The use of ecological and social network analysis to study food webs and nutrient cycles in ecological systems that include humans

Joseph J. Luczkovich, Department of Biology, Institute for Coastal and Marine Resources

East Carolina University, Greenville, NC 27858,

Keywords: Food webs, Nutrient Cycles, Social Network Analysis, Ecological Network Analysis, Network Visualization


Many ecological and social and phenomena can be modeled as networks of interactions.

For instance, in ecological systems, food webs and nutrient cycles can be represented using species (or groups of similar taxa) as nodes, and flows of energy, carbon, or nitrogen as arcs.In social systems, information, money or other services are the arcs and people (or groups of people) are the nodes in the network.

At a recent Network Biocomplexity workshop sponsored by the National Science Foundation held in NC (USA), 40 sociologists and ecologists met to discuss the similarity among the approaches used in these two approaches to modeling networks (Science Perspectives article).

Today, I will discuss the use of network analysis methods to produce models and visualizations of the food webs and nutrient cycle in two systems:


The estuarine seagrass ecosystem at St. Marks, Florida

Luczkovich, Borgatti, Johnson, Everett (2003),

Luczkovich, Ward, Johnson, Christian, Baird, Neckles and Rizzo (2002),

Baird et al. 1998,

Christian and Luczkovich 1999)

Map of St. Marks Wildlife Refuge, FL, USA

Sampling for network analysis at St. Marks


The Norwegian Nitrogen Cycle (Bleken and Bakken 1997).

I will use these examples to display the food web models in a three-dimensional view of the arcs and nodes, using a multi-dimensional scaling (MDS) of the nodes to arrange them in space.


The MDS is based on the similarity of the nodes in terms of their ecological (trophic) role.

The trophic role is measured using an algorithm called Regular Equivalence (REGE) in a social network analysis package called UCINET, in which two nodes are judged to be similar if they consume prey of the same REGE class and have predators that are from the REGE class.

The algorithm is expressed as follows (from Luczkovich et al, in press):

We represent community food web data as a directed graph, or digraph, G(V,E), which consists of a set of nodes V (also known as vertices) representing species or compartments, and a set of directed ties (also known as edges or arcs) E which represent predation, parasitism or any other trophic relationship.

The notation (a,b) E indicates the presence of a tie from a to b. Similarly, (b,a) E, indicates a tie from b to a.

We can also define a real-valued function F on E which assigns a value (such as a quantity of carbon flow) to each tie, so that f(u,v) = .27 would indicate a flow of .27 units of carbon or nitrogen from u to v.

The set of nodes adjacent to a given node v is called the neighborhood of v and denoted N(v).

In a directed graph, a node’s neighborhood consists of two parts:

an out-neighborhood, defined as the set No(v) = {p| (v,p) E}, and

an in-neighborhood, defined as the setNi(v) = {q | (q,v) E}.

In the case of food web predation data, the out-neighborhood No(u) is the set of species that are predators of species u, and the in-neighborhood Ni(u) is the set of species that are prey of species u.

An equivalence relation R of a digraph G(V,E) is regular if, for all nodes u,v V, u v implies that if there exists a tie (u,y) E, then there exists a node z such that (v,z) E and yz, and if there is a tie (p,u) E, then there exists a node q such that (q,v) E and p q.

In other words, in a regular equivalence, if nodes u and v are equivalent, then if one has a tie to a third party, then the other one has a corresponding tie to an equivalent third party (but not necessarily the same one).

Applied to food webs, this means that regularly equivalent species prey on equivalent species and are preyed upon by equivalent species.”

A simple example:

On the left diagram, nodes 5 and 6 are regularly equivalent, because the have the same in-neighborhood (green, blue) and out-neighborhood (white)

On the right diagram, nodes 5 and 6 are NOT regularly equivalent, because they do not have the same in-neighborhood (blue, green for node 5; blue for node 6)


The REGE algorithm assigns species or taxa to classes based on this iterative and recursive method, starting with all taxa in the same class (for details of the algorithm, see Luczkovich et al, in press).

In the first iteration, the producers (plants, algae) are placed in their own class (green) because they are consumed by other species but they are not consumers [Fig. 1; the Appendix below lists the taxa and their numerical codes].

Figure 1. The non-metric multi-dimensional scaling plot of the St. Marks carbon flow food web network after 1 iteration of the REGE algorithm, with plants and algae shown as a separate group (green nodes).

In the next iteration, the top carnivores (birds) are placed in a second class (red), because they consume other species but they are not consumed in the food web (for this model, we have assumed that their biomass is decomposed elsewhere, because they migrate away from the seagrass ecosystem before they die) [Fig. 2].

Figure 2.The non-metric multi-dimensional scaling plot of the St. Marks carbon flow food web network after 2 iterations of the REGE algorithm, with plants and algae shown as green nodes, top-carnivore (birds) shown in red.Yellow nodes are all the remaining taxa, which are intermediate consumers.Node 51 is detritus (sediment particulate organic carbon).

