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/

Coral reef data now available on Dryad

In addition to the publication (see previous post), data for the Greater Antillean coral reef food webs are now available on Dryad.

• Roopnarine PD, Hertog R (2013) Data from: Detailed food web networks of three Greater Antillean coral reef systems: the Cayman Islands, Cuba, and Jamaica. Dataset Papers in Ecology doi:10.5061/dryad.c213h

From Dryad: ”

Dryad is an international repository of data underlying peer-reviewed articles in the basic and applied biosciences. Dryad enables scientists to validate published findings, explore new analysis methodologies, repurpose data for research questions unanticipated by the original authors, and perform synthetic studies. Dryad is governed by a consortium of journals that collaboratively promote data archiving and ensure the sustainability of the repository.”

Coral reef food webs are out!

Tags

biodiversity, coral reef, corals, food webs, marine communities, real world networks, trophic guild

The first paper dealing with our Caribbean coral reef work is finally out. This paper is really just a detailed account of the data and webs compilation, but the data are now available to all. Enjoy!

Roopnarine, Peter D. and Rachel Hertog. 2013. Detailed Food Web Networks of Three Greater Antillean Coral Reef Systems: The Cayman Islands, Cuba, and Jamaica. Dataset Papers in Ecology, Vol. 2013, Article ID 857470, 9 pages.

Abstract: Food webs represent one of the most complex aspects of community biotic interactions. Complex food webs are represented as networks of interspecific interactions, where nodes represent species or groups of species, and links are predator-prey interactions. This paper presents reconstructions of coral reef food webs in three Greater Antillean regions of the Caribbean: the Cayman Islands, Cuba, and Jamaica. Though not taxonomically comprehensive, each food web nevertheless comprises producers and consumers, single-celled and multicellular organisms, and species foraging on reefs and adjacent seagrass beds. Species are grouped into trophic guilds if their prey and predator links are indistinguishable. The data list guilds, taxonomic composition, prey guilds/species, and predators. Primary producer and invertebrate richness are regionally uniform, but vertebrate richness varies on the basis of more detailed occurrence data. Each region comprises 169 primary producers, 513 protistan and invertebrate consumer species, and 159, 178, and 170 vertebrate species in the Cayman Islands, Cuba, and Jamaica, respectively. Caribbean coral reefs are among the world’s most endangered by anthropogenic activities. The datasets presented here will facilitate comparisons of historical and regional variation, the assessment of impacts of species loss and invasion, and the application of food webs to ecosystem analyses.

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.

Resource overlap in Caribbean reef fish

Tags

competition, food webs, interaction strength, marine communities, nature, science, trophic level

I introduced a weighted index of interspecific resource overlap in the previous post. The overlap is measured as the number of prey resources shared by two species, as indicated in a food web network (or more properly, its adjacency matrix). The index is the ratio of the squared overlap to the product of the in-degree of the two species:

where C is the index for species m and n, I is the resource overlap, and k is the in-degree of a species. The index is symmetric for the species, equals 1 for a species compared to itself, and will also equal 1 if two species share identical prey and are of the same in-degree. Note that C falls short of a measure of interspecific competition in the absence of crucial demographic data about both species, as well as the strengths of interaction with prey.

So what can you do with this? Lots I think, but here’s something that we’ve been looking at. The first figure plots the ranked C values for the Caribbean reef shark, Carcharhinus perezi, versus all other species (or guilds) in the Cayman Islands food web, including invertebrate taxa. C is zero, or near zero, for many of those comparisons, because most nodes in the web share no or few prey resources with the shark. Note that the shape of the plot reflects this with its very long, flat tail. C rises sharply for highly ranked comparisons (left end of plot), indicating that the shark’s resource use overlaps with very few species, but when there is overlap, it is distinctly greater than most of the other comparisons. The red symbol is the species with which there is greatest overlap, the Yellowfin grouper, Mycteroperca venenosa. Does this indicate potentially significant competition between these two species? That’s difficult to tell from a single set of C values, so we’ll turn to the comparative method.

The second plot is also of ranked C values, but this time for the large Nassau grouper, Epinephelus striatus. Note two things right away. First, highly ranked C values are much larger than they are for the shark, indicating greater resource overlap between the grouper and a number of other species than there is for the shark. Second, the shapes of the plots are quite different! Whereas for the shark there are a few strong overlaps and a majority of weak ones, the grouper has strong overlap with a large number of species. In fact, the overlap between the shark and the Yellowfin grouper would only rank around 60 for the Nassau grouper! Things are certainly busier for the Nassau grouper. By the way, the most highly ranked overlapping species with the Nassau grouper is the gray snapper, Lutjanus griseus.

