Graph and circuit theory connectivity models of conservation

Ecological Applications, 23(7), 2013, pp. 1554–1573� 2013 by the Ecological Society of America

Graph and circuit theory connectivity models of conservationbiological control agents

INSU KOH,1,3 HELEN I. ROWE,2 AND JEFFREY D. HOLLAND1,4

1Department of Entomology, Purdue University, 901 West State Street, West Lafayette, Indiana 47907- 2089 USA2School of Life Sciences, Arizona State University, 427 East Tyler Mall, Tempe, Arizona 85287 USA

Abstract. The control of agricultural pests is an important ecosystem service provided bypredacious insects. In Midwestern USA, areas of remnant tallgrass prairie and prairierestorations may serve as relatively undisturbed sources of natural predators, and smallerareas of non-crop habitats such as seminatural areas and conservation plantings (CP) mayserve as stepping stones across landscapes dominated by intensive agriculture. However, littleis known about the flow of beneficial insects across large habitat networks. We measuredabundance of soybean aphids and predators in 15 CP and adjacent soybean fields. We testedtwo hypotheses: (1) landscape connectivity enhances the flow of beneficial insects; and (2)prairies act as a source of sustaining populations of beneficial insects in well-connectedhabitats, by using adaptations of graph and circuit theory, respectively. For graphconnectivity, incoming fluxes to the 15 CP from connected habitats were measured using anarea- and distance-weighted flux metric with a range of negative exponential dispersal kernels.Distance was weighted by the percentage of seminatural area within ellipse-shaped landscapes,the shape of which was determined with correlated random walks. For circuit connectivity,effective conductance from the prairie to the individual 15 CP was measured by regarding theflux as conductance in a circuit. We used these two connectivity measures to predict theabundance of natural enemies in the selected sites. The most abundant predators wereAnthocoridae, followed by exotic Coccinellidae, and native Coccinellidae. Predatorabundances were explained well by aphid abundance. However, only native Coccinellidaewere influenced by the flux and conductance. Interestingly, exotic Coccinellidae werenegatively related to the flux, and native Coccinellidae were highly influenced by theinteraction between exotic Coccinellidae and aphids. Our area- and distance-weighted flux andthe conductance variables showed better fit to field data than area-weighted flux or Euclideandistance from the prairie. These results indicate that the network of seminatural areas hasgreater influence on the flow of native predators than that of exotic predators, and that theprairie acts as a source for native Coccinellidae. Managers can enhance conservationbiocontrol and sustain the diversity of natural enemies by optimizing habitat networks.

Key words: Anthocoridae; Aphis glycines; circuit theory; Coccinellidae; conductance; conservationbiocontrol; conservation planting; correlated random walk; dispersal; insect predator; soybean aphid.

INTRODUCTION

Control of pests is an important ecosystem service

provided by natural enemies. Natural enemy popula-

tions are supported by complex landscapes with a high

proportion of natural or seminatural vegetation (Bian-

chi et al. 2006, Gardiner et al. 2009b). The influence of

landscape composition on the abundance and diversity

of natural enemies has been studied by several research-

ers; however, the effect of the spatial arrangements of

large networks of habitat has received less attention

(Bianchi et al. 2006). For example, habitats that are well

connected to each other may enhance the population of

predators, but little is known about how predators move

across the networks of these habitats. In this paper, we

adopted graph and circuit theoretical frameworks to

measure connectivity of the networks and then tested the

effects of connectivity on the abundance of natural

enemies of soybean aphids.

The soybean aphid, Aphis glycines Matsumura, is an

invasive exotic agricultural pest and a major threat to

soybean production in the USA. This pest was

discovered in Wisconsin in 2000 and has spread

throughout the Midwest, much of the Great Plains

states, and southern Canada (Venette and Ragsdale

2004). In eastern Asia, the soybean aphid is controlled

by a variety of natural enemies including predators,

parasitoids, and fungal pathogens (Chang et al. 1994,

Wu et al. 2004). In North America, native and exotic

generalist predators can be effective at controlling A.

glycines (Rutledge et al. 2004). The exotic ladybird

beetle, Harmonia axyridis (Pallas) was introduced as a

Manuscript received 18 September 2012; revised 13 March2013; accepted 8 April 2013. Corresponding Editor: C. Gratton.

3 Present address: Gund Institute for Ecological Econo-mies, University of Vermont, Johnson House 207, 617 MainStreet, Burlington, Vermont 05405 USA.

4 Corresponding author. E-mail: [email protected]

1554

biological control agent to control exotic pests in pecans

and red pines and is the most efficient biocontrol agent

for A. glycines (Koch 2003), but it has been argued that

H. axyridis has a negative impact on native ladybird

populations (Harmon et al. 2007). The regulation of

aphid populations by natural enemies provides biolog-

ical control (or conservation biological control in the

case of native predator species), an important ecosystem

service. However, in landscapes dominated by intensive

agriculture, natural and seminatural areas that may

serve as relatively undisturbed refuges for these natural

enemies can be sparse.

Landscape composition has been studied as a main

factor affecting the diversity and abundance of the

natural enemies in agricultural landscapes. In 74% of

studies reviewed, natural enemy populations were

enhanced in complex landscapes compared to simple

landscapes that are mostly dominated by agricultural

croplands (Bianchi et al. 2006). Within wheat fields, for

example, populations of beneficial predators are posi-

tively correlated with vegetation diversity and the

proportion of non-crop area in the surrounding

landscape (Elliott et al. 1999). Recently, Gardiner et

al. (2009a) showed that pest control service provided by

Coccinellidae in soybean fields is positively influenced by

increasing forest and grassland habitats in the surround-

ing landscapes.

Compared to the study of the effects of landscape

composition, the effects of landscape configuration on

natural enemy populations are little studied (Bianchi et

al. 2006). A few studies address the effects of spatial

configuration of non-crop habitats on pest control. In a

landscape with insufficient non-crop habitats, higher

parasitism rates have been observed in the edges than in

the centers of crop fields (Tscharntke et al. 2002). A

simulation study showed that the control of aphids by

Coccinella septempunctata L. is maximized when the

non-crop habitats are evenly distributed (Bianchi and

van der Werf 2003). These studies indicate the impor-

tance of spatial arrangement of the non-crop habitat

elements for pest control. From this perspective, the

relationship between the connectivity of these elements

and the movement of natural enemies in agriculturally

intensive agroecosystems should lead to better under-

standing of this conservation biocontrol service.

To examine the flow of natural enemies across a

complex habitat network, we applied an adaptation of

graph theory that includes circuit theory to measure the

connectivity of non-crop habitat elements. Graph

theory, which originates from mathematics and sociol-

ogy, is associated with measuring flow efficiency in

networks. It was first introduced in landscape ecology to

measure either structural or functional connectivity

because of its representation of patchy landscape by

nodes (e.g., habitats or patches) and edges (e.g.,

connections or paths between habitats) and its efficient

computation (Urban and Keitt 2001). With its use of

graph edges to represent individual flows and dispersal,

which imply ecological fluxes, the graph-connectivity

model is particularly linked to metapopulation models

(Hanski 1994, Urban et al. 2009). In metapopulation

models, source and sink can be represented by connec-

tions (i.e., edges) with different inward and outward

fluxes (i.e., emigration and immigration). Thus, graph

edges can be implemented to model differential move-

ment rates of individuals into and out of a habitat/node

(Minor and Urban 2007, Urban et al. 2009). Since its

first introduction, graph-connectivity has been applied

rapidly for many organisms including plants, insects,

amphibians, vertebrates, and coral reefs (O’Brien et al.

2006, Jordan et al. 2007, Treml et al. 2008, Minor et al.

2009, Awade et al. 2012, Decout et al. 2012, Kang et al.

2012). More recently, the graph model has incorporated

electrical circuit theory by replacing graph edges with

resistors conducting current flow. Circuit theory pro-

vides electrical connectivity measurements such as

effective resistance or conductance, which measure a

network’s ability to carry current between paired source

and sink nodes separated by a network of resistors

(McRae et al. 2008). These measurements account for

parallel and serial connections of resistors, and alterna-

tive and least resistance pathways, between a source and

a sink across a landscape network (McRae et al. 2008).

Circuit-connectivity shows a better prediction of species

dispersal than Euclidean distance or the least-cost

analysis (McRae and Beier 2007). Therefore, circuit

theory offers an advantage because different flows along

all possible paths can be modeled in measuring

connectivity between a paired source and sink through

a network with multiple intermediate nodes, which

cannot be measured with graph theory alone (McRae et

al. 2008, Urban et al. 2009).

