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Welcome to the Lab's research page. Please click on one of the tabs above to learn more about our work.

A full list of our publications with links is available under Publications. Ongoing projects are described under the Projects tab. The Tools/Techniques tab describes some of our methodology. The Software & Data/Models tab has links to software the lab has developed and links to a large set of ecosystem models collected from generous colleagues and the literature. This data set incompletely overlaps with Dr. Ulanowicz's set of models on his website. If you use this data, please make sure to cite the original authors.

Below is a list of publications from members of the laboratory. If you do not find a link to the paper and cannot access it at your library, please email Dr. Borrett (borretts [at] uncw [dot] edu) and he will send you a PDF copy.

In Preparation

Billman, D., W. Bridewell, S.R. Borrett. Model Revision in Science: Human-Computer Partnership Viewed through Prometheus


Borrett, S.R. and M. Lau. enaR: An R package for Ecological Network Analysis.

Abbott, K.C., J. Karst, L. Biederman, S.R. Borrett, A. Hastings, J.D. Bever, V. Walsh, L. Miller. Spatial heterogeneity in soil microbes alters establishment success of an introduced plant.

Hines, D.E., J.A. Lisa, B. Song, C.R. Tobias, S.R. Borrett. Estimating the impacts of sea level rise on the coupling of estuarine nitrogen cycling processes through comparative network analysis. Preprint: arXiv:1311.1171 [q-bio.QM]

Whipple, S.J., B.C. Patten, S.R.Borrett. Comparative Network Environ Analysis of a Seven-Compartment Model of Nitrogen Storage in the Neuse River Estuary, USA: Time Series Analysis.

In Print

Borrett, S.R., J. Moody, A. Edelmann. 2014. The rise of Network Ecology: Maps of the topic diversity and scientific collaboration. Ecological Modelling. doi: 10.1016/j.ecolmodel.2014.02.019. Preprint: arXiv:1311.1785 [q-bio.QM]

Hines, D.E., S.R. Borrett.  2014. Comparison of Network, Neighborhood, and Node levels of analysis in two models of nitrogen cycling in the Cape Fear River Estuary. Ecological Modelling. doi: 10.1016/j.ecolmodel.2013.11.013.

Brasso, R., B. Drummond, S.R. Borrett, A. Chiaradia, M. Polito, A. Raya-Rey. 2013. Unique pattern of molt leads to low intra-individual variation in feather mercury concentrations in penguins.  Environmental Toxicology & Chemistry 32:2331-2334 doi: 10.1002/etc.2303 [PDF]

Borrett, S.R. 2013. Throughflow centrality is a global indicator of the functional importance of species in ecosystems. Ecological Indicators 32:182-196 doi:10.1016/j.ecolind.2013.03.014 Preprint: arXiv:1209.0725v1 [q-bio.QM]

Borrett, S.R., R.R. Christian, R., R.E. Ulanowicz. 2012.  Network Ecology (Revised). In: A.H. El-Shaarawi and W.H. Piegorsch (Eds.). Encyclopedia of Environmetrics (2nd edition). John Wiley and Sons: Chinchester, pp. 1767-1772. doi:10.1002/9780470057339.van011.pub2 [PDF]

Lau, M.K., S.R. Borrett and D.E. Hines. 2012. enaR: Tools for ecological network analysis. R package version 1.01. http://CRAN.R-project.org/package=enaR. Updated 7/2013. version 2.0.

Hines, D.E., J.A. Lisa, B. Song, C.R. Tobias, S.R. Borrett.  2012 A network model shows the importance of coupled processes in the microbial N cycle in the Cape Fear River Estuary. Estuarine, Coastal and Shelf Science 20:45-57. doi:10.1016/j.ecss.2012.04.018

Fann, S.L. and S.R. Borrett., 2012. Environ centrality reveals the tendency of indirect effects to homogenize the functional importance of species in ecosystems. Journal of Theoretical Biology 294: 74-86. doi:10.1016/j.jtbi.2011.10.030 arXiv:1110.5385v1 [q-bio.PE]

Borrett, S.R., M.A. Freeze, A.K. Salas. 2011. Equivalence of the ecological network analysis realized input and output oriented indirect effects metric. Ecological Modelling 222: 2142-2148 doi:10.1016/j.ecolmodel.2011.04.003. Download the models analyzed. arXiv:1103.6276v1 [q-bio.QM]

Borrett, S.R. and M.A. Freeze. 2011. Reconnecting environs to their environment. Ecological Modelling. doi: 10.1016/j.ecolmodel.2010.10.015. Download the models analyzed.

