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How Habitat Edges Change Species Interactions:
A Synthesis of Data and Theory
William F. Fagan,13
Robert Stephen Cantre11,2
and Chris Cosner2
'Department of Biology
Box 871501
Arizona State University
Tempe, AZ 85287-1501
2 Department of Mathematics
University of Miami
Miami, FL 33124
Correspondence Author:
3
Email: [email protected]
FAX: (602) 965-2519
Phone: (602) 965-8263
Keywords: edge, patch, edge effects, habitat heterogeneity, habitat fragmentation, partial
differential equations
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INTRODUCTION
Ecological edges, the interfaces between different types of habitat patches, are often
treated as little more than ecological curiosities. Indeed, throughout much of ecology's history,
researchers have gone to great lengths to conduct research in homogeneous habitats devoid of
edges and similar complicating factors. When ecological aspects of edges were studied, research
traditionally emphasized patterns of increased species richness at habitat edges (the original
"edge effects," Leopold 1933, Odum 1971) and analyses of vegetational transitions near edges
(Wales 1972); that is, they studied the ecology of the edges themselves. More recent studies
detailing extensive abiotic edge effects (e.g., Kapos 1989, Chen et al. 1995) and linking them to
specific population and community impacts (e.g., Saunders et al. 1991, Aizen and Feinsinger
1994a,b) have demonstrated a variety of instances in which habitat edges influenced dynamic
ecological phenomena, ranging from biogeochemical nutrient transport (Kitchell et al. 1979) to
the outcome of species interactions (Kareiva 1987, Roland 1993). Such studies demonstrate a
marked shift in scientists' interests from traditional edge effect patterns to what we term "edgemediated effects," in which the focus is not on edge-related patterns themselves but rather on the
mechanisms through which edges fundamentally alter ecological processes.
Increasing recognition of the importance of edges has led many researchers (e.g., Haila
1986, Bierregaard et al. 1992, Dale et al. 1994, Malcolm 1994, Aberg et al. 1995) to call for
studies of the functional links between habitat edges and community dynamics. A common
theme is the critical need to understand the fundamental processes through which habitat edges
impact species' dispersal and community composition in fragmented landscapes. At a broader
level, researchers have noted that increased research on edge-mediated effects may advance our
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understanding of some of ecology's major questions, including the scaling of spatial processes
(Wiens et al. 1985, Gosz 1993, Wilson 1996), the limitations of island-biogeography theory for
terrestrial systems (Janzen 1983, 1986, Boecklen and Gotelli 1984, Doak and Mills 1994), and
species-area relationships (Lovejoy et al. 1989, Bierregaard et al. 1992).
Understanding the functional roles of edges is increasingly important because human
activities are rapidly influencing the extent (e.g., Groom and Schumaker 1990) and type (e.g.,
Yahner 1988) of edges found on earth. Altered patterns of "edginess" in ecological landscapes
seem inevitable because edge creation, destruction, and modification are concomitant features of
such increasingly prevalent human activities as habitat fragmentation, river channelization
(Naiman et al. 1988), chemical drift (Landsberg et al. 1990), and selective resource extraction
(Suzan et al. 1997).
Lovejoy et al. (1989), Malcolm (1994), and Wilson (1996), among others, have noted that
robust conceptual connections between the pattern and structure of habitat edges and their
impacts on species interactions and community dynamics were historically rare in this literature.
While we echo these authors' calls for further investigations of the dynamical consequences of
habitat edges, we argue here that much is already known about the community impacts of edges,
though the piecemeal distribution of this information through a taxonomically and conceptually
diverse set of sources impedes easy understanding. Indeed, our analyses have revealed similar
types of edge-mediated effects on community dynamics in systems featuring everything from
intertidal algae to large mammals and extending from the wildlife management literature through
abstract mathematics. Our purpose in this paper is to synthesize what this diverse collection of
knowledge has to say about the impacts of habitat edges on species interactions and community
dynamics.
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To this end, we present a unified mechanistic approach to modeling edge-mediated
effects based on partial differential equations, and we examine the implications of that approach
with respect to four major classes of edge-mediated effects. Many of the particular theoretical
conclusions we have garnered from the mathematical literature regarding these four mechanisms
through which edges change species interactions are strikingly similar to those suggested by a
wide variety of field experiments and observations. We will explore these four classes of effects
in much greater detail later; however, we note their essence here, namely 1) edges' roles as
dispersal barriers or filters, 2) edges' influences on mortality, 3) edges' involvement in spatial
subsidies, and 4) edges' roles as generators of novel interactions. The critical roles of amongspecies differences in edge-related dynamics and the extent to which the consequences of such
dynamics parallel established ecological concepts (such as disturbance mediated coexistence and
apparent competition) are but two of the emerging patterns we find intriguing.
However, before diving into such issues, we first provide a terminological and conceptual
overview of the similarities and differences between ecologists' and mathematicians' views of
edges and edge-mediated dynamics. We then explore in depth the four general categories of
mechanisms through which ecological edges can fundamentally alter species interactions as we
attempt to synthesize the diversity of theoretical and empirical findings that are relevant to edgemediated effects. Lastly, we highlight potentially fruitful avenues of future theoretical and
empirical research on edge-mediated effects.
Some comments on terminology and approaches
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An "edge" is one of those ecological features that is hard to define verbally but yet
immediately recognizable to observers in the field. Edges are often identifiable as the
boundaries separating regions featuring different species of stationary organisms (e.g., mature
trees vs. early successional species in fragmented forests; mussel beds vs. algal mats in the
intertidal). Such boundaries need not entail sharp, stepwise switches in cover type; gentle
gradient-like transitions can also be ecologically important edges (Fig. 1). At larger scales,
broad ecotones featuring habitats intermediate to, yet distinct from, surrounding regions can
function as edges. But not all species perceive edges visually the way humans do. Edge-like
changes in soil chemical content (Landsberg 1988), humidity (Kapos 1989), or noise levels
(Ferris 1979), among other attributes, can influence species responses in the same manner as
physical edges. Yahner (1988) has identified structural and process-oriented differences between
natural and so-called "induced" edges that are generated by human landscape-modifying
activities like resource extraction and chemical contamination. Clearly, an edge separating two
adjacent habitat types can feature many complementary components that trigger responses
differently among species.
We will use the term "patch" to describe a focal unit of a landscape that is set off from
surrounding habitats by an ecologically meaningful edge. Similarly we will make frequent use
of the term "matrix" to describe the region surrounding a focal patch (Fig. 1). While we
recognize that these terms oversimplify the character of most ecological landscapes (e.g., many
patches are delineated piecewise by an assortment of edges that separate them from, not one, but
many different regions [Schonewald-Cox and Bayless 1986]), we hope our consistent use of
these terms will emphasize the mechanistic commonalities that exist among a diverse assortment
of edge-mediated effects.
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At a theoretical level, much of the research related to the dynamical implications of
ecological edges utilizes a framework of partial differential equations (hereafter PDEs). Such
equations, which are excellent mathematical tools for addressing dispersal, critical patch sizes,
boundary dynamics, and other edge-related ecological phenomena (Holmes et al. 1994), take the
general form
au.
ati
= v • Di (X)Vui + f(x , it)
aiui +
au.
al ; = g(u1 )
in
on
x (0, co)
Eq.
1A
0S-2 X (o, co)
Eq.
