A comparison of network, neighborhood, and node levels of analyses in two models of nitrogen cycling in the Cape Fear River Estuary

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COMOD-7067; No. of Pages 11

Ecological Modelling xxx (2013) xxx– xxx

Contents lists available at ScienceDirect

Ecological Modelling

jo ur nal ho me page: www.elsev ier .com/ locate /eco lmodel

comparison of network, neighborhood, and node levels of analysesn two models of nitrogen cycling in the Cape Fear River Estuary

avid E. Hinesa,b,∗, Stuart R. Borretta,b

Department of Biology & Marine Biology, University of North Carolina Wilmington, 601 South College Road, Wilmington, NC 28403, USACenter for Marine Science, University of North Carolina Wilmington, USA

r t i c l e i n f o

rticle history:vailable online xxx

eywords:cological network analysisetwork environ analysisscendencyierarchyentralitycological buffer capacity

a b s t r a c t

Ecological network analysis is a set of algorithms that provide a holistic approach to the study of ecosys-tems. These analyses operate on at least three different hierarchical levels: network, neighborhood, andnode. Network level analyses capture whole-system interactions and provide a broad view of the sys-tem; neighborhood level analyses provide relational information for specific parts or sub-networks; nodelevel analyses offer descriptive characteristics of individual nodes. This work investigated the insightsgained from each of these levels of analysis in an ecological network analysis case study. We comparedtwo nitrogen cycling network models constructed at sites with different salinities, one oligohaline andone polyhaline, in the Cape Fear River Estuary, NC, USA as a case study to demonstrate the differencesbetween levels of analysis. We evaluated the nitrogen cycling models at both the network and node lev-els, and compared these results to existing results of a neighborhood level analysis. We further comparedthe ecological implications of the nitrogen network comparison produced by each hierarchical level totest the null hypotheses that there would be no difference between the conclusions resulting from theselevels of analysis. We found that while network level analyses showed little difference between thetwo nitrogen models, differences with potential ecological importance for the availability of nutrients to
phytoplankton could be seen using node level analyses. The results of the existing neighborhood levelanalyses exhibited characteristics with similarities to the results of both the network and node level anal-yses. We show that higher hierarchical levels, which integrate the information contained at the lowerlevels, can mask potentially important signals when describing network attributes. Therefore, we con-clude that ecosystem networks should be analyzed at multiple hierarchical levels to provide a completedescription of system function.
. Introduction

Network scientists use ecological network analysis (ENA) for aariety of purposes such as the description of the movement ofnergy and material in ecosystems (Baird and Ulanowicz, 1989;ulff and Ulanowicz, 1989; Scharler and Baird, 2005; Gattie et al.,

006b), the identification of system interactions that are diffi-ult to observe without a holistic perspective (Patten, 1978, 1983;lanowicz and Puccia, 1990; Salas and Borrett, 2011; Li et al., 2012),

Please cite this article in press as: Hines, D.E., Borrett, S.R., A comparison oof nitrogen cycling in the Cape Fear River Estuary. Ecol. Model. (2013), http

nd the identification of key ecosystem components (Christian andhomas, 2003; Whipple et al., 2007; Borrett, 2013). ENA includesnalyses that span multiple vertically differentiated hierarchical

∗ Corresponding author at: Department of Biology & Marine Biology, Universityf North Carolina Wilmington, 601 South College Road, Wilmington, NC 28403, USA.el.: +1 910 962 3000; fax: +1 910 962 4066.

E-mail addresses: [email protected] (D.E. Hines), [email protected]. Borrett).

304-3800/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.ecolmodel.2013.11.013

© 2013 Elsevier B.V. All rights reserved.

levels (Ahl and Allen, 1996; Allen et al., 2001; Wu and David, 2002),and thus can provide information about the study system at differ-ent levels (Bosserman and Harary, 1981; Whittaker et al., 2001;Wu and David, 2002). In this work, we construct a conceptualframework to organize the different hierarchical levels of analysisinvolved in ENA. We then apply this framework to compare ENAresults at three levels of analysis in models of nitrogen cycling inthe Cape Fear River Estuary (CFRE), NC, USA. We use the compar-ison results to highlight the differences between the informationobtained at each analysis level and emphasize the importance of amultiple-level approach.

There appear to be at least three levels of analysis in ENA: net-work, neighborhood, and node (Fig. 1). The highest level of analysis,network level, refers to analyses that integrate all components ofa network to produce indicators of the overall organization of a

f network, neighborhood, and node levels of analyses in two models://dx.doi.org/10.1016/j.ecolmodel.2013.11.013

system (Margalef, 1968; Dame and Patten, 1981; Ulanowicz, 1996;Fath et al., 2007). These indicators provide single value representa-tions of properties for each network. Below network level analysesare neighborhood level analyses that integrate interactions among

dx.doi.org/10.1016/j.ecolmodel.2013.11.013


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ECOMOD-7067; No. of Pages 11

2 D.E. Hines, S.R. Borrett / Ecological M

A

B C D

E

Network

Neighborhood

Node

Fig. 1. Diagram of hierarchical levels of analysis using a five node hypothetical net-work model. Dotted shapes highlight levels of analysis; green square encompassesnetwork level, blue curved triangle surrounds neighborhood level, and red circlest

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of each network formed a single strongly connected component

hows node level. (For interpretation of the references to color in this figure legend,he reader is referred to the web version of the article.)

odes to produce relational indicators of node interactions. Heree use the neighborhood concept in a broader context than someetwork science definitions, which refer to the neighborhood of

node as the set of nodes within a given geodesic distance ofhat node (Brandes and Erlebach, 2005). However, the neighbor-ood level analysis concept is consistent with the network scienceefinitions in that both consider the relationships among networkomponents. The lowest level of analysis in ENA, node level anal-ses, tends to capture properties of the individual node entities.or example, network centrality measures such as degree, eigen-ector, throughflow, and betweenness centralities, are node levelndicators of the relative position or importance of a node in theetwork (Bonacich, 1987; Borgatti and Everett, 2006; Jordán et al.,006; Estrada and Bodin, 2008; Pocock et al., 2011; Borrett, 2013).

