shifts from clustered to
regular distributions (Goslee et al. 2003). Furthermore,
mesquite plants on our site have extensive shallow
lateral root systems that extend well beyond their
canopies (Cable 1980). These shallow roots are important to plant water balance (Ansley et al. 1991) and
ostensibly inﬂuence intraspeciﬁc competition for soil
resources. Indeed, ﬁeld data from the Santa Rita site
have documented decreases in shrub growth rates
(Glendening 1952) and declines in the probability of
shrub recruitment (Browning and Archer 2011) with
increasing shrub abundance. Furthermore, continentalscale assessments suggest that mean annual precipitation
(MAP) sets the upper limit for potential shrub cover
(Sankaran et al. 2005). Shrub cover on landscapes with
soils similar to those on the long-term plots in our study
have approximated the predicted upper limit (approximately 37% for 370 mm MAP; Browning et al. 2008),
suggesting there has been ample time for shrub–shrub
interactions to inﬂuence patterns of association. Thus,

there are numerous reasons to expect the intensity of
shrub–shrub interactions to increase with time on this
site. Why then have we not seen evidence of self-thinning
on our long term plots?
Field-estimated shrub cover on our long-term plots in
2006 (15–22% on grazed and protected areas, respectively; Browning and Archer 2011) was well below the
predicted maximum for our annual rainfall (37%,
Sankaran et al. 2005). These low cover values likely
reﬂect a pasture-wide herbicide application in 1964 and
1965 conducted as part of range management study.
This would not necessarily have inﬂuenced patterns of
association, as shrubs vegetatively regenerated quickly
after the herbicide application (see Browning and Archer
[2011] for details). Even so, it reduced shrub cover and
may have relaxed the intensity of plant interactions. It
could also be that intraspeciﬁc competition in this
system is minimal. This possibility is consistent with the
tendency toward more pronounced spatial aggregation
with time on the protected area (Figs. 1, 3, 4) and with
results from ﬁeld experiments showing little or no shrub
response to neighbor removals in other systems (Miller
and Huenneke 2000, Simmons 2003).
If intraspeciﬁc competition is not important, what
then what might explain the limits to woody cover
imposed by mean annual precipitation predicted by
Sankaran et al. (2005) and locally documented by
Browning et al. (2008) for our study site? One hypothesis
is related to potential hydraulic constraints on shrub size
in dryland systems (e.g., Sperry and Hacke 2002, Hacke
et al. 2006). As shrubs approach their upper size limit
for a site with a given soil texture, depth, topographic
setting, etc., their ability to maintain continuity in xylem
water transport may become increasingly jeopardized
and lead to higher probabilities of branch or wholecanopy mortality. This loss of plant branch systems or
canopies would constitute reductions in canopy cover
that would have to be compensated for by recruitment
of new plants or growth of other, smaller plants if standlevel canopy cover were to be maintained. Support for
this proposition comes from observations of height
asymptotes and shifts in leaf–stem biomass allocation
for mesquite in a variety of Chihuahuan Desert
landforms (Martinez and Lopez-Portillo 2003); and the
utility of allometry theory in characterizing size–
abundance relationships within creosote bush stands
(Larrea spp.; Allen et al. 2008).
Mechanisms imposing the upper limits of woody plant
stature and density on this site thus remain open to
speculation. However, their elucidation has important
implications for predicting the effects of tree and shrub
proliferation in drylands, a globally extensive phenomenon, on land-surface–atmosphere interactions, primary
production, and carbon cycling.
ACKNOWLEDGMENTS
We acknowledge the extraordinary legacy of W. McGinnies
and G. Glendening. Historic maps were provided by the SRER
Archive Database at the University of Arizona. Funding was

September 2014

74-YEAR SPATIAL PATTERNS OF TRANSITION

provided through the U.S. EPA STAR Graduate Fellowship
FP-91637801-3 to D. M. Browning, NSF grant DEB-0824708
to J. Franklin, and NASA grant NAG5-11238 and NSF grant
DEB-9981723 to S. R. Archer. U.S. EPA has not ofﬁcially
endorsed this publication and the views expressed herein may
not reﬂect the views of the U.S. EPA, NSF, or NASA. We
thank K. Predick, M. McClaran, K. Havstad, J. Brown, J.
Karl, and S. J. Rey for helpful comments and insightful
discussions. We thank two anonymous reviewers who provided
thoughtful feedback that improved the clarity of the manuscript.
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