The REGE algorithm proceeds to recursively assign nodes to classes in successive iterations, computing pairwise coefficients that relate the degree of trophic role similarity.

After 51 iterations, there are ten classes with REGE coefficients that exceed a cut-off level of REGE coefficients [Fig. 3].

Fig. 3. The non-metric multi-dimensional scaling plot of the St. Marks carbon flow food web network after 51 iterations of the REGE algorithm. There are now 10 groups: the lime green group, which was the main producer, the seagrass Halodule wrightii (2); the dark green group, which included other benthic producers [epiphytic algae (3) benthic algae (5)] and benthic bacteria (12); the cyan group, which included phytoplankton (1) and bacterio-plankton (6); the white group, which included zooplankton (8); the yellow group, which included various benthic invertebrates [nodes 7, 9, 13, 15, 17, 19, 21, 22, 25, 27, 28], some fishes (31) and suspended POC (50);the blue group, which included the remaining benthic macroinvertebrates [nodes 10, 11, 16, 18, 20, 23, 24, 26, 29, 30] and most fishes [nodes 32, 33, 35, 37, 38, 39, 40, 41]; the purple group, which included the remaining fishes [nodes 34,36,42]; the magenta group, which included herbivorous ducks (43); the red group, which included carnivorous birds [nodes 44, 45, 46, 47, 48]; and the brown group, which included meiofauna (14), and non-living groups [dissolved organic carbon (DOC) (49) and sediment particulate organic carbon (POC) (51)].Most producers(nodes 1, 2, 3, 5) and non-living compartments (nodes 49, 51) appear on the right side of the MDS plot, the intermediate consumers (nodes 7-42) in the center of the plot, and the carnivorous birds (nodes 44-48) at the lower left side of the plot. Herbivorous ducks (43) are at the far left, implying that they are a top predator (and they are not preyed upon by other compartments in this web), although they are separated from other top carnivore birds.

The resulting REGE coefficients are entered into a three-factor MDS, which places them into three-dimensional space as a function of their similarity.

Thus, any two nodes are similar if they plot together in space, and very different if the plot far apart in space.

At the workshop, using MAGE, a software package for visualization of molecular models, I will display the three-dimensional model of the St. Marks seagrass ecosystem carbon flow food web.

Finally, I will display a similarly derived network model of the N-Cycle of Norway.

Bleken and Bakken (1997) examined the nitrogen involved in the food production system of Norway.In this work, the authors analyzed the nitrogen flows within Norway’s society and their dissipation into the environment.

In their analysis, the food-producing sectors of society had the greatest interaction with other aspects of the nitrogen cycle and the largest nitrogen flow.

For example, in their Figure 1, the “wholesale food supply” compartment had flows into it that summed to 26.1 Gg of N per year.Other compartments with large flows included plant production (126 Gg of N per year) and animal production (101.5 Gg of N per year).

I performed a network analysis of these data using the regular equivalence (REGE) approach outlined described above on these data, which groups compartments together in 3 dimensions based on their similar roles (and similar flows) in the nitrogen cycle.

The resulting nitrogen network diagram [Fig. 4] is arranged so that low trophic-level compartments (such as“synthetic fertilizer”, ”fishing industry” and “sea catch” where N comes into the system) are at the bottom and high trophic-level compartments are at the top and outside of the diagram.

Fig. 4.The N-cycle of Norway, visualized using the REGE algorithm and 3-dimesional MDS approach (data from Bleken and Bakken 1997).

The three compartments with the greatest flows (“plant production”, “animal production”, and “whole sale food supply”, are clearly grouped together in the center of trophic role similarity analysis diagram, suggesting that they all play a similar and large role in regulating flows of N in this system.

Nodes associated with waste (“sewage”, “food waste”, and “open sea waste”) are all located near the top and outside of this 3D graph of the network, suggesting that these compartments are the way N is exported from the system.

One interesting conclusion of visualizing the Bleken and Bakken (1997) data in this way is that one can appreciate the very large role “synthetic fertilizer” plays in the production of food in Norway, much larger than the nitrogen arising from “biological fixation” and “atmospheric deposition”.Although this source of nitrogen has always been assumed to play a significant role, unlike a traditional box and arrow diagram, the relative size of the nodes in this network visually communicate the relative importance of the nodes.

Node radii (ball sizes) are scaled according to the log-transformed amount of nitrogen contained in each node.

The thicknesses of the arrows also represent the magnitude of the flows among nodes (log-transformed flows).

The nodes for “plant production”, “fodder”, “animal production” and the “wholesale food supply” are large and show a distinct dominant pathway leading from synthetic fertilizers to human consumption.

Other nodes are instantly visualized as less significant, such as “wild game” and “open sea waste”.