I find it fascinating that two large, and high trophic level predators on the reef exist under such different conditions of overlapping resource use. One very important thing to keep in mind, however, is that our food web reflects the (current) rarity of other large sharks on the Cayman reefs, and the situation could well be quite different where some of those species are present. Furthermore, as explained before, the reef food webs omit a fair number of species because the available trophic data are simply insufficient. And finally, I have to plug my invertebrate friends here, stating that I look forward to doing this sort of analysis on some of the very rich and functionally diverse molluscan and crustacean clades!

Competition in food webs and other complex networks

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competition, coral reef, food webs, interaction strength, link strength, Network theory, networks, science

Competition is considered by many ecologists to be a major structuring factor in communities. It is a notoriously difficult thing to identify, classify and measure in the field and has been, in my opinion, an inspiration for some of the more elegant field studies. There is no doubt that species compete for resources in nature, but more elusive are answers to how much that competition matters to the stability of a species population, and the community as a whole, and what role competition might play on longer, evolutionary timescales. Typically, when we wish to measure competition, we require a few pieces of basic data, such as population sizes, interaction strengths and frequencies with the resource(s) being competed for, age structuring and so on. How can we go about doing this with complex food webs lacking these data? As usual, my answer is that you cannot, simply because of a lack of data. Nevertheless, I think that complex food webs do have something to say about competition, as long as one realizes that there is a trade-off between details of microscopic interspecific interactions and grabbing a macroscopic view of the community. Recently I’ve been mulling over appropriate ways to do this, and here are some ideas. I will preface them by saying that the interest stems from examining the potential impact of an invasive species as a competing consumer.

Let us begin with a (asymmetric) binary adjacency matrix, A, whose elements indicate whether species i preys on species j. The question is, what is the interaction between two consumer species, i and m. My first step is to simply count the number of prey shared between i and m, measured as the Hamming distance between the and rows; let’s designate that (). We can refine our view a bit by asking what fraction of a species’ prey is represented by that overlap, which is simply

where is the in-degree, or number of prey for species i in the food web network. You can think of this as the potential impact of species m on i. This is not quite satisfactory though, because and may be vastly different. For example, in our Caribbean coral reef food webs, many reef foraging piscivores (fish eaters) are specialists, preying mostly on maybe six other species, with those prey also being part of the repertoire of more generalist piscivores such as carcharhinid sharks who also forage on the reef and have k in the range of 70-80. It would be difficult to conceive of two such consumers as being strong competitors if the interactions of the generalist are distributed broadly over its prey. I therefore assume, in the absence of data on population densities, interaction strengths and functional responses of predators to prey, that this network measure of competitive interaction will be a function of both prey overlap (H) and consumer dietary breadth (k). There will be a trend of increasing pairwise strength of competitive interaction from generalist-generalist to generalist-specialist to specialist-specialist.

We can now extend our formulation in the following manner. First, count the number of prey shared between the consumers, . Then weight the interaction strength between m and its prey uniformly according to (ala CEG). The total interaction strength is

which is also the fraction of i’s prey that is being affected by m’s predation. The unaffected fraction, standardized to i’s dietary breadth is

yielding a standardized impact of

Note that this index is symmetric for i and m, i.e., it is the SAME for both species.

As a worked example, consider four species, A, B, C and D, with k’s of 60, 70, 2 and 2 respectively. The overlap of resources are: AB-35, AC-2, CD-1. The competitive indices are


and

I use in keeping with a conventional symbol for competitive interaction, but again point out that this is a very unparameterized measure compared to what is normally considered for use in Lotka-Volterra-type models or as measured empirically. You’ll notice that the values increase as the specialization of the interactors increases. It would be nice to scale these to a unit maximum to facilitate comparison, but I haven’t done that yet.

In a follow-up post I’ll provide some worked examples of all the above using real species from a real coral reef food web!

A Plague of Sea Stars | The Ocean Portal | Smithsonian Institution

A Plague of Sea Stars | The Ocean Portal | Smithsonian Institution.

“Sea stars are important members of marine ecosystems, especially in the tropics. We may think of tropical coral reefs as being home mainly to fish and corals, but in fact these habitats are home to a huge diversity of ecologically important invertebrates…”

BBC News – Coral reefs heading for fishing and climate crisis

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climate change, coral reef, corals, extinction, marine communities, pollution

BBC News – Coral reefs heading for fishing and climate crisis.