Network level analyses are quantified by statistics that repre-ent a single value description of the structure and function forhe whole system (Fath et al., 2001; Ulanowicz, 2004; Ulanowiczt al., 2006; Lau et al., 2013). Several of the properties describedy network level indicators, such as network aggradation, net-ork non-locality, network homogenization, network cycling, and

elative ascendency, are hypothesized to be general among ecosys-em networks (Patten, 1991; Ulanowicz et al., 2006; Jørgensent al., 2011). Each of these statistics and properties provide alobal perspective by incorporating both direct and indirect net-ork interactions, and therefore provide a holistic measure ofetwork properties. Increases in some of these indicators associ-ted with these analyses can be interpreted as a form of networkevelopment (Ulanowicz, 1980, 2000; Jørgensen et al., 2000; Scotti,008).

In contrast to these whole network indicators, analyses athe neighborhood level provide results that show the relation-hips among two or more nodes. These interactions can rangen scale from dyadic relationships between two nodes to inter-ctions within sub-networks of different sizes. There are severalorms of neighborhood level analyses that span both local andlobal perspectives such as the direct (local) and integral (global)


ow intensity matrices of ENA (Fath and Patten, 1999b; Ulanowicz,004). Local neighborhood level analyses consider only the directly

nteractions among nodes, while global analyses take into account

PRESSodelling xxx (2013) xxx– xxx

all interactions within a network. A variety of neighborhood levelanalyses exist including flow environ analysis (Patten, 1978, 1981,1982), storage environ analysis (Small et al., in this issue; Whippleet al., in this issue), cycle analysis (Ulanowicz, 1983), compartmentanalysis (Krause et al., 2003), and analysis of strongly connectedcomponents (Allesina et al., 2005; Borrett et al., 2007).

Node level analyses produce one value for each node in thenetwork, providing information on the properties of each node,and are often used to identify the key components of ecosystems.Node level properties can also range from local, considering onlydirectly adjacent node connections, to global, considering wholenetwork interactions, in nature (Estrada, 2007). Further, Estrada(2010) showed that some of these properties can be tuned betweenthese two extremes. The ability of some node level analyses to cap-ture global system information and summarize it at resolution ofindividual nodes is particularly useful when assessing the roles ofcomponents in ecosystems, which are often related through indi-rect interactions (Wootton, 1994).

In this study, we used two nitrogen cycling networks con-structed at freshwater (oligohaline) and a saltwater (polyhaline)sites, respectively, in the Cape Fear River Estuary (CFRE), NC,as a case study to highlight the different information providedby network, neighborhood, and node level analyses. These nitro-gen cycling models were originally constructed to investigate thepotential impacts of seawater intrusion on the estuarine nitro-gen cycle (Hines et al., submitted for publication) because severalmicrobial nitrogen cycling processes are hindered by higher salini-ties (Rysgaard et al., 1999; Dong et al., 2000). Specifically, Hines et al.(submitted for publication) used these models to show that seawa-ter intrusion may decouple nitrogen cycling processes in estuaries,while the nitrogen removal capacity of these ecosystems may notbe altered. These models are ideal case study subjects for com-parison between levels of analysis because ecologically importantdifferences have been identified between them at the neighbor-hood scale and both models have identical topologies, facilitatingtheir comparison (Baird et al., 1991). We applied network level andnode level analyses to the CFRE nitrogen networks, and used exist-ing results for neighborhood level analysis (Hines et al., submittedfor publication) to examine the differences between the levels ofanalysis. We then tested the null hypothesis that the indicatorsof all three hierarchical levels of analysis would lead to the sameconclusions.

2. Materials and methods

2.1. Models

We compared the CFRE nitrogen cycling networks presented inHines et al. (2012) and Hines et al. (submitted for publication) as acase study to evaluate the network, neighborhood, and node levelsof analysis. Each of the CFRE networks was composed of nodes rep-resenting standing-stock pools of nitrogen and edges representingtransformations between the pools in both the water column andthe sediment. The nitrogen pools were ammonium (NH4), nitrateand nitrite (NOx), the nitrogen stored in microbial biomass (M),and organic nitrogen (ON), which included both dissolved and par-ticulate material. These four nitrogen pools were duplicated inwater column and sediment (W- and S-, respectively) for a totalof eight nodes in each model (Fig. 2). The 23 internal edges and19 boundary fluxes of each network represented specific nitro-gen transformation and transport processes. The nodes and edges


(Skiena, 1990; Allesina et al., 2005; Borrett et al., 2007), and a com-plete justification and description of the model design can be foundin Hines et al. (2012).


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y6(c)

y7(d)

y8(e)

y5(a) +y6(a)

Fig. 2. Generic ecological network for the CFRE nitrogen cycling models used in this case study. Internal fluxes (fij), boundary inputs (zi), and boundary losses (yj) are orientedfrom node j to node i. Boundary losses (a)–(e) were kept separate from other boundary losses to maintain resolution of specific nitrogen cycling processes. These boundaryfluxes represent the processes of anaerobic ammonium oxidation, denitrification, nitrate/nitrite burial, microbial biomass burial, and organic nitrogen burial, respectively.The model nodes were (1) water column ammonium (W-NH4), (2) water column nitrate/nitrite (W-NOx), (3) water column microbial biomass (W-M), (4) combined watercolumn dissolved and particulate organic nitrogen (W-ON), (5) sediment ammonium (S-NH4), (6) sediment nitrate/nitrite (S-NOx), (7) sediment microbial biomass (S-M),a netwow ne site

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flow intensity from one node to another over a path length of one.Raising the G′ matrix to a power of m produces the flow intensityfrom one node to another over a path length of m. The integral flowintensity matrix N′ = [n′

ij] is then calculated as a sum of the infinite

Table 1List of the network properties examined in this work, along with the network levelindicator for each property and its formulation.