In much of the midwestern USA, there are few

patches of natural or seminatural habitat remaining to

support native natural enemy populations. Larger areas

such as prairie remnants may be the most stable source

of native natural enemies. Smaller such habitats and on-

farm conservation practices and seminatural areas may

function as stepping-stone habitats between the larger

remnant sources and farms, but may be more prone to

extirpation. The flow of natural enemies from a large

stable source habitat across agricultural landscapes will

be complex and follow multiple paths. Understanding

this flow may allow managers and farmers interested in

conservation biological control to place conservation

practices strategically across the landscape to enhance

the benefits of this ecosystem service. In this study we

hypothesized that high connectivity between these

habitats and agricultural fields enhances the flow of

natural enemies and that prairie remnants act as a

source of predators that sustain populations in well-

connected habitats. We tested the following predictions

for different predator insect families: (1) the abundance

of natural enemies will increase with increasing flux, a

graph-connectivity measure, in a network; and (2) the

abundance of natural enemies will increase with

October 2013 1555CIRCUIT FLOW FOR PREDATORS

increasing conductance, a circuit-connectivity measure,

between a prairie remnant and crop fields (see Plate 1 foran abstract illustration). We tested these predictionsseparately for native and exotic Coccinelidae as these

may use and move across habitat networks differently.The other predator families studied consisted of native

species.

METHODS

Study region, study sites, and habitat maps

Our study area was Newton County in Indiana, USA,which has an agroecosystem landscape representative of

much of Indiana and Midwestern USA (Fig. 1A).Newton County is dominated by corn and soybeanagriculture, and also includes an extensive tallgrass

prairie restoration complex, forests, urban areas, andmany small conservation plantings. We targeted two

common United States Department of Agriculture(USDA) Natural Resource Conservation Service(NRCS) conservation planting types for sampling in

our study: CP21 plantings are low-diversity filter stripsof cool-season grasses, and CP33 plantings are moder-

ate-diversity wildlife buffers of grass and floweringplants. In this region, we selected 15 conservationplantings (hereafter CP): 10 CP21s and 5 CP33s adjacent

to soybean fields for predator sampling. AdditionalCP33s next to soybean fields were not available in 2011

due to the increase in corn planted that year at theexpense of soybean acreage. The study sites were

selected to span as much of the county as possible.As a first step toward graph and circuit analyses, we

created a map of seminatural habitat. Seminatural

habitat is less subject to disturbance such as tilling andpesticide application, and we therefore assumed that

these areas are less hostile over an annual cycle thancrop fields and act as refuges for beneficial predatorinsects. Forest, shrub, grassland, pasture, and woody

wetland of 16 land cover classes in the 2001 30-mresolution national land cover data (NLCD) as well as

polygons of CP21, CP33, remnant tallgrass prairie, andprairie restoration were considered seminatural habitat

and mapped. We aggregated the prairie remnant andadjacent prairie restorations into one prairie feature(hereafter prairie complex). We also aggregated semi-

natural habitat grid pixels when they were within 30 mof each other. The resulting map of seminatural habitat

was binary, with seminatural habitat pixels having avalue of 1 and all other pixels 0. The extent of this mapwas Newton County plus a 10-km buffer (Fig. 1A).

From this map of seminatural habitat, we created ahabitat polygon map and extracted 490 patches that met

at least one of the following criteria: larger than 5 ha,and CP21s or CP33s within 7 km of the prairie complexand study sites (Fig. 1A). Only a subset (n ¼ 15) of the

CP21 and CP33 patches were sampled.

Graph-connectivity model

A graph is defined by two types of elements: nodes

and edges. These nodes and edges can represent discrete

habitat patches and their connectivity in a landscape.

The edges can be defined in binary and probabilistic

ways. A binary connection model defines an edge from

patch i to patch j as 1 (connected) or 0 (not connected).

A probabilistic connection model can define an edge as a

dispersal probability between two habitat patches

(Urban and Keitt 2001). This probability can be

calculated by a dispersal kernel, a negative exponential

function of inter-patch distance, for example:

Pij ¼ e�kdij

where k is a distance–decay coefficient (k . 0), and dij is

the distance between two patches, i and j. For both

binary and probabilistic approaches, when edges are

based on distance alone, an undirected graph is

produced in which the value of an edge from patch i

to patch j is the same as the value of an edge from patch j

to patch i. However, when these edges are redefined

based on dispersal fluxes, i.e., the rate or relative number

of individual dispersing, these fluxes may be influenced

by habitat size or quality, or other factors leading to

asymmetrical dispersal. Therefore, a flux value from a

large patch i to a small patch j will be greater than that

from patch j to patch i. This directed edge graph can be

measured by area-weighted flux (Urban and Keitt 2001,

Minor and Urban 2007) as follows:

Fluxaij ¼ Aie�kdij

where Ai is area of patch i (ha). Area-weighted flux

shows the incoming flux from patch i to patch j (Fluxaij)

is different from outgoing flux from patch j to patch i

(Fluxaji ), when the areas of patch i and j are different. As

a result, the matrix of this flux between every pair of

patches is asymmetric. This flux measure employs an

approach similar to Hanski’s meta-population model.

The flux measure we used, based on Euclidean

distances between patches, may have less biological

meaning because it does not consider the interruption of

movement, or resistance to movement, by nonnatural

areas. To take into account these effects, a few studies

have measured least-cost path distance and counted

successful dispersal events (Bunn et al. 2000, Lookingbill

et al. 2010). A least-cost path is calculated by an

algorithm to find the optimal, least costly, single path

for an animal movement on a map representing

resistance to movement (e.g., Foley and Holland

2010). However, it is often indicated that a least-cost

path is not necessarily the path used and does not allow

for more realistic movement along many alternative

paths simultaneously (Fahrig 2007, Pinto and Keitt

2009). Counting successful dispersal events between all

pairs of patches has been conducted using a correlated

random walk simulation (e.g., J-walk software) on a

heterogeneous landscape with different probabilities of

movement and mortalities according to land cover

(Gardner and Gustafson 2004, Lookingbill et al. 2010,

Morzillo et al. 2011). Circuit theory is another approach

INSU KOH ET AL.1556 Ecological ApplicationsVol. 23, No. 7

to modeling dispersal, and it allows for estimation of

movement by individuals along an unlimited number of

different pathways within a network simultaneously

(McRae et al. 2008). All of these approaches have

strengths and we used a combination of them in this

study.

Correlated random walk simulation

We assigned resistance to edges between nodes based

upon the nature of the area over which dispersing insects

are likely to have encountered. To estimate the area over

which dispersing predators moving from a patch i to

another patch j are likely to have encountered, a

correlated random walk (CRW) simulation was per-

formed on a homogeneous landscape. The CRW

simulation required three parameters: step lengths,

turning angles, and a maximum total steps per dispersal

event (Kareiva and Shigesada 1983, Turchin et al. 1991).

To determine these parameters, we used published data

for Coccinellidae species because this family has been

well-documented in the literature on dispersal compared

to the other families of natural enemies in our study. We

defined the step length as a movement distance for an

hour to facilitate the use of published movement data.

We chose a gamma distribution with mean and standard

deviation (6SD) of 50 6 35 m, for the step lengths in

order to match the movement distance reported from

Coccinellidae species (Appendix A). For turning angles,

we selected a normal distribution with mean 6 SD (0 6

27 degrees), closely corresponding to the observed

probability distribution of the species’ turning angles

reported for Coccinella septempunctata (Banks and

Yasenak 2003), which was the only species for which

we could find data (Appendix A). Last, for the

maximum number of steps, we referred to the life cycle

of Harmonia axyridis, which typically lives for 30–90

days as an adult (Koch 2003). We determined the total

number of steps to be 1000 steps, which is approximately

the same as 900 movement hours, when we assumed that

FIG. 1. Study sites and insect sampling design. (A) Land cover map of Newton County, Indiana, USA. The Inset map showsthe location of Newton County within Indiana. Study sites 1–10 and 11–15 soybean fields are located beside CP21 and CP33 fields,respectively. Two USDA Natural Resource Conservation Service (NRCS) conservation planting (CP) types include low-diversityfilter strips of cool-season grasses (CP21) and moderate-diversity wildlife buffers of grass and flowering plants (CP33). (B)Transects for insect sampling in study sites.


the species lives 60 days and can move 15 hours per day

during a summer season.

