Systems Paleoecology – Allee Effects I

Tags

Allee effect, extinction, paleoecology, stochastic extinction

WHAT IS ECOLOGICAL STABILITY? In 2019 I posed this question informally to colleagues, using Twitter, a professional workshop that I lead, and a conference. Respondents on Twitter consisted mostly of ecological scientists, but the workshop included paleontologists, biologists, physicists, applied mathematicians, and an array of social scientists, including sociologists, anthropologists, economists, archaeologists, political scientists, historians and others. And this happened…

Previous posts in this series

1. Welcome Back Video
2. Introduction
3. Malthusian Populations
4. Logistic Populations
5. Logistic Populations II
6. Deviations from Equilibrium
7. r, R, and Bifurcations
8. Quasiperiodicity and Chaos
9. Chaotic Stability

10. Environmental Variation: Expectations and Averages
11. Nonlinearity and Inequality
12. States, Transitions and Extinction
13. Regime Shifts I
14. Regime Shifts II

In the previous post, we discussed the dramatic decline of the Atlantic cod (Gadus morhua) off Newfoundland over the past 60 years. I left us with the question of why, given the very limited catch sizes since the 1990’s, there was little evidence of population recovery (at least up until 2005). An Allee effect is a likely explanation for the failure of the population to recover during that extended period of reduced fishing pressure.

Beginning around 1994, the population may have become limited by an Allee phenomenon, or more appropriately mechanism, where a population’s size is limited far below the presumed carrying capacity, or observed maximum population size, because of reduced population size itself. Analogous to carrying capacity, where an upper limit is set on population growth rate by the effects of a relatively large population size, an Allee effect is an upper limit set by relatively small population size. Intuitive examples are easy to find, e.g. (1) species that require sufficient numbers for successful defense against predators will be increasingly limited by predation at low population size; (2) species for which habitat engineering by a sufficient number of individuals is necessary for offspring success; (3) species that depend on a minimum number of participants for the formation of successful mating assemblages. G. morhua, in which individual fecundity increases with age and body size (to a limit) (Fudge and Rose, 2008), is known to form, or have formed, large pelagic assemblages during spawning. Allee effects, therefore, describe situations where individual fitness depends on the presence of conspecifics, and is positively correlated with population size.

One vulnerability of populations subject to Allee effects is that small population size becomes an inescapable trap, with the likelihood of extinction increasing as population size declines. The reasons for this are twofold. First, if growth rates decline to zero or even become negative below an Allee threshold, then the state of zero population size becomes a stable state and extinction is assured. If you recall, our earlier models of population growth considered X= 0 (extinction) to be an unstable steady state; unstable because the addition of reproducing individuals to the population would result in divergence away from the zero state —population growth. Second, even if growth rate never becomes negative below the Allee threshold, a sufficiently large or sustained decline of population size increases the probability of extinction due to random events, a phenomenon termed stochastic extinction. Stochastic extinction, the probability of which could increase with deteriorating environmental conditions, is of interest to anyone studying extinction, including paleontologists, and will be discussed in a later section. Here, however, we will first explore several simple models of Allee effects.

Models of Allee effects

In the logistic model (Eq. 1 here), mortality rate increases as population size, X, approaches carrying capacity K, and population growth rate subsequently declines. The logistic model has two alternative steady states, X=K and X= 0, the latter of which is unstable as discussed above. The extinct state is a stable attractor, however, in the presence of an Allee effect. There are several simple models that demonstrate the effect, but to appreciate them, and the Allee effect itself, let us first examine the relationship between population size and growth rate under the logistic model. If we plot growth rate (dX/dt) against population size in the logistic model (Fig. 1), we see that the rate increases steadily at small population size, reaches a maximum when population size is half of the carrying capacity —X(t) =K/2— and declines steadily thereafter, reaching zero at carrying capacity. This value can be arrived at analytically because what we are visualizing is the rate of change of growth rate itself, technically the second derivative of the logistic growth equation. If we expand the logistic growth rate equation


and take the derivative, we derive the acceleration (or deceleration) of the rate of change of population size as a function of population size itself.

