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Cross–Scale Interactions and
Changing Pattern–Process
Relationships: Consequences for
System Dynamics
Debra P. C. Peters,
1,
* Brandon T. Bestelmeyer,
1
and Monica G. Turner
2
1
USDA ARS, Jornada Experimental Range, MSC 3JER, NMSU, Las Cruces, New Mexico 88003-0003, USA
2
Department of Zoology, University of Wisconsin, Madison, Wisconsin 53706, USA
ABSTRACT
Cross–scale interactions refer to processes at one
spatial or temporal scale interacting with processes
at another scale to result in nonlinear dynamics
with thresholds. These interactions change the
pattern–process relationships across scales such
that fine-scale processes can influence a broad
spatial extent or a long time period, or broad-scale
drivers can interact with fine-scale processes to
determine system dynamics. Cross–scale interac-
tions are increasing recognized as having important
influences on ecosystem processes, yet they pose
formidable challenges for understanding and fore-
casting ecosystem dynamics. In this introduction to
the special feature, ‘‘Cross–scale interactions and
pattern–process relationships‘‘, we provide a syn-
thetic framework for understanding the causes and
consequences of cross–scale interactions. Our
framework focuses on the importance of transfer
processes and spatial heterogeneity at intermediate
scales in linking fine- and broad-scale patterns and
processes. Transfer processes and spatial heteroge-
neity can either amplify or attenuate system
response to broad-scale drivers. Providing a
framework to explain cross–scale interactions is an
important step in improving our understanding
and ability to predict the impacts of propagating
events and to ameliorate these impacts through
proactive measures.
Key words: ecological surprises; landscape ecol-
ogy; propagating events; spatial heterogeneity;
transfer processes.
INTRODUCTION
Cross–scale interactions are increasingly recognized
as important features of ecological systems that
challenge our ability to understand and forecast
dynamics (Holling 1992; Levin 1992; Thompson
and others 2001). Cross–scale interactions (CSI)
refer to processes at one spatial or temporal scale
interacting with processes at another scale that of-
ten result in nonlinear dynamics with thresholds
(Carpenter and Turner 2000; Gunderson and Hol-
ling 2002; Peters and others 2004a). These inter-
actions generate emergent behavior that cannot be
predicted based on observations at single or mul-
tiple, independent scales (Michener and others
2001). Cross–scale interactions can be important
both for extrapolating information about fine-scale
processes to broad-scales or for down-scaling the
effects of broad-scale drivers on fine-scale patterns
(Ludwig and others 2000; Diffenbaugh and others
2005). The relative importance of fine- or broad-
scale pattern–process relationships can vary
through time, and compete as the dominant factors
Received 2 October 2007; accepted 20 October 2007; published online 22
June 2007.
*Corresponding author; e-mail: debpeter@nmsu.edu
Ecosystems (2007) 10: 790–796
DOI: 10.1007/s10021-007-9055-6
790
controlling system dynamics (for example, Rodo
´
and others 2002; King and others 2004; Yao and
others 2006).
Although CSI are recognized as important, a
critical challenge in ecology is how fine-scale pat-
tern–process relationships are connected to broader
patterns and drivers to result in ecosystem change
(Thompson and others 2001; Turner 2005). In
addition, the Millennium Ecosystem Assessment
indicated that CSI are an urgent research priority
for ecologists (Carpenter and others 2006). Our
goal is to provide a framework for explaining how
domains of scale are connected to generate non-
linear dynamics. We focus on transport processes
and spatial heterogeneity at intermediate scales as
the key to linking fine- and broad-scale processes.
We start this special feature with a description of
the framework and its development from existing
bodies of theory. The following papers in the spe-
cial feature provide support for the framework from
a diverse array of ecosystem types and observer
perspectives. The CSI concept provides a powerful
tool for improving our understanding of ecosystem
dynamics and their often surprising and far-
reaching consequences.
Related Frameworks
Most frameworks for nonlinear ecosystem behavior
are hierarchical such that a small number of
structuring processes control ecosystem dynamics;
each process operates at its own temporal and
spatial scale (Allen and Starr 1982; O‘Neill and
others 1986). Finer scales provide the mechanistic
understanding for behavior at a particular scale,
and broader scales provide the constraints or
boundaries on that behavior. Functional relation-
ships between pattern and process are consistent
within each domain of scale such that linear
extrapolation is possible within a domain (Wiens
1989). Thresholds occur when pattern–process
relationships change rapidly with a small or large
change in a pattern or environmental driver
(Groffman and others 2006; Bestelmeyer 2006),
although both external stochastic events and
internal dynamics can drive systems across
thresholds (Scheffer and others 2001). Crossing a
threshold can result in a regime shift where there is
a change in the direction of the system and the
creation of an alternative stable state (Allen and
Breshears 1998; Davenport and others 1998;
Walker and Meyers 2004).
