Habitat Earth

Tags

california academy of sciences, food webs, marine communities, networks, real world networks

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“Habitat Earth“, the new film by the Visualization Studio at the California Academy of Sciences opened this weekend in the Morrison Planetarium. The film documents the ecological interactions that take place continually in natural systems, featuring San Francisco Bay, a northern California kelp forest, and redwood forest watersheds in the northwest of North America. I was one of the science advisers and content persons for the film and am simply in awe of the visualization team. The science is authentic and researched in detail, but most impressive is the sheer amount of data incorporated and visualized. These data range from well-known ecological stories such as the sea otter role in maintaining diversity in kelp forests, to the thousands of food web interactions from my San Francisco Bay food web dataset, to documented tracks of thousands of migrating species and human ship traffic. It’s a masterpiece of science visualization, and I was very happy to be a small part of it. Here is a short trailer to the film, narrated by Frances McDormand. In the next few posts I will link to interviews with a number of the scientists involved. In the meanwhile, enjoy the trailer and, if you are in San Francisco, please stop by and see the film in the world’s largest all-digital planetarium dome!

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Modern and paleocommunity analogues

Tags

connectance, coral reef, food webs, marine communities, modeling, Network theory, networks, paleo-food web, paleontology, real world networks, Scientific models, trophic guild, trophic level

Last week I gave a keynote presentation at the annual conference of the Geological Society of America in Vancouver. Here is the abstract, and a link to the presentation (pdf file).

ANCIENT AND MODERN COMMUNITIES AS RECIPROCAL ANALOGUES OF PERSISTENCE AND STABILITY

ROOPNARINE, Peter, Invertebrate Zoology and Geology, California Academy of Sciences, 55 Music Concourse Dr, Golden Gate Park, San Francisco, CA 94118, proopnarine@calacademy.org
Paleocommunities are spatio-temporally averaged communities structured by biotic interactions and abiotic factors. The best data on paleocommunity structures are estimates of species richness, number of biotic interactions and the topology of interactions. These provide insights into paleoecological dynamics if modern communities are used as analogs; e.g., the recent lionfish invasion of the western Atlantic is the first modern invasion of a marine ecosystem by a high trophic-level predator and serves as an analog for the invasion of paleocommunities by new predators during the Mesozoic Marine Revolution. Despite the invader’s broad diet, it targets very specific parts of the invaded food web. This will lead to non-uniform escalation on evolutionary timescales.

Theoretical ecology provides a rich framework for exploring dynamics of community persistence. Persistence–the stability of species richness and composition on geological timescales–is central to paleoecology. Ecological stability, a community’s return to stability after perturbation, is not necessary for geological persistence. However, it does dictate a community’s response to perturbation, and thus a species’ persistence or extinction. What then is the relationship between paleoecological richness/composition and ecological stability? How do communities respond to losses of species richness or ecological function? Questions of stability and diversity loss are addressed with an examination of transient responses and species deletion stability analyses of end-Permian terrestrial paleocommunities of the Karoo Basin. Transience is measured as the degree to which a perturbation is amplified over ecological time, even as a community returns asymptotically to stability. Transience during times of frequent perturbation, as during times of environmental crises, decreases the likelihood of a persistently stable community. Species deletion stability measures the dynamic response of a community to the loss of single species. It is an open question whether communities become more vulnerable or more resistant during environmental crises. That process, which has occurred repeatedly in the geological past, is important to the fate of threatened modern communities.

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/

PNAS: Late Cretaceous restructuring of terrestrial communities facilitated the End-Cretaceous mass extinction in North America

Tags

Cretaceous, dinosaurs, extinction, food webs, mass extinction, modeling, networks, paleo-food web, paleontology, Robustness, Scientific models, simulations, Tipping point, trophic guild

That’s the title of our new paper, hot off the PNAS press. This study was a lot of fun, because it combines my food web work with one of the best known events in the fossil record. The lead author is Jonathan Mitchell, a graduate student at the University of Chicago. Jon became familiar with the food web work via Ken Angielczyk at the Field Museum, also in Chicago, a former post-doctoral researcher in my lab and close collaborator.  Jon wondered what Late Cretaceous, dinosaur-bearing communities would look like when subjected to CEG perturbations (just search this blog for info. on CEG!), and presented his results two years ago at the Annual Meeting of the Geological Society of America. The results were so intriguing that we decided then to explore the question in much greater detail, and ask what sorts of community and ecosystem changes unfolded in the years before the Chicxulub impact, and what role they might have played in the subsequent extinctions. And here are the results! I will list the full reference below, and you can obtain a complete copy of the paper from PNAS (sorry, not open access). Also, here are links to some news websites that have covered the paper, as well as the paper’s abstract. Enjoy!

EurekAlert, Science Daily, Science Codex

Jonathan S. Mitchell, Peter D. Roopnarine, and Kenneth D. Angielczyk. Late Cretaceous restructuring of terrestrial communities facilitated the End-Cretaceous mass extinction in North America. PNAS, October 29, 2012

ABSTRACT

The sudden environmental catastrophe in the wake of the end-
Cretaceous asteroid impact had drastic effects that rippled through
animal communities. To explore how these effects may have been
exacerbated by prior ecological changes, we used a food-web
model to simulate the effects of primary productivity disruptions,
such as those predicted to result from an asteroid impact, on ten
Campanian and seven Maastrichtian terrestrial localities in North
America. Our analysis documents that a shift in trophic structure
between Campanian and Maastrichtian communities in North
America led Maastrichtian communities to experience more second-
ary extinction at lower levels of primary production shutdown and
possess a lower collapse threshold than Campanian communities.
Of particular note is the fact that changes in dinosaur richness had
a negative impact on the robustness of Maastrichtian ecosystems
against environmental perturbations. Therefore, earlier ecological
restructuring may have exacerbated the impact and severity of the
end-Cretaceous extinction, at least in North America.