Property Network statistic Formulation

Network aggradation APL TST∑n

i=1zi

Network non-locality I/D

∑(N−I−G)�z∑

G�z

Network homogenization HMG CV(N)CV(G)

nd (8) combined sediment dissolved and particulate organic nitrogen (S-ON). This

ere altered in each model to reflect the conditions at the oligohaline and polyhali

We calculated five network level indicators and three node levelndicators in each of the CFRE models. We compared these analyti-al results between the two models to draw conclusions about theffects of seawater intrusion on the nitrogen cycle in the CFRE. Weurther compared the results across the network, neighborhood,nd node levels by examining the conclusions produced by theetwork and node level analyses conducted in this paper and neigh-orhood level analysis first presented in Hines et al. (submitted forublication).

.2. Network level analyses

The five network level indicators used in this study spanned twoelated but distinct analyses in network ecology: flow analysis andscendency analysis. The indicators for network aggradation, non-ocality, homogenization, and cycling stemmed from flow analysisFinn, 1980; Patten, 1983; Fath and Patten, 1999a), while the rel-tive ascendency indicator stemmed from ascendency analysisUlanowicz, 1997). A summary of the network level indicators usedn this study along with the formulation of each can be found inable 1.

.2.1. Network level analyses from flow analysisIn flow analysis, the fluxes of material moving through a net-

ork are isomorphically represented as a set of matrices andectors. Internal fluxes are represented by the matrix F = [fij], where


ij is the flow from node j to node i. The boundary fluxes to and fromhe network nodes are captured in the boundary vectors �z = [zi]nd �y = [yj], respectively (Fig. 2). The throughflow (T) for each net-ork compartment (n) is defined as the sum of either the material

rk topology was used for both of the CFRE models, however the values of each fluxs, respectively.

exiting a node �Toutj

=∑n

i=1fij + yj from the output direction or

entering a node �Tini

=∑nj=1fij + zi from the input direction. At

steady state, throughflow is identical from the output and inputdirections such that �Tout

j= �Tin

i. Total system throughflow (TST) is

the sum of all throughflows where TST =∑n

j=1Toutj

=∑n

i=1Tini

, andprovides a single measure of whole-system activity. The analysespresented in this work focused on the input orientation, which isdenoted by ′. The next step in flow analysis after calculating nodethroughflows is to divide the network flows fij by Ti to obtain adirect flow intensity matrix G′ = [g′

ij] = f ij/Ti, which represents the


Cycling FCI

∑n

i=1((n′

ii−1)/(n′

ii)×Ti )∑n

i=1Ti

Relative ascendency A/C AMI×TSTpC


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ARTICLECOMOD-7067; No. of Pages 11

D.E. Hines, S.R. Borrett / Ecolo

ower series shown in Eq. (1), and provides the flow from one net-ork node to another over all path lengths as m approaches infinity.

′ =∞∑

m=0

G′m = G′0︸︷︷︸Boundary

+ G′1︸︷︷︸Direct

+ G′2 + · · · + G′m + · · ·︸︷︷︸Indirect

(1)

he N′ matrix maps the network outputs into throughflow so that� = �yN′. A more complete description of the calculations involvedn flow analysis can be found in Finn (1976), Fath and Borrett (2006),nd Schramski et al. (2010). We used the elements of flow analysiso conduct four network level analyses.

Network aggradation is a form of network growth that isescribed by the average number of nodes material travels acrosss it passes through the system (Jørgensen, 2012). As ecosystemsature, the number of nodes encountered by material moving

hrough the system is hypothesized to increase (Jørgensen et al.,011), and is quantified by the average path length statistic (APL;inn, 1976). APL is a single statistic description of the aggrada-ion property, and was obtained by dividing TST by the sum of theoundary inputs (or outputs) as in Table 1. Interest in this type ofetwork indicator extends beyond network ecology to other formsf science as well. For example, economists refers to this propertys the multiplier effect (Samuelson, 1948).

Network non-locality is the tendency for indirect effects toxceed direct effects in ecosystems (Patten, 1983). Flows that occurver path lengths greater than one are considered to be indirectows, while flows that occur over paths of length one are consid-red to be direct flows. Indirect, direct, and boundary flows areontained in the N′ matrix as is shown in Eq. (1). The networkon-locality property is quantified by the ratio of indirect-to-directows (I/D; Table 1), and indirect flow is said to be dominant overirect flow if the I/D statistic is greater than one (Higashi and Patten,986, 1989; Borrett and Freeze, 2011). This property highlights the

mportance of network interactions. For example, analysis of a foodeb network for the Big Cypress National Preserve, FL revealed

hat the American alligator provides a net benefit to some of itsrey species by consuming other local predators (Bondavalli andlanowicz, 1999).

Network homogenization is the tendency for integral flow inten-ities (boundary +direct +indirect) to be more evenly distributedhan the direct flow intensities in ecosystem models (Fath andatten, 1999a). The homogenization statistic (HMG) quantifies theatio of the variation in these flow distributions and can be used tohow how network interactions distribute resources. For example,ath and Patten (1999a) show how indirect flows distribute net-ork flows more evenly than direct flows in both a hypothetical

cosystem and an oyster reef ecosystem. HMG was calculated ashe ratio of the coefficients of variation for the N′ and G′ matrices,s is shown in Table 1.

Network cycling is the passage of the same quanta of energy-atter more than once through a single network component before

he substrate exits the system boundary. Finn’s cycling index (FCI;inn, 1980) is commonly used to quantify cycling in ecosystemetworks by comparing the ratio of cycled total system through-ow (TSTc) to TST in a network, where TSTc is the ratio of the sumf the differences between the diagonal entries of the N′ matrix andne and the product of the diagonal entries of the N′ matrix and �TTable 1). This statistic can provide a measure of efficiency and hasmplications for the retention time of energy-matter in ecosystems.

ature ecosystems are often associated with high FCI statistics,


owever it has also been suggested that high levels of cycling maye an indication of ecosystem stress (Ulanowicz, 1984; Baird et al.,991), highlighting the importance of context-based interpretationor ENA results.