1B
where u, is the population density of species i inside the habitat patch SI, D, is its rate of diffusive
movement, RT is a location in 1 or more spatial dimensions, V is the gradient operator, a, and 13
are coefficients modifying species i's density and rate of change at the patch edge (the edge itself
is denoted AP respectively, and 11 is an outward unit normal along the patch edge. Note
Equation 1A governs the dynamics inside the patch, while Equation 1B determines what happens
at the patch edge (i.e., Equation 1B determines the "boundary conditions" of the system). One
can construct the function f(K, to incorporate terms for species' mortality and reproduction,
alternative movement dynamics, and interactions with other species, among other considerations.
Similarly, one can form the function g(ú) to reflect different types of boundary conditions. In
more complicated investigations, the coefficients of Eq. 1 may be dependent on time, density, or
other factors. A review of some applications of PDEs to ecological questions by Holmes et al.
(1994) helps make central concepts of this body of theory accessible to a broad range of
ecologists.
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Mathematical and ecological perspectives on patch edges
Before proceeding, we find it helpful to compare and contrast the ways in which
mathematicians and ecologists view patch edges. Such an cross-disciplinary overview provides
the common footing necessary for further syntheses of the dynamics associated with edgemediated effects.
Regardless of the particular structure of the equations, mathematical analyses of
ecological dynamics inside finite patches require information on the behavior of the system's
components at the patch edges. The situations described in Figs I A and 1B, namely sharp edges
and broader edges or ecotones, require slightly different mathematical treatments. In the case of a
sharp edge, its effect can be described by stipulating movement and mortality on the edge
through the boundary conditions given in Equation 1B. In the case of broad edges or ecotones,
boundary conditions (per se) should be stipulated along the exterior boundary of the ecotone,
with the edge between the ecotone and core habitat viewed as an "internal interface" (e.g.,
Cantrell and Cosner 1993). Internal interfaces can often be described by spatial changes in the
coefficients of Equation 1A, although complex behavior at such an interface may require more
sophisticated modeling.
Mathematicians identify three general classes of boundary conditions suitable for
describing sharp ecological edges: reflecting, absorbing, and mixed. These categories of
boundary conditions have distinct physical interpretations that are pertinent to the ecological
study of edges.
A habitat patch with reflecting (or "Neumann") boundary conditions is one in which
emigration does not occur because any organisms (or propagules) encountering the patch edge
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"bounce off' and move away from the edge. To produce reflecting boundary conditions one
writes Equation 1B with a = 0 and 13 > 0. In ecological models with reflecting boundaries,
movement (technically the "flux") of the species across the edge tends to zero. As an example,
edges between old growth forests and clearcuts are reflecting boundaries for red-backed voles,
which shun the clearcuts because of the absence of the fungal sporocarps on which they feed
(Mills 1995). In comparable systems, reflecting boundaries can engender so-called "fence
effects" in which population densities of small mammals increase with decreasing patch size due
to a general reluctance to cross edges (Lidicker 1967; Hestbeck 1982).
In the opposite—but equally extreme—case, patches may feature absorbing (or
"Dirichlet") boundary conditions. For such edges, the region outside the patch is interpreted as
being immediately lethal. To produce absorbing boundary conditions one writes Equation 1B
with a> 0 and 13 = 0, forcing species densities to tend to zero at the patch edge. Terrestrialaquatic edges are absorbing boundaries for seeds of plant species incapable of surviving in both
habitats, as is the legislative boundary of Yellowstone National Park for bison dispersing into
Montana (where they are shot, ostensibly to control the spread of the disease brucellosis [Dobson
and Meagher 1996]).
Although ecological cases directly comparable to both reflecting and absorbing boundary
conditions certainly exist, most real edges represent a fusion and moderation of the two
mathematical extremes, corresponding to mixed (or "Robin") boundary conditions. For mixed
boundary conditions one writes Equation 1B with a > 0 and 13 >0. One can formulate mixed
boundary conditions to describe a variety of ecological edges including cases where 1) the
exterior of a patch is only partially hostile; 2) some individuals cross the patch edge but others do
not, and 3) organisms will cross the edge only at particular times. One can interpret mixed
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boundary conditions as saying that individuals crossing the patch boundary are not immediately
lost from the population and may return or contribute offspring to the patch. Studies of the
spatial dynamics of the spruce budworm (Ludwig et al. 1979) are a now-classical ecological
application of mixed boundary conditions.
Ecological examples of all three types of mixed boundary conditions commonly occur.
For example, dispersal of Yellowstone grizzly bears into degraded habitat, which though not
immediately lethal does reduce their probability of surviving, is a good example of the
consequences of partially hostile patch edges (Doak 1995). Similarly, partially crossable patch
edges can influence the spatial dynamics of invasive plants (Hester and Hobbs 1992) and
foraging animals (Bider 1968) when only a fraction of the seeds or animals encountering a
habitat edge actually venture across it. In the third case dispersal behavior at patch edges may
vary with time over daily, lunar, seasonal or successional timescales. (Such variation would be
reflected by time dependence in a and p). Examples of periodic boundary conditions include
risk-averse foraging of mice near field edges as a function of lunar cycles (Bowers and Dooley
1993), seasonal variation in edge permeability induced by crop cultivation practices (Cummings
and Vessey 1994) or snowfall (Oehler and Litvaitis 1996), and the water level-dependent
activities of invertebrate gazers in intertidal "browse zones" (e.g., Paine and Levin 1981).
Traditionally, mathematical models assume that patch edges (whether absorbing,
reflective, or mixed) are imperceptible to the dispersing organisms. In such cases, dispersing
species are often assumed to flow across edges by simply following density gradients downhill
(e.g., Pacala and Roughgarden 1982, Stamps et al. 1987). Depending on one's management
perspective, this type of dispersal behavior can have both positive (Man et al. 1996, McClanahan
and Kaunda-Arara 1996) and negative (Schonewald-Cox and Bayless 1986, Buechner 1987,
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Doak 1995) effects. However, to more closely match biological scenarios in which edgedetection is believed important, gradients in edge detectability, sensitivity, or responses can be
built into more complex models (Cantrell and Cosner, in press, Bommarco and Fagan
unpublished manuscript).
The principal eigenvalue quantifies "core habitat"
An important connection between edge-related theory and data deals with ecologists'
conceptualizations of "edge" and "core" regions of a habitat and the importance of the relative
extent of such regions to the maintenance of biotic diversity (Temple 1986, Lovejoy et al. 1986,
1989, Naiman et al. 1988, Bierregaard 1992). For example, Groom and Schumaker (1990)
found that gauging the remaining amount of "core habitat" in remnant old-growth forest
fragments on Washington's Olympic Peninsula was far superior to other edge-related indices
(such as mean fractal dimension, shape index, or perimeter/area ratio of fragments) as an index
for quantifying the degree of regional fragmentation and differentiating among regions with
respect to the intensity of logging activities. Similarly, in a simulation study, Stamps et al.
(1987) found that the fraction of individuals' home ranges in the core of a habitat patch (i.e., the
fraction of home ranges isolated from patch edges) was an important determinant of emigration
for a territorial species. Such recognition of the importance of edge and core habitats by
ecologists has an important parallel in analytical analyses of theoretical models. In PDE models
like Eq. 1 and others outlined below, a critical factor governing the outcome of particular species
interactions in a patch is frequently the principal eigenvalue of the eigenvalue problem
associated with the PDE model. A good verbal interpretation of this abstract mathematical
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quantity is that its reciprocal represents the amount of a patch that is insulated or otherwise
immune from the edge-mediated effects under investigation—a result strikingly similar to the
core habitat notion latched onto by ecologists (Fig. 2). Importantly, the principal eigenvalue,
which essentially subsumes other patch descriptors such as size and perimeter/area ratio, can be
calculated from field data once the pertinent parameters (e.g., species' reproductive and mortality
rates and interaction strengths with other species) of a PDE model are estimated.
