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

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!

Heavy metal oysters

Tags

california academy of sciences, Deepwater Horizon, environment, oil spill, science

On April 18th, as the second anniversary of the Deepwater Horizon accident approached, the California Academy of Sciences published a press release regarding some of our research on coastal oysters in the Gulf of Mexico. You will find a nice reprint of it here in Science Daily. In a nutshell, our study compared specimens collected in the Gulf during the 20th century, in May 2010 prior to landfall of the spill, and August 2010 (and some intervals after that) after landfall of the spill. We also included a specimen collected off North Carolina in 2010. Our main conclusions are:

1. Concentrations of several heavy metals, vanadium, cobalt and chromium, are significantly higher in shells exposed to the spill.
2. Concentrations of several heavy metals, vanadium, cobalt and lead, are significantly higher in gill and muscle tissues of specimens exposed to the spill.
3. Eighty seven percent of specimens exposed to the spill and examined by us show transformation (metaplasia) of gill tissues.

It is very important to note that these results are preliminary, and both our sample sizes and coverage (temporal and geographic) will be increased as time goes on. It is also important to note that we are not claiming that the levels of these metals are dangerous to humans. Much more work, and additional expertise, are required to make that decision. We are ultimately interested in the environmental impact of the spill, and the ability to assess and trace the impacts of future such accidents.

Nevertheless, our results have proven to be quite unpopular with some folks, and has drawn both ire and support from various quarters. A very nice summary of the controversy, and the exchanges, can be found in this article from Food Safety News. To the supporters, you have my sincere appreciation.