2.2.2. Network level analysis from ascendency analysisIn ascendency analysis, the components of networks are again

isomorphically represented as a set of matrices and vectors sim-ilar to those used in flow analysis; however, there are small butimportant differences. Like flow analysis, internal network flows inascendency analysis are represented in a matrix FT = [f T

ij]. Ascen-

dency analysis adopts a row to column orientation instead of thecolumn to row orientation used in flow analysis; therefore, thetransposed matrix FT = [f T

ij] represents the internal flow from node

i to node j. This row to column orientation is maintained in theboundary input and output vectors �zT = [zT

j] and �yT = [yT

i], respec-

tively.Ascendency analysis also uses a slightly different measure of

total system activity than flow analysis (Ulanowicz et al., 2006).While flow analysis uses total system throughflow (TST), ascen-dency analysis relies on total system throughput (TSTp; Fath et al.,2012). TSTp is defined as the sum of all internal and boundary flowssuch that TSTp =

∑ni=1

∑nj=1f T

ij+∑n

j=1zTj

+∑n

i=1yTi. Thus, relative

to TST, boundary fluxes are incorporated twice into TSTp. Whenboundary inputs and outputs are added to the flow matrix FT asrow n + 1 and column n + 2, respectively, the result is the extended

flow matrix FT = [f T

ij]. TSTp is the summation of F

Tand thus is a

measure of its size. A complete description of the extended flowmatrix can be found in Allesina and Bondavalli (2003).

Relative ascendency is a measure of the flow diversity of anecosystem network (Ulanowicz, 1980, 2000) that provides a viewof material fluxes in the context of the highest level of complexitypossible for the system of interest (Patrício et al., 2004). This prop-erty is quantified by the ascendency to capacity ratio (A/C), whichcompares the ascendency of a network to its maximum possiblevalue. The A/C statistic is often interpreted to be optimized whena system is fully mature (Ulanowicz, 1986; Mageau et al., 1998;Scotti, 2008). Ascendency (A) was calculated as the product of theaverage mutual information (AMI) in the system and TSTp as in Eq.(2)

A = AMI × TSTp, (2)

where AMI is defined as in Eq. (3).

AMI =n+2∑i=1

n+2∑j=1

f Tij

TSTp× log2

(f Tij

× TSTp∑nj=1 f T

ij×∑n

i=1 f Tij

)(3)

Capacity (C), as calculated in Eq. (4), is a measure of the com-plexity of an ecosystem (Patrício et al., 2004; Scotti, 2008), and isthe maximum limit of ascendency.

C =n+2∑i=1

n+2∑j=1

f Tij × log2

(f Tij

TSTp

)(4)

The ascendency to capacity ratio (A/C) was calculated to produce ameasure of the level of development within each network (Table 1).

2.3. Neighborhood level analyses

We compared the results of the network and node level analysesconducted in this work to the neighborhood level environ analysisconducted by Hines et al. (submitted for publication). Briefly, theinput environs used by Hines et al. (submitted for publication) area measure of the material entering a node from the input direction.Input environs are the network subgraph induced by extracting oneunit out of a given node (Patten, 1978, 1981, 1982). These neighbor-


hoods show the origin of material in the network with respect to aparticular node’s outputs. Researchers have applied environ analy-sis to examine the movement of material through a specific portionof an ecosystem or to examine the relationships between specific


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odes. For example, Schramski et al. (2006) use environ analysis toetermine the roles of different nitrogen pools in the nitrogen cyclef the Neuse River Estuary, NC.

Each node in a network has it’s own input environ. Unit inputnvirons e′

ijk, which have an output of one unit, were calculated by

rst creating a square matrix ı′�j

from the elements of the N′ matrixs in Eq. (5).

′�j =

{n′

ikif � = j

0 if � /= j(5)

he ı′�j

matrix was then multiplied by the appropriate elements ofhe G′ matrix as in Eq. (6) to produce unit environs.

′ijk = g′

i� × ı′�j (6)

ealized environs e′ijk, which enable the interpretation of results

n terms of units of the model, were calculated from unit environsy scaling the unit environs by the appropriate boundary flow ykGattie et al., 2006b; Whipple et al., 2007; Borrett and Freeze, 2011),s in Eq. (7).

′ijk = yk × e′

ijk (7)

he resulting product was a set of matrices, the sum of whichecover the original network. Each environ is a sub-matrix thathows the relationships between all network components withespect to the environ boundary flux.

Hines et al. (submitted for publication) used realized environsrom the two CFRE networks to evaluate the potential impact of sea-ater intrusion on the coupling of nitrogen cycling and removalrocesses. They defined coupling as the sequential use of spe-ific biogeochemical processes by nitrogen traveling through theetwork, each of which was explicitly represented by one of theetwork fluxes in Fig. 2. They focused on the removal of nitrogen

rom the network boundary by coupling among four processes: thewo nitrogen removal processes of denitrification (y6(b); Fig. 2) andnaerobic ammonium oxidation (y5(a) + y6(a); Fig. 2), and the twoitrogen cycling processes of nitrification (f65; Fig. 2) and dissim-

latory nitrate reduction to ammonium (f56; Fig. 2). For example,itrogen first crossing the edge f65, then immediately crossing thedge y6(b) was considered to be nitrification coupled to denitrifi-ation. In contrast, nitrogen crossing the y6(a) edge without firstrossing another edge was considered to be direct denitrification.hey evaluated these couplings in both networks and comparedhe results. Here, we use the Hines et al. (submitted for publication)esults to provide an example of neighborhood level analysis and toomplete the case study of the CFRE networks across the network,eighborhood, and node levels of analysis.