At the most basic level, the principal eigenvalue averages spatial effects on a population's
intrinsic rate of growth and yields a number analogous to the intrinsic rate of population growth
observed in a logistic ordinary differential equation. This averaging across space to yield an
intrinsic growth rate is comparable to the way that the principal eigenvalue of a structured
population model (e.g., a Leslie matrix) averages reproduction and mortality over classes within
a population. In the case of multi-species models, the principal eigenvalue for any given species
may depend on the presence or absence or other species. If a species has a positive principal
eigenvalue when other species are present, then it can increase its numbers from low densities
and hence invade the community. The principle that invasibility implies coexistence permits
interpretation of the sign of the principal eigenvalue in terms of community structure. This point
of view was introduced by Pacala and Roughgarden (1982) in their work on competition in
patchy environments and given mathematical rigor in Cantrell et al. (1993).
Edges can have diverse effects on the movement and dynamics of individual species
At habitat edges, substrata (Smith 1974, Baur and Baur 1995), vegetation (Wales 1972,
Matlack 1994), abiotic conditions (Kapos 1989, Saunders et al. 1991), and even rates of
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ecosystem processes (Naiman et al. 1988) change. Changes in these fundamental ecological
attributes and processes have the potential to influence species' spatiotemporal dynamics through
impacts on movement, growth, survival, and reproduction. Perhaps because edges are at their
heart spatial phenomena, dispersal is more frequently studied in connection with habitat edges
than other population traits such as reproduction, growth, or mortality. For example, numerous
authors (e.g., Bider 1968, Wegner and Merriam 1979, Schonewald-Cox and Bayless 1986,
Wiens et al. 1986) have drawn comparisons between ecological edges and cellular membranes or
other biological filters, noting that some edges, like membranes, can be semi-permeable, acting
as complete barriers to the movement of some species or products while reducing the cross
boundary flow of other items only partially or not at all. For a great diversity of taxa, edge
permeability is often asymmetric (i.e., immigrants actively cross into patches but are quite
hesitant to leave). Such unidirectional filtering by habitat edges can result in intense, but shortlived, "supersaturation" of remnant patches as animals flee recently modified matrix habitat for
nearby remnants, only to have their densities decline below preisolation levels as resources are
exhausted (Whitcomb et al. 1981, Bierregaard and Lovejoy 1988).
Using single species simulation models, Stamps et al. (1987) showed that species'
emigration rates are monotonically saturating functions of edge permeability, meaning that the
biggest changes in cross-edge movement take place when edge modifications make a formerly
reflective edge slightly porous. We show in the Appendix that an analogous effect occurs in
PDE models of dispersal. An alternative perspective on edge permeability depends on
quantifying, for different species, how likely an individual is to turn around or continue on when
it encounters an edge, as might be influenced by the relative quality of adjacent patches. From a
theoretical vantage point, such edge turning probabilities can be coupled with otherwise random,
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diffusive dispersal to describe "skew Brownian motion" (Harrison and Shepp 1981). Cantrell
and Cosner (in press) consider how dispersal via edge-sensitive skew Brownian motion
influences the need for and design of buffer zones around habitat reserves. In addition, in some
circumstances dispersal via skew Brownian motion may result in aggregation along the habitat
edge, a result strikingly similar to those found in laboratory studies of mite dispersal by Kaiser
(1983) and the foraging behavior of generalist predators in patchy landscapes (Bider 1968).
Among-species differences in edge responses:
a simple but widespread theme linking landscape ecology to community dynamics
The preceding section highlights many mechanisms through which edges can influence
spatiotemporal dynamics of individual species. Yet, to progress beyond such single species
viewpoints we have to recognize the potentially complex relationships between habitat edges and
different species' habitat preferences, abiotic tolerances, dispersal rates, and responses to
environmental cues. Such interspecific contrasts can be important to species' distributions even
in expansive monotypic habitats devoid of edges. But in patchy landscapes where edges are
predominant features, the importance of such interspecific variability is multiplied many fold. A
pervasive finding of our syntheses is that when edges (or their mathematical surrogates,
boundary conditions) affect interacting or potentially interacting species in disparate ways, such
differential effects have consequences for both the nature and outcome of particular species
interactions, and for the dynamics of the community in which they are embedded. Consequently,
understanding the extent to which and mechanisms through which habitat edges differentially
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affect interacting species is a critical conceptual link between community dynamics and
landscape ecology.
Four principal classes of edge-mediated effects on species interactions
Published literature is surprisingly rich with examples in which processes that create,
destroy, modify, or simply maintain habitat edges impact species interactions and influence the
composition and dynamics of ecological communities. Rather than delineate our findings
according to different types of species interactions (e.g., pollination, competition, predation), we
instead search for commonalities in the ways similar edge-mediated effects alter dissimilar
species interactions. We suggest that existing empirical and theoretical results can be grouped so
as to reveal four general categories of mechanisms through which ecological edges
fundamentally alter species interactions:
1) Habitat edges can differentially restrict or facilitate the movement of organisms or
propagules among species within a landscape.
2) Habitat edges can differentially contribute to species' mortality.
3) Habitat edges can result in "cross-boundary subsidies" in which dispersers' impacts
on residents of one patch type are subsidized by their feeding and reproductive
activities in another patch.
4) Edges themselves can serve as a unique habitat type, facilitating interaction between
species that otherwise would not interact.
Which of these classes of edge-mediated effects occur can depend sensitively on edge
characteristics and the species involved. Furthermore, these four principal categories are far
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from mutually exclusive: particular examples of edge-mediated changes in species interactions
may feature components of all four major classes of effects. Nevertheless it is important to draw
distinctions among the different mechanisms, because understanding their consequences for the
dynamics of ecological communities can require radically different concepts. Similarly, from a
conservation perspective, countering the different mechanisms through which anthropogenic
edges cause the degeneration of species interaction regimes can require radically different
management approaches.
Class 1: Edges can change species interactions by altering species' movement patterns
The simplest, and perhaps most widespread, class of edge-mediated effects involves
habitat edges that facilitate or restrict the dispersal of organisms or their propagules. Such
effects are increasingly important because of the tangible connection between landscape
modifications like habitat fragmentation and the creation or alteration of habitat edges (Groom
and Schumaker 1990, Chen et al. 1995). Consequently, it is not surprising that many researchers
have highlighted natural edges (e.g., Abramsky and Van Dyne 1980, Kareiva 1985, Bach 1984)
and newly induced edges (e.g., Pahl et al. 1988, Laurance 1990, 1991a, Aizen and Feinsinger
1994b, Dale et al. 1994, Mills 1995) as major sources of disruption for species' dispersal in
fragmented habitats. However, edge-mediated disruptions of dispersal have consequences that
extend far beyond the single species realm. When habitat edges alter the dispersal patterns of
organisms or their propagules so as to change mobile species' encounter frequencies or the
dispersion of stationary species, edges can alter the intensity of particular species interactions
and have far-reaching effects on community dynamics.
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The community consequences of dispersal disruptions have long been of interest to those
studying plant pollination and seed dispersal in edgy landscapes (e.g., Janzen 1983, Terborgh
1986). By impeding the movements of pollinators, habitat boundaries can restrict pollen flow
among plants, dramatically reducing the neighborhood size of reproductive individuals (Aizen
and Feinsinger 1994b). Edge-mediated movement disruptions may also explain decreased
abundance of euglossine bees in remnant rainforest fragments, a pattern which may influence
pollination of orchids and other tropical plants (Powell and Powell 1987). In general, if edges
are prominent landscape features, as they are in severely fragmented habitats, edge-mediated
changes in pollinator behavior and density can lead to profoundly altered plant composition in
forest fragments (Rathcke and Jules 1993).