Under some conditions, thresholds may be rec-
ognized when changes in the rate of fine-scale
processes within a defined area propagate to
produce broad-scale responses (Gunderson and
Holling 2002; Redman and Kinzig 2003). In these
cases, fine-scale processes interact with processes at
broader scales to determine system dynamics. A
series of cascading thresholds can be recognized
such that crossing one pattern–process threshold
induces the crossing of additional thresholds as
processes interact (Kinzig and others 2006). For
example, a series of thresholds defined by increases
in the rate of fire spread occur in wildfire as the
dominant processes and scales change over time
(Peters and others 2004a). Wildfires are often ini-
tiated with a single lightning strike that ignites a
tree or patch of herbaceous vegetation. Initially, the
rate and extent of fire spread is related to individual
tree properties, such as the density and spatial
arrangement of green versus brown leaves or
needles. Fire spread to another tree within a patch
of trees depends on fuel characteristics of the patch
interacting with individual tree properties. Some
trees will ignite easily whereas other trees with
similar characteristics may not burn or will burn
slowly because of low connectivity with adjacent
trees. As the fire continues to spread, additional
patches of trees will ignite depending on interac-
tions among fuel load characteristics connecting
patches, fuel load within the patch, and individual
tree properties. The dominant process changes
through time from the scale of individual trees to
within-patch variation to among-patch connectiv-
ity. For very large fires, land–atmosphere interac-
tions can become operative to create fire-generated
weather that results in a rapid increase in the rate
of fire spread. At this point in time, broad-scale
processes drive system dynamics by overwhelming
processes at tree and patch scales. Thus, wildfire
behavior can only be explained by considering
interactions among pattern–process relationships
occurring at each spatial and temporal scale.
Recent theories and ideas about system behavior
have used hierarchy theory as a basis for describing
interactions among processes at different scales.
Such theories include complex systems (Milne
1998; Allen and Holling 2002), self-organization
(Rietkerk and others 2004), panarchy (Gunderson
and Holling 2002), and resilience (Holling 1992;
Walker and others 2006). CSI are an integral part of
all of these ideas. However, these frameworks do
not explain how patterns and processes at different
scales interact to create nonlinear dynamics. Be-
cause CSI-driven dynamics are believed to occur in
a variety of systems, including lotic invertebrate
communities in freshwater streams (Palmer and
others 1996), lakes (Stoffels and others 2005),
mouse populations in forests (Tallmon and others
Cross–scale Interactions and Pattern–Process Relationships 791
2003), soil microbial communities (Smithwick and
others 2005), coral reef fish recruitment in the
ocean (Cowen and others 2006), human diseases
(Rodo
´and others 2002), and grass–shrub interac-
tions in deserts (Peters and others 2006), it is crit-
ical that ecologists find ways to measure CSI. We
hope that the ideas presented in this and the fol-
lowing set of papers facilitate this endeavor.
FRAMEWORK FOR CROSS–SCALE
INTERACTIONS AND CHANGING
PATTERN–PROCESS RELATIONSHIPS
We hypothesize that intermediate-scale properties
of transfer processes and spatial heterogeneity
determine how pattern–process relationships
interact from fine to broad scales (Figure 1).
Although we recognize that a continuum of scales
exists and our framework is sufficiently general to
accommodate additional scales, we focus on three
domains of scale: ‘‘fine‘‘ at the scale of individual
plants and animals, ‘‘intermediate‘‘ at the scale of
groups of individuals of the same or different
species, and ‘‘broad‘‘ refers to large spatial extents
such as landscapes, regions, and the globe. Fine-
scale pattern–process relationships include both
biotic (for example, recruitment, competition,
mortality) and abiotic processes (for example,
sediment loss, soil water dynamics) that influence
the distribution and abundance of individuals.
Intermediate-scale pattern–process relationships
refer to the spatial patterns of groups of individ-
uals (for example, patches or populations) that
both influence and are structured by transfer
vectors (for example, wind, water, fire, dispersing
animals) that move materials and effects hori-
zontally and vertically (for example, propagules,
nutrients, disturbances). Broad-scale pattern–pro-
cess relationships include atmospheric circulation
processes that influence pattern from landscapes
to regions and continents. Environmental drivers,
such as climate, disturbance, and human activities,
influence pattern–process relationships at each
domain of scale.
