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!

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.

Fighting to exist

Tags

competition, extinction

“A new study published today (June 14) in Ecology Letters provides experimental evidence for a an assumption of evolutionary biology accepted since Darwin first proposed it in 1859′s On the Origin of Species—that competition is greater among closely related species.”

That is the opening quote from a recent news article in The Scientist. The full article may be found here. The original research paper is in the most recent issue of Ecology Letters. The article doesn’t quite get this right, does it? It has NOT been a long-standing assumption of Darwinian theory that phylogenetic relatedness on its own drives competition. Phylogenetic relatedness is correlated with the frequency and intensity of competition to the extent that it reflects phenotypic overlap or similarity, which in turn will be a major factor in the extent of overlap in resource utilization. Extinction risk, therefore, is not a direct function of phylogenetic relatedness, at least not from the standpoint of competition for prey and other resources. It could play a role in terms of, say, resistance to predation or disease. To emphasize, two distantly related species will face the same risk if their phenotypic resource utilization is comparable to that of two significantly more closely related species. The journal article tests the effects of both trait and phylogenetic similarity, and conclude that phylogenetic similarity is a better predictor of the outcome of coexistence. I don’t understand how this could be the case, unless unmeasured traits are underlying factors. Am I missing something here?

New paper: Ecological modeling of paleocommunity food webs

Tags

cascades, competition, connectance, edge strength, extinction, food webs, interaction strength, link strength, modeling, Network theory, networks, nonlinear, paleontology, power law, probability, real world networks, Robustness, Scientific models, simulations, small world networks, Tipping point, top-down cascade

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/

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.