Using these three parameters, CRW simulations were

performed between two virtual round-shaped patches,

corresponding to source and target patches. The patches

were separated by different distances of 250–4000 m.

We randomly placed 100 000 random walkers along the

edge of the source patch. For each step, a step length

and a turning angle were sampled from the Gamma and

the Normal distributions, respectively, except for the

first step’s turning angle, which was determined from a

random selection from�180 to 180 degrees. The turning

angles were relative to the direction of the previous step.

When a random walker hit the target patch, this

successful path from the source to the target was

recorded. For each successful path, we calculated two

maximum perpendicular distances from the line linking

the centers of the source and the target and from the

center line separating them corresponding to a major

and minor radius for drawing an ellipse with a center

point on the intersection between the two lines (Fig. 2;

Supplement). The ellipse was regarded as a potential

region in which a successful random walker is likely to

pass between the source and the target for each patch

separation distance. A dispersing individual that leaves

this area is less likely to arrive at the target patch j,

although it may end up at another patch node in the

study region. This process was repeated for distances

250, 500, 750, 1000, 1500, 2000, 3000, and 4000 m.

The major and minor radii of all successful random

walkers were averaged within each distance, and the

averaged ellipse polygon was defined as a final potential

region. As distances between source and target patches

increase, the relative lengths of the averaged major and

minor radii of the final ellipse decline toward 60% and

40% of the distance separating the patches, respectively

(Fig. 3). This trend was not sensitive to changes in the

size of source and target patches, nor to changes in the

distribution of turning angles or step length. However, it

largely depended on the total step count, which, in this

study, was limited to the largest possible step count

based on the insect’s longevity.

Using this relationship between distance between a

pair of patches and the size and shape of the area likely

encountered, we calculated the proportion of seminat-

ural area within the resulting ellipse encompassing every

pair of connected nodes. We made the assumption that

altering the movement parameters for different insect

predators would not have a large influence on the shape

of the resultant elliptical landscape, i.e., the ratio

between the major axis (fixed by inter-node distance)

and minor axis will not be greatly affected. Finally,

fluxes were measured by weighting distance by the

naturalness (% seminatural) as follows:

Fluxadij ¼ Aie�kð1�NijÞdij

where Nij is the proportion of seminatural area within

the ellipse delineating likely successful paths of preda-

tors between two patches. We refer to this estimate of

dispersal as area- and distance-weighted flux (Fluxad).

This measure decreases with i�j distance and increases

as natural and seminatural areas increase within the

elliptical area likely crossed. In this way, all seminatural

FIG. 2. A successful path of a random walker based oncorrelated random walk simulation for source and targetpatches with a distance of 3000 m and an ellipse-shaped regioncovering the successful path. The points in the boundaries ofthe source and target patches show the starting point andhitting point.

FIG. 3. The relationship between the radii of the averagedellipse polygon and distance between source and target patches,dij (m). The averaged ellipse polygon was obtained for allsuccessful random walkers of 100 000 walkers. The majorradius can be calculated by the equation (e(�0.001dij þ 5.294) þ60)/100 3 dij. The minor radius can be calculated by theequation (e�0.001dij þ 5.557 þ 40)/100 3 dij.


areas, regardless of patch size, were incorporated into

the final model either as nodes or as determining

resistance.

Using this flux, we calculated incoming flux for a

certain habitat node. Because incoming flux can be

ecologically interpreted as the number of immigrants

(Minor and Urban 2007), it was used for measuring

graph-connectivity as follows:

inFluxadj ¼Xn

i¼1

Fluxij

where inFluxadj is incoming flux for patch j, and n is the

total number of habitat patches (in this study, n¼ 490).

Circuit-connectivity model

For applying circuit theory to a graph, edges of a

graph are defined as resistors, the reciprocal of

conductors (McRae et al. 2008). Conductance (G, in

Siemens) is a measure of a resistor’s ability to carry

electrical current, and resistance (R, in Ohms) is the

opposite. According to Ohm’s law, the current I (in

amperes) flows directly proportional to its applied

voltage V and its conductance (the reciprocal of

resistance): I ¼ VG ¼ V/R. In a circuit, when two

conductors are connected in series, equivalent or effective

conductance Ge is calculated by Ge¼G1G2/(G1þG2). In

the case of parallel connection, the effective conductance

is calculated by Ge ¼ G1 þ G2. As a result, effective

conductance between current source and sink nodes

considers additional available pathways. Therefore, this

circuit connectivity measure can be ecologically inter-

preted as the flow capacity for a species between pairs of

habitat nodes along many pathways across the land-

scape.

To apply this electric circuit concept to our graph, we

regarded the flux value as conductance between two

habitat nodes. Because the flux is a measure of

movement rate between two habitat nodes, this substi-

tution is ecologically feasible. However, the flux graph is

a directed graph, where conductance in each direction is

not necessarily the same, so that effective conductance

will not be calculated by a single algebraic operation

(Thomas 2009). Instead, we followed the iterative

procedure developed by Thomas (2009) to calculate an

effective conductance in a directed circuit graph by

searching equilibrium voltages or currents with no

conflicting current flows.

The graph- and circuit-connectivity concepts are

summarized and represented in Fig. 4. The flux between

nodes depends on the size of the patch of origin, so that

the flux can be represented as directed edges. Even

though node b in Fig. 4C has one more link than in Fig.

4A, the incoming flux for node b in Fig. 4A and C are

the same because fluxes are weighted by area. When one

node is connected to the current source and a second

node is tied to the current sink or ground, current flows

without conflict from the source to the ground node

(Fig. 4B, D). Using this current flow path, effective

conductance can be calculated. Effective conductance is

larger in a circuit with an additional path (Fig. 4D).

Graph- and circuit-connectivity computing

based on threshold distances

We did not know the shape of the dispersal kernel for

our species, so we ran parameter sweeps on a range of

threshold distances and dispersal probability cutoffs.

The threshold distance was the distance beyond which

nodes were not connected in the graph. At the threshold

distance, if the dispersal probability is given as 5%, i.e.,

5% dispersal probability cutoff, the distance–decay

coefficient k of the negative exponential dispersal kernel

can be calculated such as�ln(0.05)/(threshold distance).

For graph- and circuit-connectivity calculations, we

used different shapes of the negative exponential

dispersal kernel based on a range of threshold distances

from 500 m to 7 km, every 100-m distance (i.e., 66

threshold distances) with 5% dispersal probability cutoff

(Appendix B). In addition, we also varied the dispersal

probability cutoff across a large range of values

(0.001%–100%) at threshold distances of 500 m to 5

km, every 500 m, to determine if this influenced the

graph and circuit theory model fit to our empirical data

because rare long-distance dispersal events can lead to

colonization and influence occurrence (e.g., Fitzpatrick

et al. 2012) (Appendix B). The dispersal probability and

threshold distance are related such that a 5% dispersal

probability occurs at a given threshold distance for a

given dispersal kernel, suggesting that 5% of dispersing

individuals travel at least this far and that this is just

sufficient for successful colonization and future dispersal

stemming from that colonization event. The parameter

sweeps indicated that the threshold distance had a much

larger influence on the model fit than did the dispersal

probability cutoff (Appendix C). For a given dispersal

kernel, the dispersal probability and threshold distance

are intricately related in that they can be thought of as

different axes or dimensions through which the kernel is

described.

Area- and distance-weighted flux matrices, Fluxadij,

for all pairs of habitat nodes were calculated using the

distance–decay coefficients corresponding to all 66

threshold distances. For calculating this flux, edge-to-

edge distances for all pairs of habitat patches were

measured on the habitat polygon map. Then, the sums

of incoming flux were measured for the selected 15 CP

sites. This flux value was used in statistical analysis to

test the first hypothesis. Procedures for the graph-

connectivity model including CRW simulation and

naturalness calculation were conducted with R software

(R Development Core Team 2011) with R packages

‘‘raster’’ for raster calculation (Hijmans and van Etten

2011) and ‘‘igraph’’ for graph visualization (Csardi

2010).