In our framework, within a domain of scale (that
is, fine, intermediate or broad), patterns and pro-
cesses can reinforce one another and be relatively
stable (Figure 1A). Changes in external drivers or
disturbances can alter pattern–process relationships
in two ways. First, altered patterns at fine scales can
result in positive feedbacks that change patterns to
the point that new processes and feedbacks are
induced. This shift is manifested in nonlinear,
threshold change in pattern and process rates. For
example, in arid systems, disturbance to grass pat-
ches via heavy livestock grazing can reduce the
competitive ability of grasses and allow shrub col-
onization. After a certain density of shrubs is
reached in an area and vectors of propagule
transport (for example, livestock, small animals)
are available to spread shrubs to nearby grasslands,
shrub colonization and grass loss can become under
the control of dispersal processes rather than
competition. Shrub expansion rates can increase
dramatically (Peters and others 2006). As shrub
colonization and grazing diminish grass cover over
large areas, broadscale wind erosion may govern
subsequent losses of grasses and increases in shrub
dominance. These broad-scale feedbacks ‘‘down
scale‘‘ to overwhelm fine-scale processes in rem-
nant grasslands. Once erosion is an important
landscape-scale process, neither competition nor
dispersal effects have significant effects on grass
cover. Second, direct environmental effects on pat-
tern–process relationships at broad scales can sim-
ilarly overwhelm fine-scale processes. For example,
regional, long-term drought can produce wide-
spread erosion and minimize the importance of
local grass cover or shrub dispersal to patterns in
grasses and shrubs.
Under the conditions that intermediate-scale
transfer processes and spatial heterogeneity are not
important, then linear extrapolation can be used to
aggregate information from fine to broad scales
(Strayer and others 2003; Peters and others 2004b;
Turner and Chapin 2005). Alternatively, if transfer
processes are negligible yet spatial heterogeneity is
important, then an area can be stratified to obtain
homogeneous, independent cells where linear
extrapolation can also be used to aggregate within
each cell. Aggregation to the entire spatial extent is
typically accomplished using weighted averaging or
similar techniques.
However, when connections among spatially
heterogeneous areas via transfer processes are
important, then a spatially-explicit approach is
needed that accounts for the rate, magnitude, and
direction of materials being transported (Strayer
and others 2003; Peters and others 2004b; Turner
and Chapin 2005). Under these conditions, exam-
ination of patterns and processes at a single scale or
even multiple scales is insufficient. Studies are
needed that include pattern–process relationships
interacting across a range of appropriate scales. For
example, recent studies show that the cross–scale
relationships between cholera and the change in
frequency and intensity of ENSO events since 1976
can only be determined using nonlinear statistical
techniques that include data collected at appropri-
792 D. P. C. Peters and others
ate scales (Rodo
´and others 2002). Previous studies
that failed to find a relationship between global
climate change and human disease transmission
often included linear approaches and scale mis-
matches (Pascual and others 2000; Patz 2002).
Transfer processes and spatial heterogeneity can
either amplify or attenuate system response to
broad-scale drivers (Diffenbaugh and others 2005).
Amplification occurs when the rate of change in
system properties increases nonlinearly. This in-
crease can result from high spatial heterogeneity
that promotes connectivity and cascading events,
such as in the wildfire example described above
(Peters and others 2004a). Cascading events in
which a fine-scale process propagates nonlinearly
to have a large impact have also been documented
in the climate system and in lakes (Lorenz 1964;
Wilson and Hrabik 2006).
Figure 1. ADiagram representing cross–scale interactions. Solid arrows represent pattern–process feedbacks within three
different scale domains with one example of pattern and process shown for each domain. Green arrows indicate the direct
effects of environmental drivers or disturbances on patterns or processes at different scales (for example, patch disturbance
vs. climate). Blue arrows indicate the point at which altered feedbacks at finer scales induce changes in feedbacks at broader
scales (for example, fine-scale changes cascade to broader scales). Red arrows indicate when changes at broader scales
overwhelm pattern–process relationships at finer scales. BOur framework for understanding cross–scale interactions
focuses on the importance of transfer processes and spatial heterogeneity at intermediate scales providing the linkage
between fine-scale processes and broad-scale pattern. Environmental drivers can influence each domain of scale. Arrows
showing cross domain interactions are not shown. Authors of papers in this special issue are listed with their broad-scale
pattern and emergent behavior.
Cross–scale Interactions and Pattern–Process Relationships 793
Attenuation occurs when the rate of change de-
creases through time, such as the decrease in wave
amplitude as the wave form associated with a tsu-
nami increases (Merrifield and others 2005). The
result is that the greatest effects of a tsunami occur
closest to the source of the seismic event, and
spatial heterogeneity in land or sea features become
increasingly important as distance from the seismic
event increases (Fernando and McCulley 2005).
Thus, small-scale variation in wave height and
impact were related to coral reef heterogeneity off
the coast of Sri Lanka following the tsunami of
2005 that did not occur at closer locations such as
Banda Aceh (Fernando and McCulley 2005). In
other cases, the relationship between transfer pro-
cesses and spatial heterogeneity is more complex.