Edge-altered patterns of seed rain or dispersal may affect plant competitive regimes in
similar fashions. A widespread theme is that when potential germination sites are limiting,
among-species differences in cross-edge seed influx may translate into a competitive advantage
by influencing the frequency of species self-replacement (Jan7en 1983). For example, edge
penetration by seeds as a function of "edge closure" (e.g., extensive leaf overlap that reduces
edge permeability) appears to have been a key factor underpinning the success and failure of
alien plants invading Australian woodlands and shrublands, respectively (Hester and Hobbs
1992). Because competition with invasive species leads to reduced seed production in native
annuals, cross-edge dispersal by seeds from non-native plants is an additional threat to
biodiversity in already fragmented habitats (Hester and Hobbs 1992). Disturbances associated
with edge creation can have profound impacts edge permeability. In the absence of soil and
seedbank disturbances, rapid vegetative growth of primary forest species at the edge may curtail
penetration by seeds of matrix species (Williams-Linera 1990) whereas smoke and heat from
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burning slash at edges may result in substantial leaf mortality, offering dispersing propagules
easy—but temporary—access to interior areas (Lovejoy et al. 1989).
The same fundamental mechanism—edge-mediated alterations of dispersal patterns—can
disrupt consumer-resource dynamics in similar manners. For example, edges are strongly
reflective for many foraging consumers, acting as a barrier to movement (e.g., Bider 1968).
Kareiva's studies of ladybird beetles foraging in fragmented goldenrod habitats demonstrate how
reflective edges can alter consumer-resource interactions: patch edges (manifested as plants with
non-overlapping leaves) alter ladybug turning rates (Kareiva and Perry 1989), delaying
aggregation of consumers to incipient prey outbreaks (Kareiva and Odell 1987), and facilitating
local explosions of the aphid population (Kareiva 1987). In a similar example, increasing the
extent of habitat edges in laboratory microcosms disrupts the movement patterns of both
predatory and herbivorous mites, impeding the aggregation of both species, and decreasing the
predator's functional response in edgier habitats (Kaiser 1983).
In many cases, edges influence consumer-resource dynamics when consumers'
perceptions of and/or responses to edges change over time. Risk-averse foraging behavior
associated with edges is a widespread example of such changes. For example, during full moon
periods, mammalian seed predators inhabiting Virginia old fields face increased mortality risks
near patch edges due to heightened predator activity (Bowers and Dooley 1993). At these times
of increased risk, the seed predators regularly underuse patch edges at the expense of patch
interiors, influencing the spatial distribution of viable seeds in this landscape (Bowers and
Dooley 1993). In a comparable system, reduced nut foraging by squirrels at the edges of hickory
forests contributes, over the long term, to spatially-varying age-structure within the hickory
population and outward progression of forest edges (Sork 1983). Analagous data on spatial
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variation in seed predation rates (Burkey 1993, Osunkoya 1994) and habitat usage (Bider 1968,
Kirkland et al. 1985) suggests that edge avoidance by risk-averse seed foragers may be a
widespread phenomenon. Johnston and Naiman (1987) suggest similar risk aversive behavior by
foraging beavers may result in altered patterns of sapling herbivory as a function of topographic
relief and the proximity of predator-free deep water along the aquatic-terrestrial edge of beaver
impoundments.
On the other hand, intertidal grazers feeding in gaps in mussel beds face greater threats
not at patch edges but in patch interiors where they are exposed to mortality from foraging
seabird predators when the tide is out and wave disturbances when the tide is in. The grazers
consequently restrict their feeding to the edge of the gap, retreating into the mussel beds for
safety (Paine and Levin 1981). Such spatially restricted, risk-averse foraging contributes to the
well known "browse zone" patterns in which the edges of mussel gaps are stripped bare of algae
and other biotic substrata but gap interiors sport diverse assemblages of sessile species (Sousa
1984). Similar browse zones occur in terrestrial habitats as well; however, the spatial patterning
is somewhat reversed: mammalian herbivores often shelter inside the "patch" (e.g., under shrubs
[Bartholomew 1970]; on patches of talus [Huntly et al. 1986]) and forage in the surrounding
area.
Class 2: Edges can impact community dynamics by differentially inducing species' mortality
A second major class of edge-mediated changes in species interactions comprises those
situations in which edges alter the nature and/or outcome of interspecific interactions through
differential influences on species' mortality. Clearly, this category of effects is related to the
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first. But yet the two categories of edge-mediated effects differ in at least one important way: the
dynamic consequences of losing an individual from a population via emigration can be less
extreme than the consequences of losing an individual through mortality. A key theme in this
section is that cross-edge movement often entails facing extra mortality risks. When such risks
occur in an unbalanced fashion among species, they can alter the intensity and outcome of
species interactions by influencing the dynamics of competitive regimes, mutualistic
combinations, and consumer-resource relationships.
Competitive interactions within this class of edge-mediated effects are conceptually and
mechanistically linked to consumer- and disturbance-mediated coexistence (e.g., Paine 1966,
Lubchenco 1978, Connell 1978) in that mortality agents have overarching effects on the outcome
of particular competitive regimes. In some cases, the edge-related mortality may in fact be due
to predators foraging in the surrounding matrix. However, other agents of cross-edge mortality
(e.g., parasites, harsher climatic conditions, vehicles) could lead to comparable dynamics.
Microclimatic conditions that differ greatly across edges (especially forest-clearcut
edges; Kapos [1989], Chen et al. [1991, 1995]) thereby influencing the survival of plant seeds
and seedlings (Janzen 1986, Saunders et al. 1991) are one widespread source of edge-mediated
differences in species' mortality that can influence competitive dynamics. In a landscape
comprising remnants of native tropical forests in a sea of harsher modified habitats, edge-related
seed mortality may hinder germination of native tree fauns at the expense of environmentally
tolerant weedy species, altering successional patterns, and making fragmented forest patches
even more dissimilar to intact forests (Janzen 1986). Similarly, selective vole predation on
seedlings of deciduous trees near forest-old field edges may facilitate conifer invasions into some
North American old fields (Ostfeld et al. 1997).
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To see the competitive consequences of edge-related mortality more generally, consider a
theoretical scenario in which cross-edge dispersal entails higher mortality for a population of a
superior competitor than for an inferior competitor. If they are sufficiently strong, such edgemediated effects might prevent competitive exclusion of the inferior competitor by the superior
one or, in a more extreme case, could result in a competitive reversal that drives the nominally
superior competitor to extinction (Cantrell et al., in press). The converse is also of ecological
interest: greater edge-related mortality for an inferior competitor would likely speed its local
extinction. To study these and related questions, Cantrell et al. (in press) used diffusive L,otkaVolterra competition equations
au
2
' = DV
1 u1 + r1
at
u1
1—
K1
au
2
2 = D V u +r 1
at
2
2
2
_
a12 IL ,
"2 "1
K1
u2
K2
Eq. 2
a21
li 114
K2 1 2
in Q x (0, co), subject to the boundary conditions
ai Vu1 •77 + ju i = 0
on ao x (o,00) where a1 =0;
INc1 (D0u ,) .
i=1,2
Eq. 3
Here u, = u,(x,t) is the population density of species
i at position x and time t in the multidimensional patch Q,
, ri, and K, are, respectively, the
in-patch diffusion rate, reproductive rate, and carrying capacity of species i, and a u and k i are
the species' interaction strengths. In the boundary condition (Eq. 3), ri is an outward normal unit
vector along the patch edge as 2, (pc:a,), is the diffusion rate of species i in the matrix outside of
-
the patch, s is an overarching mortality rate induced by a given level of matrix hostility, and c, is
a proportionality constant scaling the effect of matrix mortality for species i.