Using the area- and distance-weighted flux, effective

conductance was calculated according to the different


threshold distances. Regarding the flux as conductance,

15 effective conductance values were calculated for the

pairs of the source and sink habitat nodes: the prairie

complex habitat was connected to current source, and

each of the 15 CP nodes was connected to ground, or

the current sink. The iterative procedure and effective

conductance calculations were conducted using R

package ‘‘ElectroGraph’’ (Thomas 2012). Because the

calculation of effective conductance for each threshold

distance takes a long time (i.e., in the case of 1-km

threshold, it takes ;3 h on a 2.33 GHz Intel E5410

central processing units (CPU), and we had 66

threshold distances and a range of dispersal probabil-

ities), we used a supercomputer, Radon, which is a

computer cluster operated by the Rosen Center for

Advanced Computing, Purdue University (West La-

fayette, Indiana, USA), for the parameter sweep

analysis. Lastly, the effective conductance for each site

was multiplied by the sampling days corresponding to

each site. This value was used in statistical analysis to

test the second hypothesis.

Natural enemies and aphids sampling

During late June to mid-September in 2011, the

abundance of natural enemies was examined in the

selected 15 CP and the abundance of natural enemies

and soybean aphids were examined in the 15 soybean

fields adjacent to these CP. We set up two transects with

sampling points at 30 m, 60 m, and 150 m along each

transect in each soybean field and each CP. In soybean

fields, the two transects ran perpendicular to the edge

between the soybean fields and the CP, whereas in the

CP, transects ran parallel to the edge because the CP are

almost always long, narrow plantings (Fig. 1B). Two

transects sampled at the same three distances were also

set up in 10 prairie restorations and five pairs in the

tallgrass prairie remnant. In the crop fields, four tall

wooden stakes were used to surround each transect 25 m

from the transect to indicate where farmers should not

spray. However, in the only four fields that were sprayed

(fields 1, 2, 12, and 15), the aphid abundance data

indicate that our instructions were likely disregarded.

Natural enemy surveys were conducted every two

weeks using sweep-net sampling. Sweep-net sampling is

FIG. 4. Simple circuit with a series and a parallel connection using an area-weighted flux graph. If we assume that the size ofnodes is 1 (for b, c1, c2, and d) or 2 (for a, c, and d) and distances among nodes a, b, c (c1 and c2), d, and e are the same, the fluxesdepend on the size of nodes: Here, we assign 1 or 2 for the fluxes. When we regard these fluxes as conductances, the edges can berepresented by resistances, the reciprocal of the fluxes. Even though the distance from a to d in the circuits depicted in panels (B)and (D) is the same, the effective conductance between a and d of the circuit in panel (D) is larger than that of the circuit in panel(B) because of the alternative paths of the circuit in panel (D). In panels (B) and (D), A is the current in amperes.


the best sampling method for capturing aphid predatory

insects in the families Anthocoridae, Nabidae, Chry-

sopidae, Hemerobiidae, and Coccinellidae (Roth 2003,

Kriz et al. 2006, Harwood 2008). We used a 20 pace–

sweep sample perpendicular to the transect at the three

sampling distances in soybean fields, CP, prairie, and

restorations. Samples were bagged and immediately

placed on ice in an ice box. At the end of each sampling

day, the samples were placed in a freezer. Natural

enemies in the samples were later identified to species

level for Anthocoridae and Coccinellidae and to family

level for others. All natural enemies were divided into

adult and immature categories. Aphids were counted on

two randomly selected soybean plants at each transect

point each week using the procedures developed by

Ragsdale et al. (2007) beginning when the plants reached

the V3 growth stage (three nodes of trifoliate leaves fully

developed).

For each study site, the predator abundance was

determined as the sum from all samplings on a given

date from the 12 points in each soybean field and

adjacent CP pair. Although there may be movement

between the CP and the crop field through the season,

we combined the predator data from field and CP at

each site because in this study we were interested in the

total predator community regardless of microhabitat. A

future study will examine farm-scale heterogeneity in

predator abundance. Soybean aphid abundance was

determined as the averaged number of aphids per plant

in each soybean field across the 12 plants on each

sampling date. Finally, we calculated the integrated area

under the abundance curves over time for the predators

and aphids for each site. These integrated predator-days

and aphid-days measures of the abundances were used

in statistical analysis. Hereafter, we refer to the

integrated abundance of predators and aphids as

predator-days and aphid-days, respectively. There was

a range of first sampling dates due to the difficulty of

finding appropriate fields. While this may introduce

some bias into the Anthocoridae abundances because

they were present early in the season, aphids and

Coccinellidae did not appear in our samples until after

surveys in all fields had begun.

PLATE 1. Abstract composition of seven-spotted ladybird beetles moving across a landscape upon which resistance values(resistors) have been superimposed. Image was created using POV-Ray and a ladybird beetle model by Giles Tran distributed underthe Creative Commons Attribution License. Image credit: J. D. Holland.


Statistical analysis

To examine the performance of graph and circuitconnectivity models, we compared the difference be-

tween the area-weighted incoming flux (Fluxa) andarea- and distance-weighted incoming flux (Fluxad)

determined by the CRW in this study based on differentthreshold distances. Because the circuit connectivity

model used Fluxad as conductance between patches, weexamined the relationship between Fluxad and the

effective conductance from the prairie complex toindividual patches (Conduct) based on different thresh-

old distances. We also compared Conduct with Euclid-ean distance from the prairie complex to individual

patches (Dist) to examine the degree to which these arecorrelated.

We used a model selection approach to test our twohypotheses (the effects of landscape connectivity on the

flow of natural enemies and the role of prairie as asource in sustaining the natural enemies) at the same

time to examine whether our flux and conductancevariables (Fluxad and Conduct) in this study show better

fits than Fluxa and Dist. Because Fluxad (or Fluxa) andConduct were dependent on threshold cutoff distances,we first examined the threshold distances with 5%probability cutoff at which each predator-days (Antho-coridae-days [Anth], exotic Coccinelldiae-days [Ecocc],

and native Coccinellidae-days [Ncocc]) was best predict-ed by aphid-days (Aphid) and flux or conductance

variables (i.e., Aphid þ Fluxad and Aphid þ Conductregression models, respectively). At the selected thresh-

old distances, we applied model selection techniques tofind the best model. Additionally, we examined how the

model fits of the selected best models varied withdispersal probability cutoffs.

For the first hypothesis, we tested whether fluxvariables influenced the predator-days by comparing

all possible linear model combinations including anintercept-only model to predict predator-days. In the

linear regressions, variables were transformed usingsquare-root or ln (x þ 1) to meet the assumptions of

normality and homogeneity of variance and to increaselinearity. We considered the flux variables as alternativevariables (either of Fluxad or Fluxa) to see which served

as better predictors. Particularly in the regressionmodels for predicting Ecocc and Ncocc, we included

as a predictor the other Coccinellidae group because ofthe reported displacement of native Coccinellidae by

exotic Coccinellidae (Evans 2004, Gardiner et al. 2009b).Coccinellidae–Aphid interaction terms were included

when both main predictors were included in the model.We then examined the correlation coefficients between

predictors in multiple linear regressions to avoidpossible problems of collinearity, such as when Pearson

correlation jrj . 0.7 (Dormann et al. 2012). In addition,to avoid the potential problem of multicollinearity

between main effects and interaction, we rescaled themain predictor variables by centering. We used these

centered variables and their interactions for predicting

Ecocc and Ncocc, which has been suggested as a

solution of reducing multicollinearity without altering

regression slopes or hypothesis tests (Jaccard et al. 1990,

Quinn and Keough 2002). To compare models using

these transformed and centered predictors, we calculated

corrected Akaike information criterion (AICc) values for

small sample size (Burnham and Anderson 2002). AICc

values were also used to derive AICc differences (DAICc)

for each model against the best model with minimum

AICc value. Finally, we presented all models with DAICc

, 4 to compare the models DAICc , 2, which are

generally considered to have substantial support (Burn-

ham and Anderson 2002). We also calculated model

weights, w, which were used to compare the strength of

evidence of the models from those with DAICc , 4

(Burnham and Anderson 2002). For the selected models

with more than one predictor, we calculated partial

correlations for all variables to assess the importance of

individual independent variables after controlling for

additional variables in the model. We applied this

procedure for testing our second hypothesis and we

compared Conduct and Dist with competing models.

All statistical analyses were conducted in R version

2.14.0 (R Development Core Team 2011). We examined

the normality and homoscedasticity of the errors of

regression models. We examined spatial autocorrelation

in the residuals of the regression models using a global

Moran’s I test (Dormann et al. 2007) and a spline

correlogram for each predator group (Bjornstad and

Falck 2001). Because of the low number of study sites

(driven by a lack of available plantings), we had a low

overall power to detect strong significance. Therefore,

we also presented marginally significant effects with P ,

0.1 when they were observed.