Salas, A.K. and S.R. Borrett. 2011. Evidence for dominance of indirect effects in 50 trophic ecosystem network. Ecological Modelling 222: 1192--1204. (preprint arXiv:1009.1841v1 [q-bio.PE]) doi:10.1016/j.ecolmodel.2010.12.002 Download the models analyzed.

Borrett, S.R., S.J. Whipple, B.C. Patten. 2010. Rapid development of indirect effects in ecosystem networks. Oikos 119: 1136-1148 doi:10.1111/j.1600-0706.2009.18104.X (preprint)

Borrett, S.R., A.K. Salas. 2010. Evidence for resource homogenization in 50 trophic ecosystem networks. Ecological Modelling 221: 1710-1716 doi:10.1016/j.ecolmodel.2010.04.004. Download the models analyzed.

Kaufman, A., S.R. Borrett. 2010. Ecosystem network analysis indicators are generally robust to parameter uncertainty in a phosphorus model of Lake Sidney Lanier, USA. Ecological Modelling 221: 1230-1238. http://dx.doi.org/10.1016/j.ecolmodel.2009.12.018.

Bridewell, W., S.R. Borrett, P. Langley. 2009. Innovative construction of explanatory scientific models. In: A.B. Markman and K.L. Wood (Eds.) Tools for Innovation. Oxford University Press, NY.

Borrett, S.R., W. Bridewell, P. Langley, K.R. Arrigo. 2007. A method for representing and developing process models.  Ecological Complexity 4: 1–12. doi:10.1016/j.ecocom.2007.02.017

Bata , S.A. , S.R. Borrett, B.C. Patten, S.J. Whipple, J.R. Schramski, D.K. Gattie. 2007.  Equivalence of throughflow– and storage–based environs. Ecological Modelling. 206: 400–406 doi:10.1016/j.ecolmodel.2007.04.005

Bridewell, W., Borrett, S.R., & Todorovski, L. 2007. Extracting constraints for process modeling. Proceedings of the Fourth International Conference on Knowledge Capture (pp. 87-94). Whistler, BC. [pdf]

Schramski, J.R., D.K. Gattie, B.C. Patten, S.R. Borrett, B.D. Fath, S.J. Whipple. 2007.  Indirect effects and distributed control in ecosystems: Distributed control in the environ networks of a seven-compartment model of nitrogen flow in the Neuse River Estuary , USA : Time series analysisEcological Modelling 206: 18-30. doi:10.1016/j.ecolmodel.2007.03.023

Whipple, S.J., S.R. Borrett, B.C. Patten, D.K. Gattie, J.R. Schramski, S.A. Bata. 2007. Indirect effects and distributed control in ecosystems: Comparative network environ analysis of a seven-compartment model of nitrogen flow in the Neuse River Estuary: Time series analysisEcological Modelling 206: 1-17.  doi:10.1016/j.ecolmodel.2007.03.002

Whipple, S.J., B.C. Patten, P.G. Verity, M.E. Frischer, J.D. Long, J.C. Nejstgaard, J.T. Anderson, A. Jacobsen, A. Larsen, J. Martinez-Martinez, and S.R. Borrett. 2007 Gaining integrated understanding of Phaeocystis spp. through  model-driven laboratory and mesocosm studiesBiogeochemistry 83:293–309. doi:10.1007/s10533-007-9089-z

Borrett, S.R., B.D. Fath, B.C. Patten. 2007. Functional integration of ecological networks through pathway proliferationJournal of Theoretical Biology 245: 98-111. doi:10.1016/j.jtbi.2006.09.024 arXiv

Borrett, S.R. and O.O. Osidele. 2007. Environ indicator sensitivity to flux uncertainty in a phosphorus model of Lake Sidney Lanier , USA . Ecological Modelling, 200: 371-383. doi:10.1016/j.ecolmodel.2006.08.011  

Bridewell, W., Langley P., Racunas, S., and Borrett, S.R. 2006. Learning process models with missing data. Proceedings of the Seventeenth European Conference on Machine Learning (pp. 557-565). Berlin : Springer. [pdf]

Nejstgaard, J.C., M.E. Frischer, P.G. Verity, J.T. Anderson, A. Jacobsen, M.J. Zirbel, A. Larson, J. Martínez-Martínez, A.F. Sazhin, T. Walters, D.A. Bronk, S.J. Whipple, S.R. Borrett, B.C. Patten, and J.D. Long.  2006. Plankton development and trophic transfer in sea water enclosures with added nutrients and Phaeocystis pouchetii. Marine Ecology Progress Series 321:99-121.