.4. Node level analyses

We calculated three node level indicators: throughflow cen-rality (Ti), realized total environ throughflow (TET), and effectiveeighted link density (LDn). Throughflow centrality and TETrovide global measures of a node’s importance as they captureoth direct and indirect flows, while effective link density grants

more local perspective by focusing on the direct effects of linksdjacent to each node. The results of node level analyses can dif-er substantially when considering direct or indirect interactionsScotti et al., 2007); therefore, we chose node level indicators with

range of perspectives for comparison against the network and


eighborhood levels.Throughflow centrality is an indicator of the relative importance

f nodes in a network with respect to the total system activityBorrett, 2013). This metric is a global indicator with resolution at

PRESSodelling xxx (2013) xxx– xxx 5

the node level because it incorporates all the network fluxes to cal-culate each node’s contribution to TST. Throughflow centrality canbe used to determine which components are most critical to theflow of energy-matter through an ecosystem. For example, Borrett(2013) used throughflow centrality to rank the most importantgroups for energy flow in 45 peer reviewed trophic networks. Ti wascalculated as the throughflow vector �T = [Ti] in flow analysis (seesection 2.2.1). The value of Ti associated with each node representsthe partial contribution of that node to TST, and

∑ni=1Ti = TST.

Total environ throughflow (TET) is an indicator of the importanceof nodes with respect to their environ contributions to TST. It pro-vides a global perspective of node importance by partitioning theenergy-matter moving through a network into what passes throughthe environ of a given node or boundary flux (Gattie et al., 2006b;Whipple et al., 2007, in this issue). Like throughflow centrality, TETprovides a quantification of each node’s relative contribution to sys-tem activity. For example, Gattie et al. (2006a) use TET to evaluatewhich portions of the nitrogen cycle contributed most to biogeo-chemical cycling in the Neuse River Estuary, NC. TET was calculatedusing input-oriented realized environs. The value of TET for eachnode was obtained by summing the values of each realized environ(Eq. (8)).

TETk =n∑

i=1

n∑j=1

e′ijk (8)

Like throughflow centrality, the values of the TET vector sum toTST.

Weighted link density is an indicator of the strength and numberof direct connections to nodes (Bersier et al., 2002). This analy-sis adopts the same row to column orientation as the ascendencyanalysis, but focuses on only the internal flows in FT. The analy-sis calculates weighted link densities in both the input and outputdirections, then averages the two to create an effective link densityfor each node. A complete description of weighted link density canbe found in Bersier et al. (2002). Briefly, the diversity of flows enter-ing (HIN

j) and exiting (HOUT

i) each node are calculated as in Eqs. (9)

and (10), respectively.

HINj = −

n∑i=1

(f Tij∑n

i=1f Tij

× log2

f Tij∑n

i=1f Tij

)(9)

HOUTi = −sumn

j=1

(f Tij∑n

j=1f Tij

× log2

f Tij∑n

j=1f Tij

)(10)

These diversities are used to calculate the reciprocals nIN and nOUT

as in Eqs. (11) and (12), respectively.

nINj =

{2

HINj if f T

ij/= 0

0 if f Tij

= 0(11)

nOUTi =

{2HOUT

i if f Tij

/= 0

0 if f Tij

= 0(12)

The reciprocal flow diversities are then weighted by the proportionof the internal node flux to the total internal flux, and input andoutput directions are averaged to obtain the effective weighted linkdensity (Eq. (13); Bersier et al., 2002).

⎛ ⎞


LDn = 12⎝ n∑

j=1

f Tij∑n

i=1

∑nj=1FT

× nOUTi +

n∑i=1

f Tij∑n

i=1

∑nj=1FT

× nINj⎠(13)




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Fig. 4. Example of the results of the neighborhood level of analysis conductedin Hines et al. (submitted for publication). Bar heights indicate the amount ofN removed by each process and set of coupled processes. Abbreviations - Oligo:oligohaline; Poly: polyhaline; DNT: denitrification; NTR: nitrification; AMX: anaer-

ig. 3. Percent difference between network level indicators for the oligohaline andolyhaline CFRE networks relative to the ranges of network level indicators in the 22mpirically based biogeochemical cycling models from the Lau et al. (2013) library.ercentages are shown as (oligohaline − polyhaline)/range × 100.

.5. Analysis of results

The five network level and three node level analyses con-ucted in this work were calculated for the CFRE nitrogen networkssing the enaR software package for R (Lau et al., 2013). Theseesults were then combined with the findings of existing neighbor-ood level analyses for these networks (Hines et al., submitted forublication), and comparisons were made both within and amonghe hierarchical levels of analysis. To compare network level indi-ators between the two networks, percent difference between sitesas calculated for each of the five statistics. Node level indica-

ors were compared both within and between the CFRE networksn R using Spearman’s rank correlation (�) tests. The distribu-ions of these indicators were further examined by calculating theoefficients of variation (CV = standard deviation/mean× 100 %) forhe throughflow centrality, TET , and effective weighted link den-ity vectors at each network. This calculation served as a measuref centralization (Wasserman and Faust, 1994) for the distribu-ion of flows in each of the node level vectors such that higheroefficients of variation were associated with higher levels ofentralization.

To compare results among hierarchical levels of analysis, weonsidered the conclusions implicated by each of the analysesonducted, as well as those conducted in Hines et al. (submittedor publication). We evaluated the differences between levels ofnalysis based on the presence or lack of corroboration betweenonclusions, and used these findings to test the null hypothesis thathe network, neighborhood, and node hierarchical levels of analysisould produce the same ecological conclusions.

. Results

.1. Network level analyses

The values for the five network level indicators examined in thistudy were greater in the oligohaline network than the polyhalineetwork for all of the network level analyses performed, with thexception of homogenization. These analyses produced APL valuesf 1.86 and 1.73, I/D ratios of 2.10 and 2.06, HMG values of 1.78 and.81, FCI values of 0.202 and 0.170, and A/C ratios of 0.306 and 0.300t the oligohaline and polyhaline sites, respectively. The percentifferences between the two CFRE networks ranged from −1.6 forMG to 16 for FCI, relative to the oligohaline network (Fig. 3).