Jamaican reefs lack specialized foragers

Tags

connectance, coral reef, food webs, generalists, link distribution, marine communities, specialists

Results from an earlier post, based on REEF data only, suggested that the Jamaican reef food web is more connected than either the Caymans or Cuba. Our augmented data set (see previous post) now confirms this. Jamaica, of intermediate vertebrate species richness (S=160) has a connectance, C=0.06032, while the Caymans are S=156, C=0.05949, and Cuba, S=176 and C=0.05972. Are these differences in any way significant? That’s a difficult question to answer, since we really don’t know if there is a distribution underlying food web connectance. We tested it, again as reported earlier, but asking the following question: “Given a regional species pool comprising all species observed on at least one of our islands, what is the expected C for a system of size S?” To answer the question, we generated numerous food webs with random draws from that regional species pool (1,000 food webs per S shown in the figure). There is an expected regular relationship between C and S (blue regression line), but Jamaica is well above the curve. Random draws for S equalling exactly the richnesses of the island food webs confirms that Jamaica is more significantly connected than would be expected if it was a random draw from the regional species pool (10,000 randomizations, p=0.0054; p=0.2296 and 0.0548 for the Caymans and Cuba respectively).

Recall that the formula for connectance is

Two questions now come to mind. First, why does C increase with S? And second, how can Jamaica be more connected than Cuba? The answer for the first question lies in the shape of the link distribution curves. They are right-skewed and long-tailed. This means that a random draw from one of those distributions is likely to yield a species of intermediate to low in-degree, that is, a species with a low density of links. But as the number of species drawn approaches the maximum number of species available, the probability of drawing species out on the long tail, that is, link dense species, increases. So as far as C is concerned, you’re getting more bang for you buck. Okay, then why is Jamaica’s connectance greater than Cuba’s? Because Jamaica is not an unbiased or random draw from the pool. Somehow, Jamaica has an unusually high component of link-dense or high degree species. It’s drawing preferentially from the long tail! A better way to view this, is that Jamaica is lacking in trophic specialists.

Comparison of in-degree distributions for reef foragers present in Jamaica (blue) vs. those missing (green)

A little data exploration shows this to indeed be the case. If we compare species present in one of our communities to species absent., but present in one or both of the other two communities, it is clear that Jamaica has a lower than expected number of specialized reef foragers. In other words, if you’re looking for species that forage only on the reef (and not seagrass beds), and that have a specialized diet, don’t expect to have as much luck finding them in Jamaica as you would in the Caymans or Cuba. Why? Well, that’s a very difficult question to answer. Perhaps specialists have a more difficult time establishing themselves as new colonists; but they don’t seem to have a problem other than in Jamaica. Maybe specialists, with their smaller number of resources, are more prone to extinction if the system is disturbed in some way. Or, maybe us Jamaicans find specialists to be tastier than generalists! We’ll explore these possibilities in future posts.

More resources for Cuban reef fish

Tags

coral reef, food webs, link distribution, marine communities

We’ve spent some time augmenting our REEF-based data in light of the uneven sampling intensities in the Caymans, Cuba and Jamaica. Major additional sources include GBIF and Fishbase. We now have both occurrence records and trophic data for 192 vertebrate species, with Cuba being the richest island (177 species), followed by Jamaica (163 species) and the Caymans (159 species). The trend coincides with reef area of the three systems, but we must be careful to not over-interpret these somewhat noisy data. So what have we learned so far?

Comparisons of the trophic in-degree distributions, or the number of prey species/resources of the vertebrate species reinforces our earlier result showing that these are modal, right-skewed and long-tailed distributions. They differ from “conventional” food web distributions which are almost never modal, with attention being focused on the long tail. Here, we see that on average, species in all three communities have a similar number of incoming links. There are more specialized species, but specialists are never most common. Also note the difference between Cuba and the other two systems. Density is essentially shifted toward the right tail, i.e. generalists, in the Caymans and Jamaica. What does this mean for the species? Pairwise comparisons of the in-degrees of species that are found in two systems indicate that species in Cuba (CU) have significantly more prey resources, in-links, than they do in the Caymans (CY) or Jamaica (JA) (Wilcoxon test of equality; CY vs. CU, n=153, p<0.0001; JA vs. CU, n=142,p<0.0001; JA vs. CY, n-142, p-0.5653; Bonferroni corrections applied). When broken down by the three major foraging habitats, seagrass beds, reefs, and both seagrass beds and reefs, the significance holds up for the latter two habitats. The meaning for populations in these systems is a bit difficult to predict, but it would at least imply a greater susceptibility to stochastic or exploitative perturbations of the Cayman and Jamaican communities.

Some of you might have picked up on an apparent paradox: the Cuban distribution has more specialists, yet species in the Caymans and Jamaica have fewer resources. There’s no paradox really; the difference lies in species that do not occur in two or more systems. I’ll show in the next post that not only are species in the spatially smaller communities of lesser degree, but that in at least one of those communities, there is a dearth of specialists.