A very brief introduction

Tags

dynamics

This is a very short video about our work and the questions that we ask. Courtesy of the Academy‘s Visualization Studio.

Experimental Space

Tags

coral reef, food webs, Network theory, networks

Cayman Islands coral reef food web

Hi everyone, if any of you will be in the San Francisco Bay Area in the coming month, there is an exhibition at the Aggregate Space Art Gallery, featuring scientific visualizations. A couple of pieces there are from my food web work! So please stop by. Here is the gallery’s announcement:

“In their search for evidence of theories that better explain our physical reality, scientists often discover unexpected and beautiful phenomena. The researchers who created the images and videos included in “Experimental Space” did not have an art gallery in mind while they worked. Nevertheless, the images, figures, and data on view are aesthetically compelling and seductive. Through this exhibition, Aggregate Space Gallery and BAASICS bring scientific images and perspectives from the laboratory and the academic journal to the realm of art, where subjectivity trumps objectivity and ambiguity is more celebrated than demystification.

Featuring Evidence by: Erin Jarvis Alberstat, PhD candidate; Roger Anguera, Multimedia Engineer; Daniel J. Cohen, PhD; Sara M. Freeman, PhD; Luke Gilbert, PhD; Angela Kaczmarczyk, PhD candidate; Arnaud Martin, PhD; Brian Null, PhD, and Dr. Peter D. Roopnarine, PhD.”

Links–
http://aggregatespace.com/
http://www.baasics.com/

The Cuban coral reef food web

Tags

biodiversity, coral reef, coral reef food web, food webs, graph, invertebrates and vertebrates, marine communities, networks, prey and predator, real world networks, sfdp

This is a rendering of the Cuban coral reef food web from our set that also includes the Cayman Islands and Jamaica. All the data will be made available very soon in an upcoming publication. This is a metanetwork, or guild-level web where nodes represent one or more species with indistinguishable prey and predator links. There is a total of 266 guilds (nodes) in the network with 3899 interactions (edges) between them. The guilds in turn encompass 860 species, including protists, macroalgae, seagrasses, invertebrates and vertebrates. Colour codes: red – primary producers; yellow – invertebrates and heterotrophic protists; magenta – vertebrates.

The web or network was rendered with Graphviz using the neato algorithm (though sfdp also produces very pleasing images). Total cpu time varied between 1-4 seconds depending on options and machine.

Under construction

Tags

coral reef, food webs, networks

One question that I get quite frequently concerns how I/we construct our food web models. Well, one node/taxon/species at a time. This is just a little animation of the process, in this case for one of the Caribbean coral reefs (click on the figure if your browser does not animate it automatically). More detailed discussions may be found in these publications:

Roopnarine, P. D. 2009. Ecological modeling of paleocommunity food webs. in G. Dietl and K. Flessa, eds., Conservation Paleobiology, The Paleontological Society Papers, 15: 195-220.

and

Roopnarine, P. D., K. D. Angielczyk, S. C. Wang, and R. Hertog. 2007. Trophic network models explain instability of Early Triassic terrestrial communities. Proceedings of the Royal Society B, 274: 2077-2086.

Food web complexity and connectance

Tags

connectance, coral reef, food webs, Network theory, networks, paleo-food web, real world networks

Another installation in the series (see previous posts on this page).

System complexity.– The complexity of a food web depends upon the taxon richness of the system, as well as the topology and dynamics of interspecific interactions. Although richness and topology are captured by graphic depictions, the utility of the depictions is often limited to impressing upon the viewer the overwhelming structural complexity of the systems. For example, here is a Greater Antillean coral reef food web comprising 265 trophic guilds and 4,656 interactions, currently one of the most detailed food web networks available. The system is definitely complicated, as expected of a coral reef community, but not much else can be concluded from the graph. In fact, it is more complicated than illustrated, being based on a dataset comprising 750 species and 34,465 interspecific interactions. Many of the species have been aggregated into sets termed trophic guilds, where members of a guild share prey drawn from the same guild(s), and likewise for predators. Species aggregation is a common way in which to reduce food web network complexity, but there are few formulaic methods for aggregation. The most common method is based on the concept of trophic species (trophospecies), where aggregated species are assumed to have exactly the same prey and predators. The trophic guild concept on the other hand was formulated specifically for fossil taxa and assumes uncertainty in species interactions. It is very important to understand the impacts of aggregation on network structure and dynamics, and the implications for species’ roles in the system. Whether different aggregation schemes yield similar insights into complex systems is currently poorly understood. I will return to this topic in a later post.