21
We constructed the boundary condition in this form (Eq. 3) to investigate the
consequences of steadily worsening exterior conditions (i.e., habitat degradation) on the patch's
competing species using the tunable "hostility" parameter s (Cantrell et al. in press). However,
in the present context, the structure of this boundary condition speaks more generally to the
important role that edge-related mortality can play in competitive dynamics. For example,
consider a situation in which environmental conditions or the foraging patterns of seed predators
outside a patch's boundaries favor the seeds of one competing plant species over another. In
such a case, the competitors' differential sensitivity to matrix mortality interacts with their rates
of crossing the patch edge (as influenced by the movement rates inside and outside the patch) to
influence the outcome of their competitive interaction (Fig. 3).
Edge-related mortality can play a critical role in consumer-resource as well as
competitive dynamics. Edges' roles as barriers to successful movement are often an important
feature in this context. For example, foragers that hesitate, or are unable, to cross habitat edges
and instead travel parallel to them may result in a disproportionate increase in forager activity
density near edges, leading to increased consumption in areas immediately near edges (Bider
1968, Gates and Gysel 1972). Conversely, edges that increase mortality of wide-ranging
foragers—or at least discourage their entry into patches—may facilitate population growth of
resources (e.g., birds in road-bounded habitats, Pasitschniak-Arts and Messier 1995). Similarly,
risk averse foragers may avoid certain habitat edges, increasing postdispersal survivorship of
some plant species' fruits and seeds at the expense of others (e.g., Bowers and Dooley 1993,
Osunkoya 1994).
In an important study, Klein (1989) demonstrates how edge-related mortality along
Amazonian forest-clearcut edges can alter rates of dung and carrion decomposition by edge-
22
sensitive beetles. Rather than being hesitant to cross forest/clearcut edges, larval and adult
beetles may regularly attempt to cross such boundaries only to die of dessication in the more
exposed habitats. The beetles' apparent inability to avoid crossing into areas of increased
mortality appears linked to a compositional shift in the carrion-feeding guild: ants become
increasingly dominant and carrion beetles relatively less important in small fragments and
clearcut areas where the effects of induced edges are most pronounced (Klein 1989). The
consequences of edge-induced beetle mortality may extend still further into the rainforest
foodweb, influencing the transmission rates for vertebrate pathogens (Klein 1989).
Likewise, in fragmented North American forest landscapes, edge-associated changes in
abiotic conditions impact outbreaks of forest defoliating lepidoptera. There, increased edge
density (km edge/ km2 landscape) increases the duration of tent caterpillar outbreaks (Geiger
1965, Roland 1993) by exposing the caterpillars' natural enemy (a nuclear polyhedrosis virus) to
increased mortality from UV radiation (Roland and Kaupp 1995), which is much more intense at
forest edges than forest interiors. In a similar system, habitat edges that expose spruce budworm
larvae to mortality from predators and parasites can limit the spatial spread of outbreaks of the
herbivores (Ludwig et al. 1978, 1979).
Class 3: Edges can alter species interactions through cross-boundary subsidies
A third class of edge-mediated effects includes those situations in which "cross-boundary
subsidies" influence the outcome of species interactions. In this category of effects, crossboundary subsidies arise as populations of some species are maintained at high levels through
gro /th, reproduction and/or feeding in other habitats but then disperse across patch edges,
23
depressing or otherwise impacting populations of patch residents. Consequently, the dynamics
of spatially subsidized competitors, consumers, or parasites and their effects on patch residents
are in many ways comparable to the dynamics of apparent competition (Holt and Lawton 1994)
or "multichannel" omnivory (Polis and Strong 1996). The mechanistic similarities are especially
obvious when the coupling of external resource acquisition with cross-edge movement
aggravates consumers' impacts on patch-resident resources in much the same way that feeding
on alternative prey species (Holt and Lawton 1994) or tapping into alternative trophic channels
(Polis and Strong 1996) facilitates reductions in the populations of focal species.
We emphasize, however, that cross-boundary subsidies have a broader applicability since
spatially-segregated resources can prop up populations of competitors and mutualists as well as
those of consumers (e.g., Abrams and Walters 1996). Consequently, the importance of crossboundary subsidies to community dynamics in an edgy landscape may be more effectively linked
to the relative occurrence of habitat specialists versus habitat generalists, when populations of the
latter type of species could be subsidized by cross-boundary activities. For example, in Sweden,
intrusion of generalist predators from neighboring modified habitats into boreal forest remnants
may be responsible for the local extinction of snowshoe hare, effectively setting a southern limit
on that species' distribution (Sievert and Keith 1985). Also working in a fragmented forest
system (the Argentinian Chaco), Aizen and Feinsinger (1994b) suggest that the consequences of
trampling and grazing of several plant species by cattle intruding from the surrounding
agricultural matrix may be so severe that they override the aftermath of fragmentation-induced
disruptions of pollination regimes.
This third class of effects includes one of the most studied edge-mediated changes in
species interactions: the so-called "ecological trap" hypothesis (Gates and Gysel 1972). In this
24
scenario, nesting passerine birds behaviorally favor the edges of forest patches (because of the
dual availability of forest cover and foraging areas) but they do so at the—perhaps
overwhelming—expense of increased mortality from edge foraging generalist predators and nest
parasites (e.g., brown headed cowbirds). This combination of habitat preference and consumers
subsidized by their feeding and reproduction in other habitats results in an "ecological trap" as
large fractions of bird populations attempt to reproduce in regions of high mortality (Gates and
Gysel 1972).
Numerous researchers have expanded upon this basic theme (e.g., Wilcove 1985).
Angelstam (1986) suggests that the severity of predation impacts on Swedish forest birds by
generalist predators (e.g., corvids, foxes, domestic animals) residing in matrix habitat increases
as human activities make the forest patch and its surroundings more and more dissimilar. In
remnant Ontario woodlots, Friesen et al. (1995) found that populations of only one group of
birds (neotropical migrants) were sensitive to intrusions by generalist predators from nearby
developments, resulting in dramatic shifts in community composition along a gradient of
increasing human presence. Other studies have yielded comparable results, highlighting matrix
type (Hanski et al 1996), the composition of the generalist predator assemblage in the matrix
(Yahner et al. 1989, Nour et al 1993), and interactions among species of matrix predators (Santos
and Telleria 1992) as important determinants of the severity of ground nest depredation. An
important concept stemming from this research is that edge-associated nest predation, which can
be quite damaging to bird populations in edge dominated landscapes (Temple and Cary 1988), is
often merely incidental to the edge-foraging consumers: their impacts on bird populations are
subsidized by extensive feeding on other species in other habitats (e.g., Pasitschniak-Arts and
Messier 1995).