RESULTS

Graph- and circuit-connectivity model performance

Graph- and circuit-connectivity measurements, in-

coming flux and effective conductance, depended

considerably on the threshold distance that determined

which nodes were connected. At a 1.5-km threshold

distance, most nodes were connected to the network and

the all study sites had at least one incoming flux edge

(Fig. 5A). At threshold distances shorter than 1.5 km,

some sites had zero incoming flux (e.g., site 2). Between

2- and 3-km threshold distances, the study sites were

completely connected to the prairie complex network

(Fig. 5B).

When the threshold distance increased, the flux value

of the study sites also increased, and two different

patterns of increase appeared showing rapid and slow

changes. The rapid flux increase was caused by

proximity to large habitat patches, that is, when a

relatively large habitat patch was connected to the study

sites, as for sites 1, 5, 8, 10, and 15 (Fig. 6A). The slow

flux increase was related to increasing dispersal proba-

bility. In most study sites, the slow increase in flux with

threshold distance was shown before and after the rapid


FIG. 5. Area- and distance-weighted (A, B) flux and (C, D) circuit graphs; the width of gray edges is proportional to flux in panels(A) and (B), and current in panels (C) and (D). (A) Flux graph based on a 1.5-km threshold distance; node circle size is relative topatch size; the width of edge is relative to averaged flux (directed edges are shown in themagnified box). (B) Flux graph based on a 3.0-km threshold distance. (C) Example of current flow from the prairie complex to site 8 based on the flux in panel (A); width of edge isproportional to current flow rate from source to sink; effective conductance calculated from the source to sink is 1.8. (D) Current flowrate from the prairie complex to site 11 based on the flux in panel (A); effective conductance is 0.7. ‘‘Nature’’ in the key refers to nodesof natural and seminatural areas, and prairie refers to the prairie restoration complex. Site numbers are shown in brown (see Fig. 1).


increases in all the study sites for all threshold distances.

However, when a habitat (e.g., site 9) was located near a

large habitat patch the incoming flux was maintained at

a high level at all threshold distances rather than

showing a rapid increase because the large patch

remained connected and contributed a large proportion

of the flux for the habitat (Fig.6B). The rapid increase in

flux with increasing graph connectedness, which was

displayed for most sites in the graph-connectivity model,

became even more apparent in the circuit-connectivity

analysis. Below a threshold distance of ;2 km, some

sites, such as 2 and 3, were not connected to the prairie

complex network and therefore had a predicted effective

conductance of zero (Figs. 5C, D, and 6B). When they

were connected to the prairie network, at ;2 km, the

zero conductances sharply increased to levels similar

with other sites (Fig. 6B). For the study sites, the

area- and distance-weighted flux (Fluxad) was highly

correlated with area-weighted flux (Fluxa). As the

threshold distance increased, this correlation increased

from 0.77 to 0.97 (Fig. 6C). Up to a threshold distance

of ;2 km, the correlation coefficient rapidly increased to

high levels (.0.9) before leveling off with increasing

threshold distance. These nonlinear increases, along

with the shape of the connected network, at least at the

1.5-km threshold (Fig. 5), limits correlation between

Euclidean distance and our two network-based predic-

tors. As the threshold increases and the network

becomes more connected, the correlation between these

three increases.

At a threshold distance of 1.5 km, effective conduc-

tance from the prairie complex to the other habitat

nodes (489 patches) including the selected CP fields was

negatively correlated to Euclidean distances to the

prairie complex (Fig. 6D). Although the trend became

quite linear once ln (x þ 1)-transformed (r ¼ �0.66),there was a high variance within the negative correla-

tion.

Aphid and natural enemies

The first Aphis glycines, a single individual on a

soybean plant, was observed on 19 July of 2011. The

total population of aphids increased to a peak between

late August and early September (Fig. 7). The two

highest field averages of aphids per plant, ;2520 and

870, were observed in site 12 on 31 August and in site 13

on 13 September 2011, respectively. At some fields (sites

1, 2, 12, and 15), pesticides were sprayed by famers

around the peak dates, so the aphid population

FIG. 6. (A, B) The comparison of area- and distance-weighted flux (Fluxad) and effective conductance (Conduct) connectivityvalues for selected 15 study sites based on threshold distances with 5% probability cutoff. (C) The relationship between area-weighted flux (Fluxa) and Fluxad and the relationship between Fluxad and conductance for the study sites. (D) The relationshipbetween conductance that was calculated at 1.5-km threshold distances with 5% dispersal probability cutoff and Euclideandistances from the prairie remnant to all other patches including the selected study sites. All variables are ln(xþ 1)-transformed.Numbers beside the lines in panels (A) and (B) and in gray circles in panel (D) indicate the selected 15 study sites.


dropped. During the sampling period in 2011, the mean

aphid-days per plant per field were 9371 (SD ¼ 5003).

A total of 2573 individual natural enemies were

collected in soybean fields and adjacent CP in the

sampling period. This number was ;10 times the

number of predators collected in the prairie remnant

and restorations (Appendix C). Based on the number of

adult insects collected, within family-level abundances

were dominated by (most to least) Anthocoridae,

Coccinellidae, Chrysopidae, Nabidae, and Hemerobii-

dae in soybean fields and adjacent CP. The two most

abundant families, Anthocoridae and Coccinellidae,

comprised ;90% of the total natural enemies collected

and were selected to test our hypothesis. Four species of

coccinellids were collected and divided into exotic

(Harmonia axyridis and Coccinella septempunctata) and

native species (Coleomegilla maculate and Cycloneda

munda). Interestingly, we did not observe Coccinella

septempunctata in the prairies and restorations, but we

did observe two additional native species there, Hippo-

domia convergens and Hippodomia parenthesis. Harmo-

nia axyridis adults comprised ;70% of the coccinellid

adults in soybean fields and CP. We focused our analysis

on the adult predators because the nymphs and larvae

are unlikely to move between patches. Anthocoridae

adults were found in most study sites before aphids

appeared, and their population increased immediately

with the increasing of the aphid population (Fig. 7).

Exotic and native Coccinellidae adults were less

common in soybean fields before the aphids arrived,

but populations increased when the aphid population

rapidly increased. In the two sites where the highest

numbers of aphids were observed, a large number of

exotic Coccinellidae were observed, but no native

Coccinellidae were observed. In only three sites (4, 7,

and 14) were native Coccinellidae found with no exotic

species collected. Anthocoridae-days, exotic, and native

Coccinellidae-days per field were (mean 6 SD) 1627 6

827, 74 6 110, and 30 6 31 within sites, respectively.

Predicting the abundance of predators using graph-

and circuit-connectivity

For each predator, linear regression models using

area- and distance-weighted incoming flux (Fluxad) and

effective conductance from the prairie complex to

individual study sites (Conduct) detected the best

threshold distances with a 5% dispersal probability

cutoff (Fig. 8). The alternative predictors, which were

area-weighted incoming flux (Fluxa) and Euclidean

distance from the prairie complex to individual study

FIG. 7. The number of soybean aphids and natural enemies (Anthocoridae, exotic and native Coccinellidae) in 15 study fieldsfor the sampling period. For aphids, at least 6–10 sampling surveys, and for natural enemies, at least 4–8 sampling surveys, wereconducted in each field. Aphid number is the averaged number of aphids per plant, and natural enemy number is the total numberof each predator collected on each sampling date in the 12 sampling points of each field (i.e., sum of predators per 20 sweeps at 12sampling points).


sites (Dist), were compared with Fluxad and Conduct,

respectively, in model selection.

For Anthocoridae-days (Anth), the regression model

with aphid-days (Aphid) þ Fluxad, showed relatively

high r2 values in a range of threshold distances between

1.4 km and 2.7 km (Fig. 8A). In this range, the AphidþFluxad model at 2.3 km showed the highest adjusted r2

value of the regressions. Although the coefficient of

Fluxad showed positive relationship with Anth (Fig. 8E),

it was not significant and the model weight was much

less than the simpler Aphid only model (Table 1).