For example, connectivity of larvae from coral reef
fishes is more locally important and regionally
more variable than previously thought based on
new analyses of dispersal constraints interacting
with physical oceanography (Cowen and others
2006).
EXAMPLES OF CSI
Although each paper in this special feature has a
unique broad-scale pattern and emergent behavior
to be understood and predicted, similar fine-scale
processes and environmental drivers are often
studied, and a small set of transfer processes and
spatial heterogeneity characteristics are required to
explain these dynamics (Figure 1B). This generality
suggests great promise in applying our framework
to many other systems and questions where pat-
tern–process relationships may change with spatial
and temporal scale.
Using our common framework provides new
insights into dynamics for a variety of systems,
ranging from fire behavior and vegetation response
in temperate forests (Allen 2007; Falk and others
2007) to gastropod biodiversity in tropical forests
(Willig and others 2007), sediment movement from
rangelands (Ludwig and others, unpublished data)
muskrat metapopulation dynamics in freshwater
marshes (Schooley and Branch 2007), and shrub
thickets and barrier island dynamics (Young and
others 2007). For example, new insights to fire
behavior and forest dieback were found by con-
sidering interactions among fire spread, water flow,
and insect pest dispersal with spatial heterogeneity
in fuel loads, bare soil patches, and insect food re-
sources; drought and livestock grazing act to mod-
ulate these interactions (Allen 2007). Falk and
others (2007) were able to explain the spatial and
temporal distribution of fires only after connectiv-
ity in fuel loads as affected by landforms and cli-
mate were explicitly considered.
In a coastal system, the apparent paradox be-
tween expanding shrub thicket areas and decreas-
ing island areas was explained by understanding
the role of variability in ocean currents and sedi-
ment transport (Young and others 2007). Sediment
movement from upland rangelands to downslope
areas also required information about the connec-
tivity of patches by water (Ludwig and others,
unpublished data).
Animal dynamics an also be understood within a
CSI framework. Variability in the biodiversity of
gastropods in tropical forests was hypothesized to
be explained by local demographics interacting
with dispersal among forest patches created by
hurricanes (Willig and others 2007). Predicting
metapopulation dynamics of muskrats in freshwa-
ter marshes requires an understanding of spatial
heterogeneity of habitat quality and patch con-
nectivity (Schooley and Branch 2007).
IMPROVING UNDERSTANDING AND
PREDICTIONS
Relating phenomenon across scales remains a
critical problem in ecology (Levin 1992). Because
CSIs often result in nonlinear or unexpected
behavior that make understanding and prediction
difficult, it is critical to identify the conditions or
systems that are susceptible to these interactions.
Approaches that have been used previously in-
clude measuring responses at multiple scales
simultaneously and then testing for significant
effects of variables at each scale (for example,
Smithwick and others 2005; Stoffels and others
2005). Experimental manipulations can be used to
examine processes at fine and intermediate scales,
and to isolate and measure impacts of broad-scale
drivers under controlled conditions (for example,
Palmer and others 1996; King and others 2004).
Stratified-cluster experimental designs show
promise as efficient methods for considering
multiple scales in spatial variables, and to account
a priori for distance as related to transport pro-
cesses in the design (Fortin and others 1989; King
and others 2004).
Quantitative approaches also show promise in
identifying key processes related to CSI. Statistical
analyses based on non-stationarity (Rodo and
others 2002) and nonlinear time series analysis
(Pascual and others 2000) are useful for identifying
key processes at different scales. Spatial analyses
that combine traditional data layers for fine-
and broad-scale patterns with data layers that use
794 D. P. C. Peters and others
surrogates for transfer processes at intermediate
scales (for example, seed dispersal) can isolate
individual processes and combinations of processes
that influence dynamics in both space and time (for
example, Yao and others 2006). Simulation models
that use fine-scale models to inform a broader-scale
model can be used to examine the relative impor-
tance of processes and drivers at different scales,
and their interactions, to system dynamics (Moor-
croft and others 2001; Urban 2005). Coupled bio-
logical–physical models that include population
processes and connectivity among populations as
well as broad-scale drivers have been used to show
the conditions when connectivity is important, and
to identify the locations that are more susceptible
or resilient to management decisions (Cowen and
others 2006).
We hope this Special Feature will help catalyze
development of new concepts and approaches for
dealing effectively with the challenges of CSI posed
by the rapid and multi-scale changes occurring on
Earth.
ACKNOWLEDGMENTS
This work was supported by the Long Term
Ecological Research Program at the National
Science Foundation through grants to New
Mexico State University (DEB 0080412), the
University of New Mexico (DEB 0217774), and
the University of Wisconsin (DEB 0083545 and
DEB 0117533).
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Ecosystems (in press).
796 D. P. C. Peters and others