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.

Competition in food webs and other complex networks

Tags

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!

Number of predators per prey after extinction I: A start

Tags

extinction, food webs, link distribution, Network theory, networks

This series of posts are inspired by two questions that Jarrett Byrnes asked:

1. Given the extinction of E predators out of N, what is the probability that a prey species will still have at least one predator remaining?
2. Given E out of N, what then is the probability that all prey species will have at least one predator remaining?

As Jarrett and I have been discovering, these are actually quite difficult questions to answer in a general manner, i.e. for all topologies of a certain size!

Say we have a two trophic level food web with N predators, what is the probability that a prey species has at least one predator remaining after the extinction of E predators? The solution provided here depends on having the out-degree of prey species, and finding the probability that all predators of a prey species become extinct as a result of E. Say that the out-degree of the prey species is , then that probability is a hypergeometric solution

which reduces to

The probability then of a prey species having at least one prey is 1 minus the above

that is, the sum of the probabilities of having 1 predator, 2 predators, etc.

Example

Let the adjacency matrix of a food web be

where predators are rows and prey are columns. Our prey out-degree set is therefore {3, 2}. For E=1, both prey will have at least one predator since their out-degrees both exceed 1. For E=2, the possible resulting topologies are

For s=2

This is correct since our prey species of out-degree 2 (second column of A) has at least one predator in two of our three post-extinction topologies. The probability should be zero for s=3 (since E<s). If we add a third prey species, with s=1, making

then for E=1, the post-extinction topologies are

The probability that this third species has at least one prey is also 2/3.

A further example

So far so good, right? Well, Jarrett posed this example,

Notice that we now have two prey of out-degree 2. For E=1, the post-extinction topologies are

Applying the above formula yields

which is correct, since two of the three topologies maintain at least one predator for each prey. When E=2, the topologies become

Obviously, . But the formula gives

What went wrong?! The answer points to just how devilish the questions are, and how deceptive! There are two species of out-degree 2 (s=2) in the food web, hence the second term in the formula is squared (see above). BUT, the predator-prey topologies of the species are different, meaning that simple hypergeometric counting cannot work. We literally must list and examine all the post-extinction topologies, but this is prohibitively impractical for food webs and networks of even modest size (a dozen species). So there we stand. We currently have a partial solution, and I will explore the difficulty and the partial solution in the next post.

Instability in the Early Triassic!

Tags

competition, extinction, modeling, networks, paleo-food web, paleontology, Permian-Triassic, Scientific models

In a recent paper in the Royal Society Proceedings B, Randy Irmis and Jessica Whiteside verify a prediction of the CEG model regarding earliest Triassic terrestrial communities of the Karoo Basin in South Africa. Ken Angielczyk and I were interviewed by Wired Science for an article about the paper. Read it all here!

We predicted that communities in the Lystrosaurus Assemblage Zone would exhibit intrinsic instability in the face of even mild disruptions of primary productivity. More recently (and here), we explained that the intrinsic instability stemmed from the rapid diversification of small to medium-sized synapsid carnivores in the aftermath of the end-Permian mass extinction, coupled with very low species richness of herbivorous tetrapod prey, and the resulting intensity of competitive interactions among the carnivores. The recent Proceedings B paper seems to support our prediction on the basis of relative abundances of species of different trophic ecologies, characterizing those species as “boom and bust”. It’s always great to have model verification!

I think that there are some unresolved questions though:

1. We also suggested that one way out of the conundrum would be the increased specialization of the carnivores. Contrary to Irmis and Whiteside, I don’t agree that uneven relative abundances necessarily lead to demographic boom and bust cycles. Community dynamics are more nuanced and flexible than that.
2. The authors also point to probable environmental instability based on carbon cycles (measured as carbon stable isotope signatures). They valiantly overlap the short Karoo signature with the much longer and highly resolved marine signature. We simply have no good correlation of these signatures, and this is at least a nice attempt to highlight this ongoing issue.

Whether you can observe a thing or not depends on the theory which you use. (Einstein)

A species’s tragedy of the commons

Tags

biodiversity, carrying capacity, cascades, competition, extinction, food webs, interaction strength, link distribution, link strength, modeling, networks, paleo-food web, paleontology, Robustness, Scientific models, simulations, Tipping point, trophic guild

My colleague Ken Angielczyk and I have a new paper out in the Royal Society‘s Biology Letters, entitled “The evolutionary palaeoecology of species and the tragedy of the commons“. If you have never read Garrett Hardin’s original paper on the tragedy of the commons, I strongly suggest that you do. It is a principle that I believe has broad application, and would well be worth a re-visit (first visit?!) by today’s leaders and economists. Our paper can be found here or here (first page only). And here is the abstract, as a little teaser!

Abstract

The fossil record presents palaeoecological pat-
terns of rise and fall on multiple scales of time
and biological organization. Here, we argue that
the rise and fall of species can result from a tragedy
of the commons, wherein the pursuit of self-inter-
ests by individual agents in a larger interactive
system is detrimental to the overall performance
or condition of the system. Species evolving
within particular communities may conform to
this situation, affecting the ecological robustness
of their communities. Results from a trophic
network model of Permian–Triassic terrestrial
communities suggest that community perform-
ance on geological timescales may in turn
constrain the evolutionary opportunities and
histories of the species within them.

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.