25
Like edge-nesting birds, many species actively seek out and move toward habitat regions
that are perceived as being of high quality. However, in edge-dominated landscapes such
movement may not always be profitable. Belgacem and Cosner (1995) performed a more
general investigation of a species' tendency to disperse up gradients in habitat quality inside a
habitat patch using the model
au
Eq. 4
auVr(x)+ r(c)u
in x (0,00)
at
where u is a species density at position x, r(x) is the local growth rate based on linear or logistic
— = DV 2 u
growth terms, and a is a constant quantifying the rate at which the population moves up the
gradient of habitat quality. Here habitat quality is envisioned as being implicitly dependent on
the relative densities of resources and natural enemies. Belgacem and Cosner examined two
different boundary conditions, the reflecting boundary case
au
an
D— –
ar(x) = 0
an
on as-2 x (O,00)
Eq. 5
and the absorbing boundary case
u=0
on aQx (O,00)
,
Eq. 6
and found that the nature of the patch edge is a critical determinant of whether quality-dependent
dispersal facilitates species persistence or extinction. (Equation 5 gives the appropriate no flux
boundary condition for Eq. 4 taking into account the additional term not present in Eq. 1). If the
edge is reflective (Eq. 5), movement up the habitat quality gradient is shown to be beneficial to
the population if it is sufficiently strong and is conjectured to be so always. In contrast, if the
edge is immediately lethal (Eq. 6), then the population impact of movement up the habitat
quality gradient depends on the location of the high quality region relative to the habitat edge:
high quality habitat located near the patch edge draws the population nearer the lethal patch
boundary with a consequent increase in edge-related mortality (Fig. 4). For habitat patches with
26
less extreme boundary conditions, the impact of movement up the habitat quality gradient would
likely depend on such attributes as the species' rates of movement, reproduction, and mortality in
the matrix.
Cross-boundary subsidies of organisms or their propagules can alter the dynamics of
competitive regimes in manners that mirror the effects of subsidies on consumer-resource
dynamics. Janzen (1983) described an example in which cross-edge seed influx from weedy,
early successional species occupying a "buffer zone" (akin to a wide edge region like that
depicted in Fig. 1B) au-rounding a remnant forest patch could prevent reestablishment of forest
interior tree species and disrupt the patch's competitive regime and successional trajectory. Such
edge-mediated shifts in competitive dynamics raise a haunting issue in that buffer zones,
however well-intentioned, could do more harm than good conservation-wise. To examine
Janzen's case study from a theoretical perspective, Cantrell and Cosner (1993) used a modified
version of Eq. 2 in which only species 2 benefitted from an additional reproductive term
corresponding to its ability to survive in the buffer zone. Consequently, in their model, as in
Janzen's example, the weed species' great success in the surrounding matrix subsidized the
influx of weed seeds into the patch at the competitive expense of resident species. The
competitive success of the weed species depended on a number of ecologically relevant factors
including the size of the remnant forest patch (specifically the size of the patch region essentially
isolated from the cross-edge influx), the width and harshness of the buffer zone, and the dispersal
abilities of the competitors. (As a mathematical aside, Cantrell and Cosner's (1993) treatment of
this core—buffer—matrix arrangement is an application of the "internal interface" approach to
modeling spatial problems using PDE's rather than enforcing boundary conditions at the both the
core—buffer and buffer—matrix junctions).
27
In studies of nest predation, seed dispersal, and similar processes, penetration of a species
or altered abiotic conditions into a patch (or the inferred consequences of such penetration) is
often quantified simply as a function of distance to the nearest edge (Fig. 5; Groom and
Schumaker 1990, Laurance and Yensen 1991). However, the utility of this "penetration profile"
approach decreases with decreasing patch size as an individual locale comes increasingly under
the influence of more than one edge. In particular, as patch size decreases, interactions among
effects of multiple edges could result in the elimination of "core" habitat long before one would
expect it to disappear based on measurements of distance to nearest edge alone. A more general
approach to dealing with such intrusive edge effects uses line integrals to summarize a site's
isolation relative to multiple edges (Malcolm 1994). As an important next step, a broad
spectrum of ecologists have called for research that will extend these ideas and facilitate the
study of the community consequences of different types of cross-edge intrusions. For example,
how do the impacts of cross-boundary foraging consumers change as a function of site isolation
vis _a vis patch edges (e.g., Andren and Angelstam 1988, Ostfeld et al. 1997)? Meshing
empirically determined penetration profiles with dynamical models offers one feasible route
toward this goal. For example, preliminary studies indicate that differently shaped edge
penetration profiles can adversely impact interacting populations by increasing the "minimum
patch size" required for the persistence of particular species or community dynamic phenomena
(Cantrell, et al. unpublished manuscript). However, biologically meaningful predictions could
still depend on the way effects from multiple edges interact with each other (e.g., Malcolm
1994).
Edge-mediated effects involving cross-boundary subsidies can also occur in the reverse
direction: going "from the inside out." Temporary emigration and cross-boundary foraging by
28
large mammals in response to density or resource pressures (Janzen 1986, Dobson and Meagher
1996) is a well known example. Although one might be tempted to view such outwardly
directed foraging in the same light as intrusive effects simply by reversing one's definition of
"patch" and "matrix," subtle, but important, mechanistic distinctions often preclude such a
straightforward solution. In contrast to intrusive effects that may often involve incidental
foraging by a species whose population is otherwise subsidized, cross-boundary foraging from
the inside of a patch outward may often focus on access to essential rather than supplementary
resources (e.g., survival during drought years [Boone and Keller 1993]). For example, consider
the case of alpine pikas, which shelter in rockslides but forage short distances into the
surrounding vegetated areas. For these animals, rockslide perimeter is an excellent predictor of
population size (Bunnell and Johnson 1974, Smith 1974). Pika foraging reduces the severity of
interspecific competition among plants by decreasing the biomass and percent cover of otherwise
dominant species, altering the species richness and composition of plant assemblages in narrow
bands surrounding the slides (Huntly et al. 1986, Huntly 1987).
In cases of outward-directed cross-boundary foraging, the security of the patch core can
influence the pattern and magnitude of extrusive edge effects. For example, beaver foraging in
riparian areas surrounding beaver impoundments depends on the relative accessibility of deeper
water where beavers are secure from terrestrial predators (Johnston and Naiman 1987). In
upland impoundments, where deep water is immediately available to terrestrially foraging
beavers, beaver foraging occurs relatively uniformly along the pond boundary. In contrast, in
less steeply sloped lowland impoundments, beaver foraging is patchily distributed (Johnston and
Naiman 1987).
29
Finally, in many instances, edge habitats themselves can provide a population subsidy for
some species. To the extent that species make differential use of such edge areas, altering habitat
edge/area (or surface area/volume) ratios among patches can determine the outcome of species
interactions. For example, studying a two-species larval anuran system in microcosms where
edge habitat corresponded to enclosure surfaces area near the air-water interface, Pearman
(1995) found that high edge/interior ratios favored the growth and survivorship of the tadpole
species that more effectively fed on periphyton growing on enclosure surfaces. Specifically, the
extent of habitat edge in these systems influenced community composition by altering the
relative importance of competition and size-dependent predation by subsidizing individuals of
one species at the expense of another (Pearman 1995).
Class 4: Edges can create new opportunities for species interactions
The fourth class of edge-mediated changes in species interactions emphasizes edges'
roles as generators of novel species interactions. Researchers have long recognized this
important function of edges and have made it a critical component of wildlife management plans
for many years (Leopold 1933, Odum 1971, Yoakum and Dasmann 1971). Landscape ecologists
have also been interested in edges' roles as generators of new species interactions, in one case
focusing on how edge-dependent browsing could influence the successional propagation of
forest edges across landscapes (Hardt and Forman 1989). In the conservation literature, attention
has focused on the negative impacts of anthropogenic edge creation through the generation of
detrimental or otherwise inappropriate species interactions (e.g., Yahner 1988). Moreover, in
Amazonia, the Biological Dynamics of Forest Fragments project has demonstrated that the
30
creation of habitat edges may quickly span multiple trophic levels as new interactions are
facilitated, impacting community dynamics(Lovejoy et al. 1989). In one example, lush plant
growth along newly created edges spawned a flush of insect herbivores that soon attracted
insectivorous species, altering the species composition of rainforest fragments relative to
contiguous forest (Lovejoy et al. 1986, 1989).