Gattie, D.K., J.R. Schramski, S.R. Borrett, B.C. Patten, S.A. Bata, S.J. Whipple. 2006.  Indirect effects and distributed control in ecosystems: Network environ analysis of a seven-compartment model of nitrogen flow in the Neuse River Estuary , USA —Steady-state analysisEcological Modelling 194: 162–177.  doi:10.1016/j.ecolmodel.2005.10.017

Borrett, S.R., S.J. Whipple, B.C. Patten, R.R. Christian. 2006. Indirect effects and distributed control in ecosystems: Temporal variation of indirect effects in a seven-compartment model of nitrogen flow in the Neuse River Estuary , USA —Time series analysis. Ecological Modelling 194: 178–188. doi:10.1016/j.ecolmodel.2005.10.011 

Schramski, J.R., D.K. Gattie, B.C. Patten, S.R. Borrett, B.D. Fath, C.R. Thomas, S.J. Whipple. 2006. Indirect effects and distributed control in ecosystems: Distributed control in the environ networks of a seven-compartment model of nitrogen flow in the Neuse River Estuary , USA —Steady-state analysisEcological Modelling 194: 189–201.  doi:10.1016/j.ecolmodel.2005.10.012

Fath, B.D. and S.R. Borrett. 2006. A MATLAB® function for network environ analysis. Environmental Modelling & Software 21:375-405. doi:10.1016/j.envsoft.2004.11.007 The matlab software is available from here.

Cowie, G.M. and S.R. Borrett. 2005.Institutional perspectives on participation and information in water management. Environmental Modeling & Software 20: 469-483. doi:10.1016/j.envsoft.2004.02.006

Borrett, S.R. 2005. Ecosystem Organization and Transformation: The Role of Network Architecture in the Development of Indirect Effects. Ph.D. Dissertation, University of Georgia, Athens, GA. [pdf]

Borrett, S.R. and B.C. Patten. 2003. Structure of pathways in ecological networks: Relationship between length and number.  Ecological Modelling 170: 173-184. doi:10.1016/S0304-3800(03)00224-2

Beck, M.B., B.D. Fath, A. K. Parker, O.O. Osidele , G.M. Cowie, T.C. Rasmussen, B.C. Patten, B.G. Norton, A. Steinmann, S.R. Borrett, D. Cox, M.C. Mayhew, X.-Q. Zeng, and W. Zeng. 2002. Developing a concept of adaptive community learning: Case study of a rapidly urbanizing watershed. Integrated Assessment 3:299-307. [pdf]

Patten, B.C., B.D. Fath , J.S. Choi, S. Bastianoni, S.R. Borrett, S. Brandt-Williams, M. Debeljak, J. Fonseca, W.E. Grant, D. Karnawati, J.C. Marques, A. Moser, F. Müller, C. Pahl-Wostl, R. Seppelt, W.H. Seinborn, Y.M. Svirezhev. 2002. Complex adaptive hierarchical systems. In: R. Costanza and S.E. Jørgensen (Eds.). Understanding and Solving Environmental Problems in the 21st Century: Toward a New, Integrated Hard Problem Science. Elsevier Science, Ltd, Oxford , pp. 41-87.

Cowie, G.M., S.R. Borrett et al. 2001. Foresight for Lanier: A workshop.  Summary of Results.  University of Georgia .   January 25, 2001.   Athens , GA.

We have a number of projects on going in laboratory. They all center on our mission to understand ecosystem organization and transformation and involve developing quantitative informatic and analytical tools and techniques.


Collaborative Research: MSB: Impact of sea level rise on sedimentary nitrogen removal processes in tidal freshwater ecosystems

PI: BK Song, Co-PI Borrett, collborative with C Tobias.

