Coral reef species link distribution

Tags

coral reef, corals, food webs, Network theory, networks, power law, real world networks, small world networks

Species-level trophic link distribution.

The data presented in the previous post examined in-link or in-degree distribution at the guild level, i.e. species are aggregated into ecological guilds. A comment on the previous post asked whether we’ve used any grouping algorithms for guild recognition, and the answer is no, at least not yet (and thanks again for the comment). The current guilds are based primarily on trophic habits and habitat, and other features such as the presence of photo- or chemosymbionts. Guild derived algorithmically would be based on species-level network topology, and ideally, the two would be very similar. Anyway, I noticed the comment when I logged on to post the current results. What I’ve done is to expand the guild-level network (metanetwork) to the species-level, and then re-examine the trophic link distribution. There is no guarantee that the two distributions should agree. For example, it is quite possible that guilds of high in-degree (lots of prey), though few in number, are very species rich, and hence one would lose the decay distribution at the species level. Conversely, guilds of low in-degree could be tremendously more species rich, and would expand disproportionately, when compared to high in-degree guilds, when expanded into member species. Nevertheless, for this dataset, when guilds are actually expanded from 255 consumer guilds to 704 consumer species, the scale-free nature of the distribution is reinforced. The new function is y=11158x^-1.981, implying a power law exponent very close to 2. Neat.

Coral reef food web II

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coral reef, corals, food webs, Network theory, networks, power law, real world networks, Robustness, small world networks

Trophic link distribution

What sort of network is the coral reef food web? In other words, how are the links or interactions between nodes in a food web distributed? Food webs have been modelled variously as everything from random (Poisson) networks to networks based on exponential, power law or mixed distributions, with or without hierarchical structure. Empirical measures suggest that link distributions in real world food webs follow exponential or power law distributions, perhaps a mixture of both (differentiated by scale). One of my worries with those measures is that they are based on food webs of varying sizes, and more importantly, levels of taxonomic and ecological resolution. So, for example, how much does it matter if your food web covers only a small part of the community’s taxonomic diversity, or only part of the trophic diversity? What about the level of aggregation of species into more inclusive groups? The high resolution of the coral food web presents an opportunity to address some of these questions, and here’s the first one: How are trophic in-links distributed at the guild level? Recall that guilds here are groups of species with potentially the same prey and predators. I say potentially, for while we have very specific trophic data for some species, e.g. heavily studied fish, data are less certain for many smaller or less well known species. Still, there are 265 guilds in this dataset, and 4,756 links (see previous post). The histogram is a basic frequency histogram of the number of links per guild. As predicted on the basis of previously studied food webs, the distribution is a (right-skewed) decay distribution, with a greater number of species possessing fewer prey, i.e. being relative specialists, and a few species having a broad repetoire of prey, i.e. relative generalists. The extreme generalists (to the right or tail of the distribution) are all large sharks, the most extreme being the tiger shark, Galeocerdo cuvier. These species range from microscopic, single-celled dinoflagellates to large carcharhinid sharks!

What type of distribution is this? A simple logarithmic transform of the data is shown in the second figure, and regression of the data yields the following function: y = 17238x^-1.9496 (r-squared=0.95). The significant and extremely good fit of a linear function to the transformed data suggests that the underlying link distribution is a power law distribution of the form , where is the link probability, is the number of prey available, and is the power law exponent. An exponent of ~1.95 is tantalizingly close to other empirical measures. Even more exciting, for me at least, is the fact that we have predicted on the basis of previous work that power law exponents that promote resistance or robustness to secondary extinctions should lie in the range 2-2.5. That work was based on terrestrial food webs from the Late Permian, 250+ million years ago!

Coral reef food web I

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connectance, coral reef, corals, food webs, networks

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.

Corals, algae and space

Tags

competition, coral reef, corals, food webs, Tipping point

A new project involves working with the CEG model and coral reef communities. The main goal is an interactive and instructive module for education, but there’s no reason why the data could not be used for some research also. The exercises are to model the impacts of coral bleaching, and reduction/removal of higher trophic-level fish from the system. Now CEG specifically models potential secondary extinction of species, but it occurs to me that one of the major impacts that we observe on reefs is the decline of corals as dominant or co-dominant benthic cover. This is usually accompanied by an expansion of macroalgae with which the corals compete for space. So the model is being modified to examine the impact of the manipulation of trophic networks (food webs) on the spatial state of the reef (along with secondary extinctions, of course). You can read a bit more about this here.

Assume that the community begins in equlibrium (with regard to spatial competition) at time 0 (). If the relative population size of species i is , then equlibrium is expressed as

where is a competition coefficient (not a constant), and there are n competing species. Therefore,

Because population sizes are changing in response to non-competitive factors (trophic), we expect changes to relative population sizes, and hence the coefficient is dynamic. Hence the difference equation governing relative population size during a CEG cascade becomes

where

is the same for all competitors, and need be computed only once per cascade step.