.2. Neighborhood level analysis


This work uses the environ analysis results presented in Hinest al. (submitted for publication) as an example of a neighborhoodevel analysis for comparison against the network and node levels.

obic ammonium oxidation; DNRA: dissimilatory nitrate reduction to ammonium.Hyphens (-) indicate coupling.

Figure modified from Hines et al. (submitted for publication).

Briefly, Hines et al. (submitted for publication) showed that the cou-pling of the microbial nitrogen removal processes of denitrificiationand anaerobic ammonium oxidation to the nitrogen transforma-tion process of nitrification was higher in the oligohaline networkthan the polyhaline network. In contrast, Hines et al. (submittedfor publication) showed that the coupling of anaerobic ammoniumoxidation to the transformation process of dissimilatory nitratereduction to ammonium was lower in the oligohaline network.However, despite these differences in the internal network flowsinvolved in nitrogen removal pathways between the two CFREnetworks, the proportions of the nitrogen inputs to each networkinvolved in microbial nitrogen removal were similar. Therefore,direct removal processes were able to compensate for the reduc-tion in coupled nitrogen removal processes resulting from seawaterintrusion in the CFRE networks (Fig. 4).

3.3. Node level analyses

3.3.1. Throughflow centralityThroughflow centrality analysis showed that fluxes through the

W-ON, S-NH4, and S-ON nodes were the top three contributors,respectively, to TST in both the oligohaline and polyhaline networks(Fig. 5a). However, differences were observed in the rank order ofthe other node contributions between the two models. The W-NH4and W-NOx nodes contributed more to TST in the oligohaline modelthan the polyhaline model, while the S-NOx node showed the oppo-site result. Despite these differences, a Spearman’s � test showed asignificant positive correlation between the rank order of the nodesin the T vectors for the oligohaline and polyhaline models (� = 0.928,p = 0.002). The coefficient of variation for T vector was smaller in theoligohaline network than the polyhaline network (77.1% and 84.2%,respectively), which indicated that flows were more centralized inthe polyhaline network.

3.3.2. Total environ throughflow


TET analysis partitioned the TST to quantify the amount of mate-rial moving through each node environ. As with the throughflowcentrality analysis, the W-ON and S-NH4 environs were the mostimportant contributors to TST (Fig. 5b). The relative magnitudes of


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ig. 5. Node level indicators for the oligohaline and polyhaline CFRE models. Pan-ls show (a) throughflow centrality, (b) total environ throughflow (TET), and (c)ffective weighted link density (LD) for each node in the CFRE networks.

he environ for each node between the two CFRE networks werelso similar to those observed in throughflow centrality analysis.

Spearman’s � test confirmed a significant positive correlationetween the nodes in the TET vectors for the oligohaline and poly-aline models (� = 0.928, p = 0.002). The coefficients of variation forhe TET vectors were 117% and 136% in the oligohaline a polyhalineetworks, respectively.

.3.3. Weighted link density


The highest weighted link densities were observed in the W-ONnd S-NH4 nodes in both of the CFRE models, which was consistentith the results of the throughflow centrality and TET analyses

Fig. 5c). There was little difference in the rank order of nodes in


the link density analysis at the oligohaline and polyhaline sites,and a Spearman’s � test indicated a significant positive correlation(� = 0.952, p = 0.001). However, unlike throughflow centrality andTET , which were higher at the oligohaline site in seven of eightnodes, effective weighted link density was higher at the polyha-line site in five of eight nodes. The coefficients of variation for theweighted link density vectors were 78.8% and 87.8% at the oligoha-line and polyhaline sites, respectively.

3.3.4. Node level cross comparisonAlthough the rank order of nodes at the oligohaline and poly-

haline sites were correlated within each node level analysis,throughflow centrality, TET , and weighted link density analyses didnot produce identical results. For example, the contributions of theW-M, S-M, and S-ON environs to TST were greatly reduced in TETanalysis compared to the contributions of the respective nodes toTST in throughflow centrality analysis, because TET analysis scalesthese contributions to the node boundary fluxes (Fig. 5). The rankorder of node contributions to TST within each model also differedbetween the two node level analyses. Spearman’s � tests comparingthe results of the node level analyses at each network showed therewas no significant relationship between the rank order of nodesin throughflow centrality and TET analyses or TET and weightedlink density analyses (Table 2). However, the rank order of nodesin throughflow centrality and weighted link density analyses weresignificantly correlated (Table 2) despite differences in the analysisresults.

4. Discussion

We consider the results of this study in two steps. We first dis-cuss and compare the results of the network, neighborhood, andnode level analyses for the CFRE nitrogen models. We then use thesecomparisons to evaluate the strengths and weaknesses of each levelof analysis and to highlight how these levels of analysis relate toeach other. We conclude by summarizing the analytical frameworkoutlined in this paper and highlighting the contributions of thisresearch to network ecology.

4.1. Network level analyses

The statistics for all five of the network level analyses conductedin this work showed differences between the oligohaline and poly-haline CFRE networks, with the largest percent difference found inFCI (16%). All other statistics showed differences smaller than 7%between the CFRE models (Fig. 3). However, the ecological rele-vance of the differences in these statistics is difficult to interpretbecause it is not clear what magnitude of difference is substan-tial. To provide a basis for interpreting the network level CFREcomparison, we referenced the library of 22 empirically based bio-geochemical cycling networks presented in Lau et al. (2013). Theminimum, median, and maximum values in the Lau et al. (2013)library were 1.73, 10.9, and 186 for APL, 2.06, 10.8, and 201 for I/D,1.78, 3.15, and 10.9 for HMG, 0.170, 0.620, and 0.980 for FCI, and0.300, 0.563, and 0.752 for A/C, respectively. Given the range ofvariation in the network level statistic of empirically based biogeo-chemical models, we concluded that the two CFRE nitrogen cyclingnetworks produced roughly equivalent network level statistics forthe properties examined in this work.