Tidal freshwater ecosystems such as rivers and estuaries are located at the interface between land and sea. These ecosystems provide important natural services including primary production, nutrient distribution and regulation, and waste management - services that are at risk due to climate change. Two aspects of climate change, sea level rise and lower precipitation in some watersheds, will shift the location of freshwater-saltwater mixing zones to upper rivers and continuously increase salinity intrusion into freshwater habitats. Sea level is predicted to rise up to 100 cm by 2100, and by itself can have multiple impacts on freshwater ecosystems, including direct toxic effects, habitat degradation and alteration of nutrient cycles. Salinity increases may also have significant effects on the nitrogen (N) dynamics of freshwater habitats. Nitrification (ammonia conversion to nitrate) and denitrification (nitrate conversion to dinitrogen) are key microbial processes controlling the intensity and duration of eutrophication caused by excess N loading. Salinity intrusion might diminish microbial N removal capacity in freshwater sediments as nitrification and denitrification are reduced due to substrate limitation and physiological inhibition. This could result in prolonged eutrophication and hypoxia at rivers and estuaries. Alternatively, anaerobic ammonium oxidation (anammox; ammonium and nitrite conversion to dinitrogen gas) may become a more important microbial N removal process and help recover N removal capacity in freshwater sediments since anammox bacteria can tolerate salinity increases. This project will study 1) the importance of anammox in tidal freshwater sediments, 2) the effects of salinity on freshwater anammox bacteria and the sedimentary N cycle, and 3) predictions of an alternative N removal pathway in sedimentary communities threatened by sea level rise. The proposed research will integrate molecular microbial techniques, chemical tracer methods and mathematical models to examine sedimentary N removal processes in the Cape Fear River and New River of North Carolina.

This proposal will result in the following benefits and outcomes; 1) revealing the structures and activities of microbial communities involved in N removal processes in tidal freshwater sediments, 2) determining differential responses of sediment communities to seawater intrusion, 3) understanding the impacts of sea level rise on sedimentary N removal processes in freshwater ecosystems, 4) predicting a key microbial process for net N removal capacity of freshwater ecosystems experiencing sea level rise. This project will also provide an in-depth understanding of microbial responses in freshwater sediment communities under threat of sea level rise. Interdisciplinary approaches will provide insight into the linkages between community structure and activity as well as salinity effects on riverine sedimentary N cycling. Broader impacts will be manifested through diverse educational components, outreach, and improved research infrastructure at the University of North Carolina Wilmington (UNCW) and the University of Connecticut. Three PIs (microbial ecologist, biogeochemist and ecosystem modeler) will provide interdisciplinary training to at least three graduate students seeking a M.S. or Ph.D. degree. Additional educational impact will be accomplished both in the classrooms and through individual undergraduate research projects at the two institutions. Research experience for high school students will be achieved by including the project within the UNCW "Summer Ocean Ventures" and "Ocean17" programs. The high school students will participate in DNA analysis and mesocosm experiments. The PI will provide a lecture on the microbial nitrogen cycle to the students and design three days of laboratory and field courses to detect and measure denitrification during the Ocean 17 camp. The graduate students recruited for this proposed research will act as teaching assistants for the high school students. The program will culminate with a Summer Ventures Symposium where students will present their work. Outreach will be facilitated by partnering with a local citizens group (NC-Coastal Ocean Federation) to recruit volunteers to participate in sampling cruises and water monitoring program, and by using the existing UNCW "Planet Ocean" lecture series as a public platform to discuss coastal water resources issues and actions.

NSF Ecosystems. $500,227


Generalization of Environ Properties in Emprically-Based Models

Patten and colleagues (Borrett and Osidele, 2007; Borrett et al., 2006; Fath, 2004; Higashi and Patten, 1986, 1989; Patten, 1983, 1991, in prep.) have argued that indirect effects are dominant components of interactions in ecosystems. This conclusion is based on their work with Network Environ Analysis (NEA), which is an environmental extension of economic Input–Output analysis (Leontief, 1966). While there are good theoretical reasons why this should be true and the hypothesis holds in ecosystem models built from community assembly rules, the hypotheses have not yet been tested across a range of empirically-based ecosysetm models. Thus, we are building a database of empirically-based ecosystem models, which we will then analyse with NEA to test the dominance of indirect effects hypothesis.


Computational Induction of Scientific Process Models

We have an ongoing collaboration with the Computational Learning Laboratory at Stanford University to develop and evaluate inductive process modeling. You can learn more about this project on the CLL web page here.

Our work continues on three related subprojects:

(1) Inductive process modeling to explain the phytoplankton dynamics in the Ross Sea, Antarctica;

(2) Process based sensitivity analysis of simulation models;

(3) Value of data type, quantity, and quality in constraining process model discovery; and

(4) Model discrimination.



Eigen Analysis of Ecological Networks

Matrix algebra and graph theory lie at the heart of most network analyses of complex systems. Many of the ecosystem properties that have been described in flow networks appear to be related to the eigenvalues and eigenvectors of the underlying matrices. We are exploring previous applications of eigen analysis to network models of complex systems and interpreting the elements for ecosystems. For example, Borrett, Fath and Patten 2007 showed that, given certain conditions, the dominant eigenvalue of the adjacency matrix is the rate of pathway proliferation in the extended pathway network.