In this fourth class of edge-mediated effects, the influences of habitat edges on the
dispersal of individuals or propagules of different species are once again critically important.
Edges that act as biological barriers (e.g., Wegner and Merriam 1979) may increase animal
movement parallel to edges resulting in "travel lanes" (Bider 1968, Kaiser 1983) that generate a
disproportionately high frequency of interspecific contacts at edges. For instance, edges that
function as travel lanes for generalist predators are key components of the ecological trap
hypothesis discussed earlier (Gates and Gysel 1972, Angelstam 1986). In addition, increased
activity and contacts in the vicinity of habitat edges may generate an interaction "vacuum" in
other portions of a patch or landscape where species spend disproportionately less time (Bider
1968). (The converse scenario would also be possible in that if species utterly avoid edges and
tend to crowd inward toward patch centers, increased contacts would take place in the patch core
while an activity vacuum developed near the patch fringes [see e.g., Bowers and Dooley 19931)
The types of novel interactions spawned by habitat edges span the entire ecological
gamut. For example, in Australian rainforests, edge generation creates opportunities for
interspecific competition among rat species, perhaps leading to the local extirpation of one
species (Laurance 1994). Similarly, edge creation in old growth forests of the Pacific Northwest
facilitates otherwise atypical predation of great horned owls on juvenile northern spotted owls
(Thomas et al. 1990, Lujan et al. 1992). Edge-linked herbivory may drive the widespread
31
"dieback" of eucalyptus trees in rural Australia as adult herbivorous insects are crowded into
forest fragments even as juvenile habitat (i.e., farmed fields) increases (Lowman and Heatwole
1992) and as cross-edge fertilizer drift and dung-deposition increases the nutritional appeal of
some eucalypts to arthropod herbivores (Landsberg 1990, Landsberg et al. 1990). Likewise, in
the Russian Arctic, where the perimeter of snow free patches is a strong predictor of abundance
for ptarmigan and passerine birds, the edges of melting snowfields facilitate bird consumption of
fresh plant growth and recently emerged insects (Summers and Underhill 1996; see Bologna and
Steneck [1993] for a conceptually related marine example involving lobsters).
Edges can also facilitate novel parasitic interactions. Well known North American
examples include edge-linked brood parasitism of passerine nests by brown headed cowbirds
(Brittingham and Temple 1983, Trail and Baptista 1993) and the transmission of brainworm
infections from white-tailed deer, where the effects of infection are relatively benign, to other
ungulates such as moose, caribou, and elk, where the infections can be lethal (Anderson 1972,
Holmes 1996). Remnant Puerto Rican rainforests feature a similar interaction wherein parasitic
botflies are transmitted to forest interior species like the endangered Puerto Rican parrot through
contacts with reservoir species at forest-matrix edges (Snyder et al. 1987, Loye and Carroll
1995). Like the edge-mediated effects spawned by cross-boundary subsidies discussed earlier,
one could roughly characterize these and similar edge-generated interactions as spatiallydependent cases of apparent competition.
Targets for future research
32
Through literature searches we have amassed a litany of observational, experimental, and
theoretical situations in which ecological edges alter the nature or outcome of species
interactions. We have proposed that a few fundamental mechanisms drive edge-mediated effects
on a diversity of interspecific interactions. These commonalities among interactions—and their
dynamics consequences—suggest further research on edge-mediated effects may be helpful in
integrating studies of community dynamics and landscape processes.
Several areas have come to mind as targets for future field research. First, like the
dispersal phenomena they influence, edges themselves may be fleeting, changing over both time
and space as adjoining patches themselves change. Consequently, an important arena for
research is understanding the degree to which edge-mediated effects are of lasting importance or
are overridden by succession, disturbance, or other longer time frame processes. In addition,
difficult gaps remain in our understanding of the differences between natural and anthropogenic
edges (e.g., Yahner 1988) and moreover, between ecological and jurisdictional edges (e.g.,
Schonewald-Cox and Bayless 1986, Ambrose and Bratton 1990). Furthermore, it would likely
be worth exploring the degree to which interspecific differences in habitat specialization can be
related to edge-sensitivity, and from there to regional incidence patterns and dynamics.
Specifically, it would be worth knowing the extent to which we can predict community dynamics
in heterogeneous landscapes based on knowledge of individual species' responses to edges.
On a theoretical side, it seems worthwhile to gain a better understanding of the ways
edge-mediated mortality influences predator-prey dynamics and mutualistic interactions in
different habitat types; such topics are of increasing practical concern given the severity of
human landscape alterations. Likewise, issues of edge-sensitivity and edge-detection have been
33
little explored from a theoretical perspective but may prove critical to our understanding of
species and community dynamics in complexly heterogeneous habitats. Many if not most
species neither perceive nor respond to habitat edges in the same manner as humans; instead they
may routinely cross over what we consider patch edges only to cease their foraging activities
some distance inside the patch, perhaps as a result of environmental cues or encountering other
organisms. Likewise, abiotic thresholds for seed germination and seedling mortality rarely mirror
human edge delineations exactly. Thus, continued studies of skew-Brownian motion and some
types of individual behavior models may prove fruitful as avenues for exploring the
consequences of variation in edge sensitivities and responses.
In sum, the community impacts of ecological edges are ripe for further investigation. In
particular, research that combines experimental and theoretical perspectives in individual model
systems would be useful in trying to understand how far and at what pace habitat edges influence
community dynamics by disrupting, modifying, or creating species interactions. Much of this
research would have to be long term, spanning several years at a minimum, but would likely
prove a worthwhile investment, especially considering the increasing prominence of habitat
edges in ecosystems around the world.
CONCLUSION
Ecologists have long decried the lack of information on the specific mechanisms of
species loss in habitat fragments (Lovejoy et al. 1986, 1989) and the implications of such losses
for community integrity (Rathcke and Jules 1993, Murcia 1995). Indeed, interest in conservation
of particular species in the face of anthropogenic extinction risks has spawned much of the
34
research on edge-mediated effects we attempted to synthesize here. Yet, the growing awareness
of the importance of habitat edges to conservation only hints at the true extent of habitat edges'
dynamical significance. Because the "edge" concept is scalable (e.g., Gosz 1993), extending
from the boundaries of individuals leaves to continental-scale ecotones separating biomes, it
touches on many of ecology's major issues. Specifically, by fundamentally altering the nature of
species interactions, habitat edges can impact critical ecological mechanisms, patterns, and
dynamics at a variety of spatial scales: edges have the potential to influence everything from
species evolution (Smith et al. 1997) to ecosystem function (Klein 1989).
At least two critical themes emerge from this synthesis. The first concerns the
importance of among-species differences in edge responses for community dynamics.
Interspecific contrasts are critical to edge-mediated effects that arise through differential
movement and mortality patterns. A second emerging theme concerns the roles of spatial
supplementation and cross-edge dispersal of competitors, mutualists, and natural enemies as
determinants of the outcomes of particular species interactions in habitat patches.
