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/

Sobering

I started to match our Caribbean coral reef food web data to assessments of Jamaican reefs today. I used 10 years of careful observations. I basically just sat there and watched my dataset fall apart as species after species failed to appear on the Jamaica list. Where have all the species gone? I’ve worked on extinction for quite some time now, I know many of the people who work on these systems well and we talk, and I talk a lot with relatives (mom included) who are Jamaican and remember the way that it was. It is depressing, it’s sobering, and it’s humbling. I don’t think that I’ve ever had a more depressing day of science. Our species is both remarkable, and remarkably stupid. Sigh.

Power law confirmed

Species-level trophic link distribution

Okay, this post just disappeared, so let’s try again. The updated and correct coral reef food web comprises 759 species. The incoming trophic link distribution, when expanded to the species level (compared to the guild level in the previous post), is a definite power law distribution. The log-transformed data (see figure) yield a function of , i.e. . See the earlier coral reef posts to understand why this is significant.

Coral reef trophic levels, & update

Guild-level trophic link distribution

Spent a great week at the Annual Meeting of the Geological Society of America. The Paleontology Society session on Conservation Paleobiology was a lot of fun, and my students also presented great posters. Now back to the coral reef.

I’ve been cleaning up the data, because with some much data, errors are bound to creep in. I believe that the current data are now accurate, and the metanetwork statistics are 265 guilds (including primary producers) and 4,651 links. That yields a metanetwork connectance of 0.066. The link distribution should therefore also be different, and indeed it is. The figure shows the no. of links per guild, and the regression plot demonstrates that the distribution is still a power law distribution. The exponent is smaller than previously calculated, (), but this is the guild-level network and does not reflect species richnesses (yet).

Trophic level vs. no. of links

The next question that I’m looking at is the distribution of trophic levels among guilds and species. I therefore calculated trophic level for all guilds. The first figure (scatter plot) plots trophic level against the number of prey or incoming links to each guild. There are two things to notice: First, the variance of trophic levels decreases as the number of links, or diet generality of the guild increases. Second, the decrease in the variance is asymmetric, in that there is a bias against being a generalist of low trophic level. This is obvious if you look at all the empty space being vacated below the data points as no. of links increases. I can think of two non-exclusive explanations for this. If you think about a food chain, consumers toward the top of the chain simply have more prey to select from (on an evolutionary timescale), and therefore there should be a natural increase in the number of generalists as trophic level increases. Also, note that there are also many specialists of high trophic level. Perhaps the ability to exert power over other species, as a predator, combined with the previous statement, explains this observation. Finally, what is the distribution of trophic levels within the community? The second figure is a simple histogram plot of all non-primary consumer guilds (i.e. omnivores and carnivores). The distribution is approximately normal, with a definite central tendency. On average, most guilds in the reef are of similar trophic level! That’s very interesting. And referring to the previous scatter plot, we know that there is a biased composition in the tails of the distribution, in that the upper tail (higher trophic level) is a mixed composition of specialist to generalist guilds, but the lower tail is basically restricted to low trophic level specialists.

Guild trophic level distribution

Some of you may have noticed that our trophic levels are non-integer numbers. Primary producers all occupy trophic level 1, and primary consumers are trophic level 2. “Above” that, trophic level is calculated on the basis of the trophic levels of your prey. Exactly how we do that will remain a secret for now.

Coral reef species link distribution

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.