The ecological implications of these findings are that the CFREmodels presented by Hines et al. (submitted for publication)showed little evidence for any impact of seawater intrusion on the


nitrogen cycle at the network level of analysis. This is a counterin-tuitive result because several individual nitrogen cycling processescan be impacted by salinity (Craft et al., 2008), and while the topolo-gies of the models are identical, the parameterization of each model




8 D.E. Hines, S.R. Borrett / Ecological Modelling xxx (2013) xxx– xxx

Table 2Spearman’s � results for three node level indicators: throughflow centrality (Ti), total environ throughflow (TET), and effective weighted link density (LD). Comparisons aremade between the oligohaline (Oligo) and polyhaline (Poly) sites.

Indicator Ti (Oligo) TET (Oligo) LD (Oligo) Ti (Poly) TET (Poly) LD (Poly)

Ti (Oligo) 1TET (Oligo) 0.714 1LD (Oligo) 0.952* 0.571 1Ti (Poly) 0.929* 0.523 0.952* 1TET (Poly) 0.667 0.929* 0.524 0.524 1

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s substantially different (Hines et al., submitted for publication).owever, at the network level of analysis, which integrates both

he neighborhood and node levels of analysis, it is possible thatifferences at lower levels of analysis may cancel each other out.he finding that network level analyses may mask important sig-als is not without precedent. Baird and Ulanowicz (1993) notedhat carbon flow networks for impacted and unimpacted estuariesroduced similar network level indicators. It is possible that ecolog-

cally important differences between the networks were not visiblet the network level.

These results also suggest that, at the network level, the CFREcosystems may be able to maintain their functionality despiteeawater intrusion. Jørgensen and Mejer (1977) identify a similaresponse, referred to as ecological buffer capacity, in phosphorousoading models. Ecological buffer capacity is the ability of an ecosys-em to change in response to its inputs. Jørgensen and Mejer (1977)ote that ecological buffer capacity tends to increase with the diver-ity of an ecosystem. Therefore, the similarity between the networkevel indicators for the two CFRE networks despite differences at theode level may be an indication that these ecosystems are diversenough to adapt to changing environmental conditions with lit-le loss of ecosystem functionality. As this study examined only aortion of commonly used network level indicators, the generalityf these findings across all network level indicators remains to beested.

Ecological buffer capacity is similar to ecosystem resilience,hich is the amount of disturbance necessary to alter the function-

ng of an ecosystem (Holling, 1996). Previous work has identifiedhe turnover rates of limiting nutrients as potential indicatorsf ecosystem resilience (DeAngelis et al., 1989; Carpenter et al.,992), suggesting that the similarity between nitrogen removal athe oligohaline and polyhaline sites may be a useful indicator ofesilience in the CFRE. The ecosystem resilience concept focuses onhe maintenance of existing function in ecosystems in the presencef a disturbance (Holling, 1996), which is supported by the networkevel indicators examined in this study.

.2. Neighborhood level analyses

The environ analysis results showed that the coupling amongifferent nitrogen cycling processes was substantially differ-nt between the CFRE networks (Hines et al., submitted forublication). Nitrification coupled to denitrification decreased fromhe oligohaline to the polyhaline network, while the importancef direct denitrification increased (Fig. 4). However, as a percent-ge of the nitrogen inputs to each network, the total amount ofitrogen removed through biogeochemical cycling pathways wasoughly equivalent (Fig. 4). In this way, neighborhood level analysisimultaneously showed similarities, as in the network level analy-


es, and differences, as in the node level analyses, between the CFREetworks. The intermediate hierarchical position of the neighbor-ood level analysis may provide information on the relationshipetween the network and node levels.

0.952* 0.452 1

Other neighborhood level analyses may illustrate the relation-ship between the network and node levels in different ways. Forexample, Ulanowicz (1983) described an algorithm for determin-ing the size and number of all cycles in a network, Allesina et al.(2005) demonstrated how the interactions among strongly con-nected components within ecological networks can be examined,and Krause et al. (2003) used compartment analysis groups of inter-acting network components. These tools provide information onthe interactions of sub-network groups of nodes that may help toshow how the conditions at different levels of analysis influenceand regulate each other.

4.3. Node level analyses

The node level indicators examined in this study exhibitedsmall, but potentially important, differences between the two CFREnetworks. Throughflow centrality showed that, in the presenceof higher concentrations of seawater, pools of ammonium andnitrate–nitrite in the water column and ammonium in the sedimentcontribute less to nitrogen cycling, while pools of nitrate–nitritein the sediment contribute more to cycling (Fig. 5a). Althoughthe rank order of nodes with respect to throughflow centralitywas significantly correlated between the two CFRE models (Spear-man’s rho, � = 0.928, p = 0.002), the differences observed betweenthe two networks were in pools of biologically available nutrients,and therefore may be of concern to ecosystem health. Becauseseawater intrusion facilitates the release of ammonium from thesediments (Gardner et al., 1991; Hou et al., 2003), excess ammo-nium could become available to phytoplankton in areas impactedby seawater intrusion. Therefore, if the ability of an estuary toremove ammonium from the water column is reduced by seawaterintrusion, throughflow centrality analyses suggests that there maybe an increased risk of phytoplankton blooms in these areas. Thisfinding is consistent with the neighborhood level results of Hineset al. (submitted for publication), which showed a decoupling ofnitrification to denitrification.

TET analysis also revealed differences between the two CFREnetworks. These results were more pronounced than the results ofthroughflow centrality analysis because the distribution of flowswere more centralized in TET than in throughflow centrality. Sev-eral nodes in the TET analysis had throughflow close or equal tozero as a result of small or absent boundary fluxes, and TST wasdistributed between only the other nodes. This was reflected bythe fact that TET showed the highest degree of centralization of thethree node level analyses examined. TET analysis corroborated thefindings of throughflow centrality by suggesting that ammoniumin the water column and sediment may contribute less to nitrogencycling as a result of seawater intrusion, while nitrate-nitrite in thesediment may contribute more (Fig. 5b). As with throughflow cen-trality, this shift in the ecological use of biologically available forms


of nitrogen suggests that estuaries that are exposed to seawaterintrusion may be at higher risk of phytoplankton blooms.

