Jamaican coral reef I

Fig. 1 - Species-level trophic link distribution for entire coral reef.

We’ve examined records of fish occurrences on Jamaican reefs for the past 10 years, and compared it to our “master” food web. Of the 196 species in our food web, 136 have records in Jamaica. Many of these species are present in very low numbers, and some reefs are noticeably depauperate, recording less than 60 species. Nevertheless, to be conservative, we assume that we can integrate over all the reefs, thereby counting all 136 species as being present. We next expanded our metanetwork, or guild-level food web (in this case almost exactly the same as a trophic species-based web) to the species level, therefore accounting for all expected links in the food web. For the master or pristine web, this yields an overall connectance of 0.059. The trophic link distribution is shown in Fig. 1. Interestingly, this is clearly not a decay distribution (e.g. power law), but has a definite modality of about 25 links. One needs to question the extent to which under-sampling of natural food webs, and aggregation into trophic species, affects interpretation of link distributions.

The next step of course is to assess the state of the Jamaican reef system. Our initial analysis has been to simply remove the “missing” species (extirpated) from the web, and to re-calculate the statistics. Connectance declines to 0.055. Is this significant? Probably impossible to answer that question for network connectance. Also, it should be noted that hundreds of invertebrate species are included here, and they will dampen the impact of any fish removals or additions. Perhaps the next question regards the link properties of the extirpated species.

New paper: Ecological modeling of paleocommunity food webs

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.

Find the paper here:
http://zeus.calacademy.org/roopnarine/Selected_Publications/Roopnarine_09.pdf
or here
http://zeus.calacademy.org/publications/

Coral reef food web I

Caribbean coral reef food web

I’ve been compiling data for a Caribbean coral reef food web. This is intended to be a “typical” coral reef of the Greater Antilles region, focusing on Jamaica. Data are drawn, however, from a more general region encompassing the Cayman Islands, Jamaica, Cuba, Hispaniola, Puerto Rico and the U.S. Virgin Islands. The U.S.V.I. were included because of the large amount of data available for the reefs there, particularly fish. It has been a rather large task to assemble species lists for this region because of the tremendous species richness of the reefs, as well as the scattered nature of the literature. Most major animal groups have been included, with notable exceptions being barnacles, sea stars, and some minor but probably important groups, such as sipuncula, echiura, crinoids and brachiopods. All major producer groups are also specified at the species level, including nannoplankton, diatoms, macroalgae, etc. The community comprises the reef habitat and adjoining seagrass beds.

The current compilation includes a total of 905 species, for which trophic data are available for 761 (84%). The 761 species are further collapsed into 265 guilds. Guilds range in size from 1 species up to 54 species (symbiont-bearing scleractinian corals). There are 4756 links among guilds, yielding a guild-based connectance of 0.068, well within the range of connectances for published, lower resolution communities. That’s a lot of stuff happening on the reef! It is surprising to realize, though, how little we know about many familiar species, or perhaps how poorly documented that knowledge is. The situation would be far worse if I accounted to the true diversity of the reef, which must range into several thousand species. One can only imagine the difficulties in attempting this with an Indo-Pacific reef or a tropical rain forest. Sadly, the current condition of many Caribbean reefs means that my compilation is an overestimate, being based on accounts dating back to the 1950’s, when the reefs were still in reasonably good shape, by 20th century standards anyway.

Food web robustness

Jennifer Dunne, in a recent paper (Dunne et al., 2009), defines the structural robustness of a food web as a minimum level of secondary extinction that occurs in response to a particular perturbation (species removal). This is roughly what I’ve termed “resistance”, but I think that structural robustness will be a very useful and more precise definition. The paper is part of a recent issue of the Philosophical Transactions of the Royal Society on food webs. Several papers in that volume point to the relationship between diversity and “robustness” (often used less specifically than defined by Dunne), but the nature of this relationship, if any, remains problematic.

Given our (the CEG group) growing collection of ancient and modern data sets, plus the array of CEG programs that we now have, I’ve decided to examine this question a bit more closely using a number of different communities. The main questions are:

1. Is there a straightforward relationship between species richness and food web robustness?
2. Does the relationship differ between marine and terrestrial communities?
3. Does it differ on the basis of geological age?
4. Does it differ between fossil and modern communities, given differences in data completeness?

Both topological or structural perturbations, as well as CEG dynamic perturbations are being performed on each data set. Answers to the above questions most likely differ dependent on whether species interactions are purely topological, or are dynamic! Perturbations are bottom-up disruptions of primary productivity, removal of top predators (top-down cascades), removal of most connected, and removal of least connected species.

The figure shows results from the Early Permian Waurika locality of Oklahoma. These data were compiled by Ken Angielczyk. The treatment is a bottom-up disruption of primary productivity at three different levels of species diversity: 1x, 2x and 3x observed (higher) taxon diversity. Treatments are also repeated for three different models for trophic link distributions, exponential , mixed power law-exponential where , and power law . Two conclusions: First, the effect of increasing total species diversity is to reduce the variance of the results, and perhaps reduce the overall mean (i.e. increase robustness), but the significance of this change has to be tested. Second, there is a striking difference among the trophic link distributions. The transition from Level I to Level II secondary extinction is discontinuous for the exponential and mixed distributions, but continuous for the power law (though the interval of transition is represented by acceleration of secondary extinction). What causes this?

San Francisco Bay community food web

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.

Nonlinear cascades

All the simulations described so far are of bottom-up perturbations to the basal level producer guilds. Network theory predicts that given networks such as food webs, with power law-like link distributions, the networks should be robust against random removal (extinction) of nodes, while being highly vulnerable to the removal (perhaps targeted) of highly linked (hub) nodes. This of course is a topological prediction, since it in no way incorporates dynamics of link strengths, compensatory modification of link strengths, or extinction thresholds (e.g. those Allee effects). Then, why do the CEG predictions and simulations of topological effects have a gradually, mildly exponential, rate of increase of secondary extinctions as the number of nodes removed is increased? The answer is two-part:

1. The probability of link loss increases with the in-degree of the consumer. Therefore most of the links being lost at any given level of perturbation are lost by highly linked species. But those species are also the most resistant to extinction.
2. The probability of secondary extinction increases almost linearly for consumers of very low degree, but almost not at all for the most highly linked species, until levels of perturbation are very high. Therefore most of the extinctions that occur at low to mid- levels of perturbation are of poorly connected species.

The nonlinear increase seen in the CEG simulations is therefore likely a response to a threshold being reached where highly linked consumers, though still robust to topological extinction, initiate significantly devastating top-down cascades because of compensatory increases of link or interaction strengths.

It is also therefore reasonable to hypothesize that very high levels of secondary extinction at low perturbation levels is the result of having a few highly connected, upper-level consumers. This could explain the great difference, at those perturbation levels, between the topological expectations and the simulations. Should low diversity communities, or communities with low diversities of high trophic level consumers, then be limited to those consumers being very specialized?