Conceptualizing and experimentally documenting the community impacts of such crossboundary subsidies helps link patch dynamics and landscape ecology to foodweb theory. On a
still broader level, edge-mediated dynamics place severe limitations on our application of islandbiogeography theory to terrestrial systems (Janzen 1983, 1986, Doak and Mills 1994) and are
primary drivers of decreasing species richness with decreasing patch size (Lovejoy et al. 1986,
1989, Bierregaard et al. 1992; see also Cantrell and Cosner 1994 for a PDE based analysis). In
these situations, the influences of edge-mediated effects on the processes of species colonization
and extinction, which comprise a conceptual core of both island biogeography and species-area
relations (MacArthur and Wilson 1967, Hanski and Gyllenberg 1997), are of central concern.
35
Overall, edge-mediated changes in species interactions—including those involving
differential cross-edge movement, mortality, spatial subsidies, and the creation of new
interactions—constitute a diverse but conceptually-related class of mechanisms that appear of
wide ecological importance. At both experimental and theoretical levels, numerous imposing
gaps remain in our understanding of edge-mediated effects on species interactions. Yet, with the
growing prevalence of edges as a motivational force and emerging commonalities among edgemediated effects in diverse habitats as guides, we suspect further advances in understanding can
be made.
ACKNOWLEDGEMENTS
50
Appendix
In an innovative paper, Stamps et al. (1987) used a single-species simulation model to
study the impacts of edge permeability (defined as the proportion of individuals encountering a
patch edge that will pass through it) on species' emigration dynamics. A principal conclusion
from their work was that emigration was a monotonically saturating function of edge
permeability. Specifically, this means that the biggest increases in emigration arise when edges
go from being impermeable to being only slightly permeable. Further increases in permeability
lead to relatively smaller increases in emigration. A comparable result is demonstrated here to
occur for a related partial differential equation model.
Consider
a2 u
2
—
ax 2 = 14/ U
&J (o ) ± A
P
aX
on x
E (0,1)
Eq. Al
=0
Eq. A2
ax
with boundary conditions
This model assumes only dispersal. Hence, w2 measures the fractional rate at which the
population emigrates across the boundary. Note that in this model, p = 0 gives reflecting
boundary conditions, I > 0 gives mixed boundary conditions, and p.
co gives absorbing
boundary conditions. One can compute that
Eq. A3
w
= w tan(—
)
2
for 13 > 0 and w e(0, Tc). Consequently, an implicit formula for the sensitivity of w to 13 is
Eq. A4
51
dw
cifl
1
)
(14)
2 (10
tan( + —) sec
2
2
2
1 + cos w
w + sin w
0 as 13 —> 0. Then from Eq. A4, as 13 —> 0, the sensitivity tends to 00. Likewise,
-
Recall that w
W ---> 7T
as 13 —> 00, causing the sensitivity decreases with w and hence with p.
5?
FIGURE LEGENDS
Figure 1. Edges, patches and matrix habitat. Stylistic representations of landscape units as used
here. Edges can be tightly delineated boundaries between patches where habitat characteristics
change quickly (A) or graded regions featuring slow changes (B).
Figure 2. Relationships between geometric patch characteristics from empirical and theoretical
perspectives. In patches A and B, the extent of "core habitat" is demarcated using two different
edge-isolation metrics. For weakly penetrating effects, both gray and hatched regions constitute
the core region of the patches. For more deeply penetrating effects, only the hatched habitat can
be considered core area. If absorbing (Dirichlet) or mixed (Robin) boundary conditions are
imposed on hypothetical patches C, D, and E, the values for the principal eigenvalue ki (of a
partial differential equation system governing the dynamics of species on those patches) are quite
similar and large for patches C and D (and hence 1/k 1 is much smaller) but small for patch E. In
contrast, the perimeter-to-area ratio is large for patches D and E but small in C. Note that
applying edge-isolation metrics like those in patches A and B to patches C, D, and E would
result in comparably large amounts of core habitat in patches C and D but a much smaller
amount in E. Consequently, the principal eigenvalue 2,.1 is related to the size of core habitat
rather than perimeter-to-area ratio. More specifically, for a region of fixed shape, k1 scales like
1M2 where is a patch's linear dimension while perimeter-to-area (or surface area to volume)
ratios scale like 1/1. The relationship is different if completely reflecting (Neumann) boundary
conditions are imposed; in that case = 0 for all patches.
53
Figure 3. Competitive reversals mediated by edge-related mortality. In A), for a given level of
edge-related mortality, species' dispersal rates on both sides of a habitat edge and sensitivities to
matrix hostility combine (as in the composite variable a, in Eq. 3) to interact with their intrinsic
competitive abilities to determine which species are competitively dominant in a patch. In B)
species dispersal rates are held constant, but an increase in matrix hostility (as might result from
habitat degradation) leads to a competitive reversal. Existing analytical techniques cannot rule
out multiple reversals of competitive dominance as matrix hostility increases; see Cantrell et al.
(in press) for more details. In both cases, the overriding effects of edge-related mortality can
prevent straightforward conclusions about the identity of competitively dominant species based
on simple comparisons of reproductive rates and interaction strengths.
Figure 4. Habitat quality distributions and the consequences for ecological dynamics. In A,
good quality habitat (which could be variously defined as a region with increased resource
availability, decreased mortality risk, etc.) is located in the central portion of the patch. In this
case, movement up gradients in habitat quality are beneficial for the species due to overall
increases in reproduction or survival. In contrast, in B, good quality habitat is located at the
patch's outer fringes, close to lethal matrix habitat. In this scenario, a species that moves up
gradients in habitat quality puts itself in jeopardy because larger portions of the population are
exposed to edge-related mortality. An ecological example of such dynamics involves the
"ecological-trap" hypothesis of Gates and Gysel (1972) in which nesting birds seek out high risk
edge habitats because of the dual availability of sheltering and foraging areas, but expose
themselves to edge-foraging generalist predators.
54
Figure 5. Graphical depiction of different edge penetration profiles that represent the density of
"nonresident" species inside habitat patches. For animal species, nonresidents could be species
typically found in other habitats that are temporarily foraging or sheltering inside a habitat patch.
For plants and fungi, edge penetration profiles reflect the cross boundary flow of fruits, seeds,
pollen, or spores or the incursion of adult forms from one habitat type into another. Exponential,
linear, and step wise declines in edge penetration have been documented in the literature.
Exponentially declining edge penetration profiles could occur when individuals of a nonresident
species exhibit a constant rate of reversing direction, while stepwise declines could result when
discrete threshold tolerances for environmental conditions or the density of prey or enemy
species were surpassed. In still other cases, species occur at relatively constant densities some
distance into a patch and then exhibit declines. More complex penetration profiles (e.g., seed rain
patterns from plants with ballistic seed dispersal) are certainly possible
B)
Edge (Ecotone)
Matrix
C
4T
A)
Nominal
Superior
Nominal
Inferior
ai / aJ CRIT
RATIO OF SENSITIVITIES TO
CROSS-EDGE MOVEMENT
R:44
4.(
B)
Nominal
Superior
Nominal
Inferior
S
uit
MATRIX HOSTILITY
A)
/
1
/
1
Habitat Quality
I
;
J
B)
i
,,
I
,.
\
,,
,, ,
,,
,,
--'
1
,,
Lethal „Patch Interior „Lethal
Exterior
Exterior
Tolerance + Linear Decline
1■1•1111•1
— Tolerance + Exponential Decline
I
I
•
Absolute Tolerance Threshold
•
Exponential Decline
•
,,
............. Linear Decline
•
.................•
Patch Interior
•
•
""••••■•■•
•