Compared to area-weighted incoming flux (Fluxa),

Fluxad increased the model fit slightly (Table 1). Similar

to the AphidþFluxad model, the adjusted r2 of AphidþConduct model was much less than that of the simpler

Aphid model, which was the best model, in most

FIG. 8. Linear regression model results and partial residual plots. Panels (A–C) show the adjusted r2 of regression models foreach predator-days at different threshold distances with 5% dispersal probability cutoff. Different shades of symbols indicate thesignificance levels of coefficients of Fluxad or Conduct in models (black shows P , 0.05; gray shows P , 0.10; white shows P �0.10). Abbreviations are: Aphid, soybean aphid (Aphis glycines Matsumura); Anth, Anthocoridae-days; Ecocc, exoticCoccinelldiae-days; and Ncocc, native Coccinellidae-days. Panels (D–K) show the relationship between predator-days and AphidþFluxad (or AphidþConduct) at the threshold distance showing the highest adjusted r2. All variable were ln (xþ 1)-transformed,except for Anthocoridae-days and native Coccinellidae-days, which were square-root(x)-transformed. Centered values areindicated. The pair of letters in parenthesis in panels (A–C) with arrows indicate the points of the highest adjusted r2 of regressionmodels.


threshold distances and the coefficient of Conduct and

Dist did not show any significance (Fig. 8A, Table 1).

The exotic Coccinellidae-days were, interestingly,

negatively correlated with flux variables. The highest

r2 value appeared at the 2.3-km threshold distance (Fig.

8B), but the coefficient of Fluxad in the model was not

significant (Fig. 8G, Table 1). Similar to Anthocoridae-

days, the simpler Aphid model was the best model for

exotic Coccinellidae-days. However, the AphidþFluxad(or Fluxa) model was also strongly supported by data

(DAIC , 2), although the flux variables did not show

any significance. Similar to Anthocoridae-days, Fluxadincreased the model fit slightly compared to Fluxa(Table 1). Conduct and Dist variables did not show any

significance in the Aphid þ Conduct (or Dist) models,

which were not considerably supported by data (DAIC

. 2).

Native Coccinellidae-days were significantly positively

influenced by the flux and conductance (Fig. 8C). The

coefficients of Fluxad in the FluxadþAphid model were

significant at all threshold distances. Relatively high

peaks of adjusted r2 values of the FluxadþAphid model

appeared at the three different threshold distances of

0.9–1.3 km, 2.8–2.9 km, and 4.5–4.6 km. The highest r2

value appeared at the 1.1-km threshold distance (Fig.

8C). Interestingly, native Coccinellidae-days was nega-

tively correlated to Aphid (Fig. 8H, Table 2). The Aphid

þFluxad model was selected as the best model, although

the Aphid þ Ecocc þ Aphid 3 Ecocc model showed a

higher r2 value. In this interaction model, native

Coccinellidae-days was not significantly correlated with

Aphid and Ecocc, but was considerably negatively

correlated with their interaction (Table 2). Similar to

the other two predator groups, Fluxad increased the

model fit slightly in predicting native Coccinellidae-days.

The coefficient of Conduct in the Aphid þ Conduct

model was significant at a range of threshold distances

beyond 4.5 km (Fig. 8C). The highest r2 appeared at the

5.2-km threshold distance. At this threshold distance,

the Aphid þ Conduct model showed the lowest AICc,

which was selected as a better model than the interaction

model. The Conduct variable in Aphid (or Ecocc) þConduct models showed better model fit than the Dist

variable in the Aphid (or Ecocc) þ Dist models. The

Aphid (or Ecocc) þ Conduct models were considerably

supported by data (DAICc , 2) more than the model

with Dist (DAICc . 2; Table 2).

The model fit for all predator groups based on a 5%

dispersal probability cutoff were similar to the results

from the application of different dispersal probability

TABLE 1. Summary of the model selection statistics for Anthocoridea-days (Anth) and exoticCoccinellidae-days (Ecocc).

Response and model DAICc wi Adjusted r2 Partial correlation

Anth

Fluxad vs. FluxaAphid* 0.00 0.62 0.31Aphid* þ Fluxad2.3km 2.95 0.14 0.30 Aphid ¼ 0.55*, Fluxad ¼ 0.24Aphid* þ Fluxa2.3km 3.06 0.13 0.29 Aphid ¼ 0.56*, Fluxa ¼ 0.22Intercept 3.58 0.10 0.00

Conduct vs. Dist

Aphid* 0.00 0.65 0.31Aphid* þ (Conduct0.5km) 3.02 0.14 0.30 Aphid ¼ 0.62**, Conduct ¼ �0.23Intercept 3.58 0.11 0.00Aphid* þ Dist 3.72 0.10 0.26 Aphid ¼ 0.58*, Dist ¼ 0.08

Ecocc

Fluxad vs. FluxaAphid* 0.00 0.43 0.34Aphid** þ (Fluxad2.3km) 0.95 0.27 0.41 Aphid ¼ 0.70***, Fluxad ¼ �0.42Aphid** þ (Fluxa2.3km) 1.25 0.23 0.40 Aphid ¼ 0.69***, Fluxa ¼ �0.40Aphid* þ (Ncocc) 3.36 0.08 0.31 Aphid ¼ 0.59*, Ncocc ¼ �0.17

Conduct vs. Dist

Aphid* 0.00 0.64 0.34Aphid* þ (Dist) 3.20 0.13 0.32 Aphid ¼ 0.54*, Dist ¼ �0.20Aphid* þ (Ncocc) 3.36 0.12 0.31 Aphid ¼ 0.59*, Ncocc ¼ �0.17Aphid* þ Conduct0.5km 3.46 0.11 0.31 Aphid ¼ 0.62**, Conduct ¼ 0.15

Notes: Variables compared: incoming area- and distance-weighted flux (Fluxad) vs. incomingarea-weighted flux (Fluxa); effective conductance (Conduct) vs. Euclidian distance from prairiecomplex (Dist). The first model listed at each predator is the minimum AICc model, and boldfacetype indicates models with DAICc , 2. The intercept-only model in the regression models isindicated as Intercept. Negative relationships between variables and predator-days are indicated inparentheses. The selected best threshold distances of Flux and Conduct are indicated as subscripts.Aphid-days (Aphid) and native Coccinellidae-days (Ncocc) were centered when the interactionterm was included in the model. All variables were ln(x þ 1)-transformed except for Anth andNcocc, which were square root(x)-transformed. Aphid and Ncocc were centered when theinteraction term was included in the model.

* P , 0.05; ** P , 0.01; *** P , 0.001.


cutoffs because this had less influence than the threshold

distance (Appendix D). For Anthocoridae-days and

exotic Coccinellidae-days, the r2 values appeared to

continue increasing beyond the boundaries of the ranges

tested, although these further values are not considered

biologically realistic. For native Coccinellidae-days, the

highest r2 values of the Aphid þ Fluxad (or Conduct)

occurred with a 1-km threshold with 30% dispersal

probability cutoff, and at 4.5 km with a 15% dispersal

probability cutoff (Fig. 9). However, the overall trends

of the model fits were very similar to the threshold

distances with a 5% dispersal probability cutoff and

changed little as the values moved away from this,

compared to altering the threshold distance (Fig. 9).

We did not find collinearity among variables and

between the centered variables and their interactions in

multiple linear regression models (all jrj , 0.7). We also

did not find significant spatial autocorrelation in the best

regression models for any predator group (all jMoran’s

I j , 0.75, P . 0.19; 95% point-wise bootstrap

confidence intervals of spline correlograms included 0

at all scales). There is the possibility that this is the result

of a Type II error in our test, but as we sampled all of

the CP33s next to soybean in the entire county (and a

large proportion of the CP21s next to soybean), our

small sample size was unavoidable.

DISCUSSION

The graph- and circuit-connectivity models success-

fully tested our two hypotheses regarding the effects of

landscape connectivity and the prairie complex as a

source for the flow of natural enemies. Graph- and

circuit-connectivity predicted native natural enemy

pressures within a certain range of thresholds in edge

distance. The similarity of the threshold distances for

Anthocoridae and exotic Coccinellidae (2.3 km and 2.9

km) suggests that this may partially be an artifact of the

specific region of the study or of the parameters

considered.

Limitations of graph- and circuit-connectivity models

The graph- and circuit-connectivity models did not

incorporate information on long-distance dispersal

TABLE 2. Summary of model selection statistics for native Coccinellidae-days.