Connectance.– A number of measures and summary statistics are used to describe and compare food webs, perhaps the most common one being connectance. Food web connectance differs from the graph connectance defined earlier, because the networks are now directional. Each node may link to every other node including itself, but a directional link from species A to B is no longer equivalent to a link from B to A. The maximum number of links possible is therefore the square of the number of nodes. Using symbols common in the food web literature,

where L is the number of directional links in the network, and S is the number of nodes or species. Connectance values are generally well below one, reflecting the relative sparsity of links in food webs, but it is difficult to compare connectances among food webs that use different aggregation schemes. Perhaps given this difficulty, it is quite surprising that there is a regular relationship between L and S spanning a large number of food webs, compiled from a variety of sources, and using different aggregation methods (see also Ings et al.). The exponential nature of the relationship shows that link density, or connectance, increases with increasing node richness. It is possible that increasing taxon richness in a community demands greater connectivity in order to maintain efficient energy transfer and hence stability, or the relationship is simply spurious and any true relationship is obscured by the heterogeneity of food web metadata. This remains, in my opinion, an open problem in food web theory.

Coral reef fish food webs

Tags

coral reef, corals, extinction, food webs, Network theory, real world networks, trophic level

Reef fish food web, Greater Antilles

Here are a couple of renderings of the vertebrate-only component of the coral reef food web. Reminder: the food web is what we expect to see for a reef in the Greater Antilles of the Caribbean, based on data collected around the mid-20th century. The vertebrate component comprises all fish and sea turtle species. The upper figure is the expected food web, and includes 196 species and 995 trophic interactions. Species are arranged on the periphery of the diagram, with interaction represented by the lines crossing the interior. The very busy, or hub species are higher trophic level predators, mostly carcharhinid sharks.

Jamaica coral reef fish food web

The lower figure is what we observe today in Jamaica. (Note: Jamaica is of particular interest for me as a starting comparison, both because of the excellent documentation of those reefs, and my Jamaican heritage; not picking on Jamaica). The number of species, out of 196, observed there over the past 10 years is dramatically smaller. Perhaps more obvious is the loss of interactions. I won’t present the actual data yet, since we will eventually prepare a paper to report all this, but the differences between the two food webs are obvious. We are currently rendering the complete food web, including primary producers and invertebrates, which will be an update of the figures presented in earlier posts. But there are a lot of species in there, and the computers have been churning now for about 17 hours!

Another view

Tags

food webs, modeling, Network theory, networks

This is another rendering of the San Francisco Bay food web (see below) using a different drawing algorithm. This view arranges guilds hierarchically instead of in a circular fashion. It is very interesting to note that “layers” roughly equivalent to trophic levels emerge naturally from the data. Primary producer guilds are at the bottom, and top predators at the top!

This figure was rendered by Rachel using AT&T’s Graphviz dot algorithm.

San Francisco Bay community food web

Tags

connectance, food webs, networks

Now that’s complex! This is a rendering of the metanetwork for the San Francisco Bay food web. The network consists of 163 nodes, each node being a guild. In total, they represent ~1,600 species of invertebrates and fish, as well as four nodes representing various types of autotrophic producers. There are 5,024 links or trophic interactions between the guilds. The dataset currently excludes birds and marine mammals. Those data are being incorporated even as I type! So, when faced with this level of complexity, how does one determine if the system is resilient, or vulnerable to the removal or addition of specific types of species, or can withstand the effects of climate change?

The figure was produced by one of my graduate students, Rachel Hertog, who has done a tremendous amount of work on this project, as well as the Dominican Republican paleocommunities. The data come almost entirely from the collections of the California Academy of Sciences, notably the Dept. of Invertebrate Zoology & Geology, and the Dept. of Ichthyology.