This method does not depend on an artist’s placement of the nodes or the approximation of the size of a node, as is almost always the case in a traditional flow model using boxes and arrows.

The UCINET and MAGE software are all that are required for a visualization of the network that is closely related to the quantitative mass flows of nitrogen in Norway.

The convenience and power of the new visualization software enables public citizens, educators, students, farmers, politicians and environmental managers to view and easily interpret complex biogeochemical data.

The complex nature of this food web and the nitrogen sources and fates of food production in Norway is more easily appreciated using such visualizations.


In both of these models, the size of the nodes has been made proportional to the amount of carbon or nitrogen passing through the node.

So, for example, in the Norwegian N-Cycle, one can see that much of the nitrogen passing through the food web is coming from synthetic fertilizer and ends up as sewage and food waste.

In the St. Marks model, the main source of carbon for the food web is detritus.

Comparisons among different food webs made at different times are thus possible.

The pathways by which nutrients flow and are stored in these food webs can be visualized using REGE and MDS display of the network.

This visualization approach can be used to explore relationships among nodes and aid in the understanding of complex phenomena in social and natural systems.

In the future, the use of the network analysis approach will allow us to model and visualize the effects humans can have on the food webs of global ecosystems.

Appendix1:A list of the identification codes and compartment names for the St. Marks seagrass carbon flow food web taken from Baird et al. (1998).See Christian and Luczkovich (1999) for a complete species list within each compartment.

(1) Phytoplankton, \- algae, (6) Bacterio-plankton, (7) Micro protozoa, (8) Zooplankton, (9) Epiphyte-grazing amphipods, (10) suspension-feed molluscs, (11) Suspension-feed polychaetes , (12) Benthic bacteria, (13) Micro fauna, (14) Meiofauna, (15) Deposit-feeding amphipods, (16) Detritus-feeding crustaceans, (17) Hermit crab, (18) Spider crab, (19) Omnivorous crabs, (20) Blue crab, (21) Isopod, (22) Brittle stars, (23) Herbivorous shrimp, (24) Predatory shrimp, (25) Deposit-feeding gastropod, (26) Deposit-feeding polychaetes, (27) Predatory polychaetes, (28) Predatory gastropod, (29) Epiphyte-grazing gastropod, (30) Other gastropods, (31) Catfish and stingrays, (32) Tonguefish , (33) Gulf flounder & needle fish, (34) Southern hake & sea robins, (35) Atlantic silverside & bay anchovies, (36) Gobies & blennies, (37) Pinfish, (38) Spot, (39) Pipefish & seahorses, (40) Sheepshead minnow, (41) Red Drum, (42) Killifish, (43) Herbivorous ducks, (44) Benthos-eating birds, (45) Fish-eating birds, (46) Fish & crustacean eating birds, (47) Gulls, (48) Raptors, (49) Dissolved Organic Carbon (DOC), (50) Suspended Particulate Organic Carbon, (51) Sediment POC

Appendix 2:A list of the identification codes and compartment names for the Norwegian N Cycle(1) whole fish, (2) wholesale food supply, (3) mills breweries, (4) plant production, (5) fodder, (6) manure, (7) animal production, (8) dairies & eggs, (9) abattoirs, (10) hides pelts wool, (11) fish industry nonfood, (12) fish farming, (13) fish industry food, (14) food waste, (15) sewage, (16) trade export, (17) wild game, (18) other vegetables food, (19) cereal products human,(20) atmospheric deposition on agricultural lands, (21)biological fixation, (22) synthetic fertilizer, (23) grazing on uncultivated lands, (24)cereals & fodder, (25)protein-rich food, (26) sea catch, (27) open sea waste.


Baird, D., Luczkovich, J. J. and Christian, R. R.(1998) Assessment of spatial and temporal variability in ecosystem attributes of the St. Marks National Wildlife Refuge, Apalachee Bay, Florida. Estuar. Coast.Shelf Sci. 47, 329-349.

Bleken, M. A. and L. R. Bakken. 1997. The nitrogen cost of food production: Norwegian society. Ambio 26: 134-142.

Christian, R. R. & Luczkovich, J. J. (1999) Organizing and understanding a winter’s seagrass foodweb network through effective trophic levels.Ecol. Model. 117, 99-124.

Johnson, J. C., Borgatti, S. P., Luczkovich, J. J. & Everett, M. G.(2000) Network role analysis in the study of food webs: an application of regular role coloration. Journal of Social Structure, 2, (8 May, 2001) on-line:

Luczkovich, J. J., S. P. Borgatti, J. C. Johnson, and M. E. Everett. In press. Defining and Measuring Trophic Role Similarity in Food Webs Using Regular Equivalence. Journal of Theoretical Biology. (available as a PDF file on-line:

McMahon, S. M., K. H. Miller, and J. Drake.2001.Networking tips for Ecologists and Social Scientists. Science, 293: 1604-1605.