We use a variety of software, tools, and techniques for computational ecology and ecoinformatics. We briefly describe many of these below and provide links to the software and tutorials we have found useful.


Apple Macintosh Computers: Our laboratory is largely built on the Macintosh operating system. This provides us with a fairly user friendly environment as well as many UNIX tools.

Switching to the Mac, Shortcuts, Terminal, Mac OS X for Oceanographers and Atmospheric Scientists, Mac Research, High Performance Computing on Mac, ssh.


Emacs: A good text editor is essential for quantitative ecology, computational work, and programming tasks. Debates rage as to which editor is superior (Emacs, vi, WinEdt, TextWrangler, etc.). I (SRB) prefere Emacs because it works across platforms, across network connections, and fairly easily performs multiple types of text editing tasks. The draw back of course is that it has a steep learing curve.

To get started: Manual, Carbon Emacs, tutorial.


Matlab/Octave: Matlab is a powerful mathematical tool and programming environment built on matrix algebra. Octave is an open source implementation.

To get started: Mathworks, GNU Octave, tutorial, Dynamic Models in Biology.


R: This is a free and open source statistical programming environment. Like Matlab, it has powerful data visualization capabilities. This has become a popular environment for many kinds of ecological data analyses and modeling in part because it is so flexible. For example, R can also be used to solve ordinary differential equaions.

To get started: R Project, R programming, Simple R, R Wiki, wikipedia.

R in Ecology: Ecological Models and Data in R, Dynamic Models in Biology.


LaTeX: This is a tool for generating and publishing papers. With a bit of effort, it generates nice looking documents, and it has a number of useful features and makes typesetting mathematics much simplier.

To get started: LaTeX project, Using Endnote with LaTeX and BibTeX, CSLI info, LaTeX Intro

NEA.m NEA.m is a matlab function that includes many of the common ecological network analysis algorithms. This is

Ecosystem Network Models

We collected 50 empirically derived and trophically based ecosystem network models from the literature and analyzed them extensively (Borrett & Salas 2010; Salas & Borrett 2011; Borrett & Freeze 2011; Borrett, Freeze & Salas 2011). We have zipped together these model data here (ecological_networks_50_trophic.tgz). The models are stored in SCOR format becuase of its wide use, rather than the input format required for the NEA.m function below. The enaR pacakge has a read.scor() function to read in this format directly. Notice that some of these models are in the collection by Dr. Ulanowicz on his website as a sample data collection. Thank you to everyone who has contributed models.

The average Lake Lanier phosphorus model (Borrett & Osidele 2007; Kaufman & Borrett 2010 and shown below) is also available in SCOR format here (avgLanier.dat).

Matlab Software for Ecological Network Analysis (NEA.m)

We have developed a couple of Matlab functions to facilitate our work. We make them available here with no guarantee or warranty. The NEA.m function performes Network Environ Analsysis, and oyster.m provides an example of the model input file for the NEA function.

The oyster model is also available as a SCOR formatted file (oyster.dat)

enaR: Software for Ecological Network Analysis

Our enaR package for ecological network analysis is available from CRAN at (http://cran.r-project.org/web/packages/enaR/index.html). If you use the software, you can cite it as follows:

> citation(package="enaR")

To cite package ‘enaR’ in publications use:

M.K. Lau, S.R. Borrett and D.E. Hines (2012). enaR: Tools ecological
network analysis. R package version 1.01.

A BibTeX entry for LaTeX users is

title = {enaR: Tools ecological network analysis},
author = {M.K. Lau and S.R. Borrett and D.E. Hines},
year = {2012},
note = {R package version 1.01},
url = {http://CRAN.R-project.org/package=enaR},

We are currently working on a manuscript to introduce the package in the literature. In the mean time, please see the vignette distributed with the package. You can open this from R using the following command:

> vignette("enaR")

Model Visualization

The R network and SNA packages are great for general network analysis needs. Here are some of our first attempts using these tools to visualize two of our network models. In these images the node sizes are proportional to the node storage (log10) and the arrows are proportional to the flux magnitude (log10). These first images only include the internal transfers. The Lake Lanier model is the average model of the 122 realizations described in Borrett & Osidele 2007 and Kaufman & Borrett 2010.

oyster model

Lanier Model