Model DAICc wi Adjusted r2 Partial correlation

Fluxad vs. Fluxa(Aphid)� þ Fluxad1.1km* 0.00 0.15 0.33 Aphid ¼ �0.51*, Fluxad ¼ 0.61**(Aphid)� þ Fluxa1.1km* 0.34 0.13 0.31 Aphid ¼ �0.50*, Fluxa ¼ 0.60**Fluxad 1.1km� 0.77 0.10 0.16Aphid þ (Ecocc) þ (Aphid 3 Ecocc)** 0.79 0.10 0.44 Aphid ¼ 0.26, Ecocc ¼ �0.26, Aphid 3 Ecocc ¼

�0.71***Fluxa 1.1km� 0.95 0.10 0.15(Aphid) þ (Ecocc) þ (Aphid 3 Ecocc)* þ

Fluxad1.1km�0.98 0.09 0.57 Aphid ¼ 0.00, Ecocc ¼ �0.20, Aphid 3 Ecocc ¼

�0.68**, Fluxad ¼ 0.56*Intercept 1.33 0.08 0.00Aphid þ (Ecocc) þ (Aphid 3 Ecocc)* þ

Fluxa1.1km�1.37 0.08 0.56 Aphid ¼ 0.01, Ecocc ¼ �0.21, Aphid 3 Ecocc ¼

�0.68**, Fluxa ¼ 0.55*(Ecocc) þ Fluxad1.1km� 2.15 0.05 0.23 Ecocc ¼ �0.38, Fluxad ¼ 0.52*(Ecocc) þ Fluxa1.1km� 2.33 0.05 0.22 Ecocc ¼ �0.39, Fluxad ¼ 0.51*(Ecocc) 2.98 0.03 0.03(Aphid) 3.17 0.03 0.01

Conduct vs. Dist

(Aphid)� þ Conduct5.2km* 0.00 0.16 0.30 Aphid ¼ �0.51*, Conduct ¼ 0.58*Aphid þ (Ecocc) þ (Aphid 3 Ecocc)** 0.03 0.16 0.44 Aphid ¼ 0.26, Ecocc ¼ �0.26, Aphid 3 Ecocc ¼

�0.71***Intercept 0.57 0.12 0.00Conduct5.2km 0.69 0.12 0.12(Ecocc) þ Conduct5.2km� 1.37 0.08 0.23 Ecocc ¼ �0.43�, Conduct ¼ 0.52*(Ecocc)� þ (Dist)� 2.09 0.06 0.19 Ecocc ¼ �0.49*, Dist ¼ �0.48�(Ecocc) 2.22 0.05 0.03(Aphid)� þ (Dist)� 2.22 0.05 0.18 Aphid ¼ �0.49�, Dist ¼ �0.49�(Aphid) 2.41 0.05 0.01(Dist) 2.47 0.05 0.01Aphid þ (Ecocc) þ (Aphid 3 Ecocc)* þ

Condcut5.2km

2.49 0.05 0.50 Aphid ¼ 0.04, Ecocc ¼ �0.27, Aphid 3 Ecocc¼ �0.63*, Conduct ¼ 0.45

Aphid þ (Ecocc) þ (Aphid 3 Ecocc)* þ(Dist)

2.66 0.04 0.50 Aphid ¼ 0.08, Ecocc ¼ �0.37, Aphid 3 Ecocc¼ �0.66**, Dist ¼ �0.44

Notes: Variables compared: incoming area- and distance-weighted flux (Fluxad) vs. incoming area-weighted flux (Fluxa); effectiveconductance (Conduct) vs. Euclidian distance from prairie complex (Dist). The first model listed is the minimum AICc model, andboldface type indicates the models with DAICc , 2. The intercept-only model in the regression models is indicated as Intercept.Negative relationships between variables and predator-days are indicated in parentheses. Native Coccinellidae-days (Ncocc) wassquare-root(x)-transformed, and other variables were ln(x þ 1)-transformed. Aphid-days (Aphid) and exotic Coccinellidae-days(Ecocc) were centered when the interaction term was included in the model. The selected best threshold distances of Flux andConduct are indicated as subscripts.

* P , 0.05; ** P , 0.01; *** P , 0.001; � P , 0.1.


beyond a threshold distance, which was applied to

identify graph edges, allowing for an efficient calculation

of flux and conductance. This threshold partially

determined graph connectedness and the shape of the

dispersal curves (dispersal kernel). However, this was a

limitation because it assumes that there is no dispersal

leading to successful colonization beyond the threshold

distance with the 5% dispersal probability cutoff. This

assumption ignores less common long-distance dispersal

beyond the threshold distance, which does not ideally

model the behavior of dispersing individuals (Moilanen

2011). This loss of long-distance dispersal information

was evident in the rapid increase of the incoming flux

and effective conductance values with increasing thresh-

old distance (Fig. 6A, B). This pattern of rapid increase

within a short range of threshold distances indicates that

certain important habitats with a high potential to

contribute dispersers were not considered to contribute

to the dispersal of natural enemies until these habitats

were connected at a threshold distance. The rate of

increase in flux and effective conductance was reduced

as habitats were connected by edges, around the 1.5-km

threshold distance for incoming flux and 2.0 km for

effective conductance. While an ideal model may use a

very large threshold (i.e., beyond the 7 km that we

focused on in this study), such as the predicted distance

for 0.001% of dispersers for successful colonization, this

would lead to a very large number of connected nodes

(i.e., edges) and become much more computationally

intensive. Because the 5% dispersal probability cutoff at

each threshold distance can represent the trend of the

lower dispersal probability and large threshold distance,

intensive computation seems to be not efficient (Fig. 9).

Additionally, such a large graph network may also be

unrealistic for some species as it would imply that

dispersers pass by many habitats to colonize a distant

patch. Another solution may be to develop area-

weighted connectedness thresholds.

Because the circuit-connectivity model built upon the

graph-connectivity measure, the two were quite corre-

lated (Fig. 6C). The sum of conductances at the

electrical ground node in a parallel connection is same

as the incoming flux (Ge ¼ G1þG2). Therefore, the

correlation of these two measures increased as the

threshold distance increased and the network became

more connected. The rapid increase in this correlation

with threshold distances greater than 2 km seems to have

been caused by large patches joining the network and

FIG. 9. Linear regression model results of native Coccinellidae-days at different threshold distances with different dispersalprobability cutoffs. The boxes outlined in black indicate the highest adjusted r2 within the two dimensions of threshold distancesand dispersal probability cutoffs. Asterisks indicate that the coefficients of the relationship between threshold distance and Fluxador conductance in the model are significant at P , 0.05.


greatly increasing both measures and by the ‘‘short-

circuiting’’ network across the gap in the southwestern

area (Fig. 6D).

Natural enemy populations

As in previous work (e.g., Rutledge et al. 2004), the

field surveys of natural enemies and aphid populations

showed that Anthocoridae was the most abundant

natural enemy in Indiana soybean fields, followed by

Coccinellidae (Fig. 7). In most of the study sites

Anthocoridae were present before aphids were detected

(Fig. 7). Orius insidious (Anthocoridae) can survive in

soybean crops before aphid arrival by feeding upon

soybean plants and soybean thrips (Isenhour and

Marston 1981, Yoo and O’Neil 2009).

Predator populations were largely driven by aphid

populations (Fig. 8D, F, Table 1), but native coccinellids

were also considerably influenced by the interaction

between aphids and exotic Coccinellidae (Table 2).The

peak arrival of H. axyridus (Ecocc) in fields occurs

around of the time of peak aphid population because

adult females are able to search for the best field to

maximize their offspring’s fitness (Koch 2003). This can

result in aggregation of exotic coccinellids in fields with

high numbers of aphids. Another reason for the

aggregation may be the trapping effect. The trapping

effect occurs when these exotic coccinellids change their

search mode from long-range movement to within

habitat foraging (Kawai 1976, Koch 2003). As a result,

they may show a strong ability to follow aphid

populations as indicated in Osawa (2000) and With et

al. (2002). These behaviors of H. axyridis might exclude

native Coccinellidae from these fields. In our study

native Coccinellidae were negatively influenced by the

interaction term between aphids and exotic Coccinelli-

dae (Table 2). This suggests that as exotic species

increase in response to aphid populations the native

species suffer. This could be due to direct predation

(Evans 2004, Yasuda et al. 2004) or competitive

exclusion (Michaud 2002). Therefore, the native species

were correlated with aphid populations in the regression

model with aphids and flux (or conductance; Fig. 8H, J,

Table 2). However, we did not explicitly test the

biological interactions of these two groups. The

ecological consequences of these interactions on native

species populations have not been clearly revealed

(Harmon et al. 2007).