Effective weighted link density also differed between the oligo-haline and polyhaline networks. As with throughflow centrality and


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eighted link density focuses solely on internal fluxes. In both mod-ls, six of the eight nodes had weighted link densities less than one,uggesting that the internal network contributions to these nodesre relatively weak. For these nodes, the majority of system activ-ty is driven by boundary fluxes. This finding is consistent with thendings of Hines et al. (2012), which show that boundary fluxes areesponsible for over 50% of TST in the oligohaline network.

Although throughflow centrality, TET , and effective weightedink density showed similar patterns between the oligohaline andolyhaline networks, these analyses did not provide identical infor-ation. For example, a Spearman’s rank correlation test between

he throughflow centrality and TET results showed no relationshipetween the analyses in either network (Table 2). Therefore, theifferences observed between the two CFRE networks using thesenalyses provide different node level viewpoints on the potentialmpact of seawater intrusion on the estuarine nitrogen cycle, whichgree that the roles of biologically available nutrient pools may beltered.

The case study presented in this work demonstrates that net-ork, neighborhood, and node level indicators provide different

rames of reference that do not always lead to the same ecologicalonclusions. Therefore, the evidence from our single case study didot support the null hypothesis that network level and node level

ndicators would produce results that lead to the same conclusions.lthough the generality of this finding across indicators at different

evels remains to be tested, it suggests that systems analysis shoulde conducted at multiple levels, especially when searching for theossibility of an environmental impact.

.4. Hierarchical framework of ecological network analysis

Similar distinctions between hierarchical levels of analysis tohose presented in this paper have been made in the past. For exam-le, Brandes and Erlebach (2005) distinguish between graph- andertex-level measures of centrality. Whipple et al. (2007) differen-iated between macro- and micro-level analyses in ENA based onhe type of information used to conduct each analysis. The hierar-hical framework presented in this work differs from the Whipplet al. (2007) distinction in that it is based on the resolution of thenalysis results, rather than the analysis inputs. Under the frame-ork presented here, network level analyses produce a single value

or the whole network, neighborhood level analyses produce setsf relational values, and node level analyses produce a single valueor each network node.

Network level analyses integrate all of the information ineighborhood and node level analyses to produce useful singletatistic descriptors of network structure and function. However,cologically important differences, which can be visible at theeighborhood and node levels, may become obscured at the net-ork level as a result of the different information available at higher

evels of analysis, and thus go undetected. For example, in theFRE case study, no difference was seen in network level indica-ors between the oligohaline and polyhaline networks, despite theact that differences were detected at lower levels of analysis.

Neighborhood level analyses provide a description of the inter-ctions among specific network components. The results of these


nalyses produce relational values, often in the form of a matrix,s opposed to the single whole-system statistics produced by net-ork level analyses. The results of neighborhood level analysesrovide information about the relationships between the network


and node levels, while offering a view of specific network inter-actions that cannot be obtained at another level of analysis. Forexample, the neighborhood analysis of the CFRE networks pre-sented in Hines et al. (submitted for publication) showed that therelationships between nitrogen cycling processes were different inthe oligohaline and polyhaline networks, although the percentageof nitrogen removed from both models was nearly identical. Otherneighborhood level analyses, such as cycling analysis (Ulanowicz,1983), may serve a similar role in evaluating ecosystems in thatthey provide information about specific network interactions whilemaintaining a broad level of resolution.

Node level analyses provide information about specific nodeswithin a network, and produce a single value for each node. Theseanalyses are useful for identifying important nodes and evaluatingnode properties. Node level analyses provide the finest resolution ofthe analyses in ENA, and may be the most sensitive to differences innetworks. However, at higher hierarchical levels, these differencescan be obscured. In the CFRE nitrogen cycling example, node levelanalyses determined that the rank importance of nodes to systemactivity differed between the oligohaline and polyhaline networks.

Relationships among network, neighborhood, and node levelanalyses result from the fact that processes and conditions at lowerlevels can influence higher levels, while the states of higher levelscan regulate lower levels (Jordan and Jørgensen, 2012). Althoughthe CFRE case study provides examples of the relationships amonganalysis levels, the exact nature, as well as the generality, ofthese relationships remains unclear. It is possible that the pat-terns observed among hierarchical levels of analysis in the CFREnetworks may not be present in all types of analysis or all ecolog-ical networks. The generality of these relationships should be thetopic of future research.

4.5. Conclusions

This work makes four primary contributions to the networkecology literature. First, it supplies an analytical framework to orga-nize the different analyses in ENA. Second, it uses the case studyof the CFRE nitrogen networks to demonstrate that differencesthat are visible at lower hierarchical levels of analysis can becomeobscured at higher hierarchical levels of analysis within the samesystem. As the field of network ecology rapidly expands (Borrettet al., in this issue), we recommend an emphasis on researchapproaches that encompass multiple hierarchical levels of analysiswhen evaluating ecological networks. Third, this work provides anexample of how ecological buffer capacity and ecosystem resiliencemay be related to hierarchical levels of analysis. We show that dif-ferences in systems at lower levels of analysis may not be presentat higher levels of analysis, and suggest that this may be evidenceof an ecosystem’s ability to adapt to changing conditions. Fourth,this work identifies the utility of each hierarchical level. Althoughdifferent levels of analysis may not always mask signals present innetworks, the case study presented in this work demonstrates thatit is possible for higher levels of analysis to hide signals that arepresent at lower levels of analysis.

Acknowledgements

This research was conducted as a contribution to the sympo-sium “Systems Ecology: A Network Perspective and Retrospective”hosted at the University of Georgia, 12–14 April 2013 in honor ofthe career of Dr. Bernard C. Patten. We thank Matthew K. Lau for


providing a friendly review of this paper, as well as the anonymousreviewers who helped us to improve it. Funding for this work wasprovided by the US National Science Foundation (DEB1020944) andNSF-OCE (0851435).


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Documents

A comparison of network, neighborhood, and node levels of analyses in two models of nitrogen cycling in the Cape Fear River Estuary