Effects of landscape connectivity and prairie on natural

enemies’ dispersal

The graph- and circuit-connectivity models success-

fully examined the different responses of three natural

enemy groups to landscape connectivity and the prairie

complex. For Anthocoridae, the results indicated that

landscape connectivity may enhance the flow of this

natural enemy, but that the prairies do not act as a

source for them (Fig. 8E, Table 1). From the best

threshold distance shown in the graph-connectivity

model (2.3 km), we obtained the distance–decay

parameter determining the shape of dispersal curves, k

¼ 0.0013. The adults of O. insidious, the most dominant

species of Anthocoridae in this study, are known to

disperse in order to forage. In early spring, they forage

on flowering herbaceous plants, and in summer many

may move onto crop plants and come back to the

perennial forbs for overwintering (Saulich and Musolin

2009). In our study area, conservation plantings may

have provided overwintering habitat for them.

We failed to reject the null hypothesis that the

abundance of exotic Coccinellidae, mostly H. axyridis

in this study, is not related to the connectivity of

seminatural areas (Fig. 8G, Table 1). This lack of a

relationship may suggest that H. axyridis are not

sensitive to landscape fragmentation at large spatial

scales because of their high dispersal ability. They are

known to not be affected by fragmentation at small

spatial scales (With et al. 2002). Exotic Coccinellidae did

not show a response to circuit connectivity (Table 2).

This may mean that the prairie complex was not a

source for them or they are less dependent on the prairie,

as indicated by Gardiner et al. (2009b). It is also possible

that populations of exotic coccinellids are bolstered by

the prairie complex, but they move across the landscape

using habitats in a different way than we have modeled

to construct our network. However, this would not

entirely explain the negative relationship between exotic

coccinellids and graph connectivity (Fig. 8G, Table 1).

Native Coccinellidae were positively influenced by

seminatural areas and connectivity to the prairie

complex (Fig. 8C, Table 2). This result highlights that

the movement of native Coccinellidae depended on the

configuration of seminatural habitats and the role of the

prairie complex as source habitat. Well-connected

seminatural habitats enhanced the flow of these natural

enemies. This result is supported by other studies, which

have showed that native Coccinellidae are more sensitive

to habitat fragmentation than exotic Coccinellidae

(With et al. 2002) and that grasslands enhance their

abundance (Gardiner et al. 2009b). The best threshold

distances for flux (1.1 km) and conductance (5.2 km)

were different. However, this large threshold distance

for conductance was similar to the threshold distances

(4.5–4.6 km) showing one of peaks of flux. The small-

scale and large-scale ranges of good model fit for flux

may suggest that habitat fragmentation is important to

these predators at multiple spatial scales. Alternatively,

it could be indicating the result of different ecological

processes such as long-range dispersal and small-scale

foraging movements, or within-generation dispersal and

longer term patterns of movement over many genera-

tions. The second hypothesis was supported by the

insect sampling data from the prairie complex. The

sampling data showed two more native Coccinellidae

species, Hippodomia convergens and Hippodomia paren-

thesis, in the prairie than in the selected soybean field

and CP sites. The data also showed that native


Coccinellidae was dominant in this habitat compared to

exotic Coccinellidae (Appendix C).

The numbers of Coccinellidae were low. About half of

the zero values occurred before soybean aphids arrived.

During this period, soybean fields are almost devoid ofinsects. We have confidence that our data did capture

real trends in abundance. The abundance of these

predators followed that of the prey aphids as one would

expect. These may actually be quite realistic numbers ofCoccinellidae predators. In a recent study, Costamagna

et al. (2007) found aphid abundances per plant similar to

ours, and a maximum average of about nine Coccinelli-

dae (all species combined) per 1 m2 detected with anexhaustive search with caged plants. We swept a much

larger area, but only sampled the tops of plants (the

accepted method). Adult Harmonia can eat 90–270

aphids per day, and larvae (not included in our analysis)

can eat 600–1200 aphids every day (Knodel andHoebeke 1996). They will therefore, be at much lower

densities than the aphids. For these reasons, we believe

that our abundance data are reflective of the true

abundances within the fields.

The developed flux measure, area- and distance-weighted flux, showed slightly better prediction accuracy

for all the selected three predator groups than the model

using a flux without distance weighting (Tables 1 and 2).

Weighting distance using the adaption of CRW simu-

lation considered a potential region of insect’s move-ment while traveling between a pair of seminatural

habitats (Figs. 2 and 3). However, because the study

region is highly dominated by agriculture, its weighting

effect on calculating flux was limited. This could limitthe potential improvement in model fit and explain the

only slight improvement in the prediction that we

observed. The circuit-connectivity model explained the

relationship between source and sink, i.e., prairie

complex and CP in this study, better than Euclideandistance. Compared to the Euclidean distances between

source and sink, using circuit theory certainly resulted in

better predictions (Tables 1 and 2). Although aphid

pressure was the factor that most influenced thepressures of natural enemies, incoming flux of the

graph-connectivity model and effective conductance of

the circuit-connectivity model were also selected as

important factors for predicting the pressures of natural

enemies, especially for native species.

Implications for conservation biocontrol

Our study found that well-connected habitat networksin landscapes enhance the flow of native natural enemies

such as Anthocoridae and native Coccinellidae, and that

prairies act as a source for native Coccinellidae. Exotic

Coccinellidae were not positively related to the large-scale connectivity of seminatural habitats. Therefore, if

landscape fragmentation of seminatural habitat occurs

heavily on agricultural landscape, the control of soybean

aphids will depend more on exotic natural enemies,

especially H. axyridis, than on native species. Relying on

one dominant species for an ecosystem service rather

having redundancy including multiple native species

carries a risk. If H. axyridis ever fell victim to

unexpected disease, predator, or parasitoid, we may

need to look to our native species for control of pests

such as A. glycines (Koch 2003). Diversity is insurance

against future changes in ecosystem services (Kremen et

al. 2002). From this perspective, how to arrange habitat

networks to support native predator species becomes

important. Further study should focus on how to

optimize landscape connectivity to maximize biocontrol

service. In this optimization, the estimated individual

natural enemy’s dispersal parameter will be useful.

Although Anthocoridae is the most abundant pred-

ator, they are individually less efficient in aphid control

than many other predators, and they often leave

soybean fields early. However, we did find that they

were present at the crucial period of colonization by A.

glycines (Yoo and O’Neil 2009). As suggested by Yoo

and O’Neil, it is possible that having Anthocoridae as

part of the predator community in soybean fields is

important because their presence at the time of soybean

aphid arrival may help control populations before they

grow rapidly. Even a slight delay in the approach to the

economic threshold of pest population (250 aphids/

plant) can be of great benefit, especially if this occurs

after the soybeans have reached the R6 growth stage

because yield is then not negatively affected and

pesticide application is no longer necessary (Krupke et

al. 2013).

ACKNOWLEDGMENTS

This research was supported by a USDA-NIFA EcosystemServices Grant. The authors thank Derek Calhoun, MonicaMain, Stephanie Hathaway, Sage McCafferty, Tommy Mager,John Shukle, and Caoilin Hoctor for field work that formed thebasis of this study. Carol Ritchie at the Newton County IndianaFarm Service Agency office was a great help with locatingfarmer cooperators and with spatial data for the study sites.Stephanie Frischie was a great help with fieldwork logistics.Many farmers graciously allowed us access to their fields. TheNature Conservancy allowed us to sample at their prairie andrestoration sites. Two reviewers provided suggestions thatgreatly improved the analysis and text. Carol Sung, JohnMichael, and Brian Raub of the Purdue SupercomputingCenter were instrumental in running parameter sweeps.Christian Krupke shared his knowledge of soybean agriculture.The authors thank Andrew Thomas for his technical help withthe ElectroGraph package.

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SUPPLEMENTAL MATERIAL

Appendix A

Two parameters for correlated random walk simulation: reported data and distributions of step length and turning angles(Ecological Archives A023-081-A1).

Appendix B

Dispersal kernels used for the parameter sweep (Ecological Archives A023-081-A2).

Appendix C

Insect sampling count data in 15 CP and prairies (Ecological Archives A023-081-A3).

Appendix D

Linear regression model results of Anthocoridae-days (Anth) and exotic Coccinellidae-days (Ecocc) with area- and distance-weighted flux (Fluxad) and effective conductance (Conduct) at different threshold distances with different dispersal probabilitycutoffs (Ecological Archives A023-081-A4).

Supplement

Detailed description of correlated random walk simulation and how to obtain an ellipse-shaped region covering successfulpathway of a random walker, including R code (Ecological Archives A023-081-S1).


http://www.esapubs.org/archive/appl/A023/081/





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Graph and circuit theory connectivity models of conservation