Setting d²X/dt equal to zero —the point at which growth rate is neither accelerating nor decelerating— we get the maximum that is illustrated in Fig. 1.


The important thing to note here is that growth rate is always positive when 0<X(t)<K, that is, when population size lies between zero and the carrying capacity.

Fig. 1: The relationship between population growth rate and population size under a logistic model. In this example carrying capacity K=100.

There are several ways in which an Allee effect can be modelled in a logistically growing population. For example, if the Allee threshold is represented as a specific population size A, then the effect can be incorporated into the logistic formula as

(Lewis and Kareiva, 1993; Boukal and Berec, 2002). The first term on the RHS of the equation is the logistic function, where growth declines to zero as X approaches K. The second term introduces the threshold, A, with growth rate declining if X < A, and increasing when X > A. Here, the effect is treated as the difference between population size and the threshold, taken as a fraction of carrying capacity, or maximum population size. Note that if A=0 —there is no Allee effect— the model reduces to the logistic growth model. A more nuanced model, where A must be greater than zero —an Allee effect always exists— treats the Allee threshold as equivalent yet opposite to K, representing a lower bound on growth rate (Courchamp et al., 1999).

If A=1 —in which a population comprising a single individual is compromised under all circumstances— then the strength of the Allee effect depends on the size of the population. In both models, growth rate becomes negative below the threshold A, effectively dooming the population to extinction (Fig. 2). This condition is often termed a “strong” Allee effect.

Negative growth rates, a feature that is common to many models of the Allee effect, can be somewhat problematic from a conceptual viewpoint because of their determinism. We’ll pick this point up in the next post, and also discuss why paleontologists might care about both Allee effects, and model determinism.

Fig. 2: Two models of strong Allee effects illustrates as plots of population growth rate vs. population size. K=100. Red shows the first model where growth rate is relative to the Allee threshold A as a function of K. Blue shows the second model where growth rate is relative to the threshold A itself.

Vocabulary
Allee effect — A positive correlation between individual fitness, or population growth rate, and population size. This means that fitness and/or growth rates decrease with declining population size.
Second derivative — The derivative of a function’s derivative (the first derivative), thus the acceleration (deceleration) of a rate. E.g. the first derivative of a body in motion, described by position and time, is velocity or speed. The second derivative is acceleration, or the rate at which the speed is changing.
Stochastic extinction — A relationship between the probability of a population’s extinction, and population size and/or environmental variability. In general, the risk of extinction increases due to random fluctuations of either factor.
Strong Allee effect — Population growth rate becomes negative below some threshold of population size.

References
Boukal, D. S. and Berec, L. (2002). Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters. Journal of Theoretical Biology, 218(3):375–394.
Courchamp, F., Clutton-Brock, T., and Grenfell, B. (1999). Inverse density dependence and the Allee effect. Trends in Ecology & Evolution, 14(10):405–410
Fudge, S. B. and Rose, G. A. (2008). Changes in fecundity in a stressed population: Northern cod (Gadus morhua) off Newfoundland. Resiliency of gadid stocks to fishing and climate change. Alaska Sea Grant, University of Alaska Fairbanks.
Lewis, M. and Kareiva, P. (1993). Allee dynamics and the spread of invading organisms.Theoretical Population Biology, 43(2):141–158

Systems Paleoecology – Regime Shifts II

Tags

alternative states, Atlantic cod, regime shift

WHAT IS ECOLOGICAL STABILITY ? In 2019 I posed this question informally to colleagues, using Twitter, a professional workshop that I lead, and a conference. Respondents on Twitter consisted mostly of ecological scientists, but the workshop included paleontologists, biologists, physicists, applied mathematicians, and an array of social scientists, including sociologists, anthropologists, economists, archaeologists, political scientists, historians and others. And this happened…

Previous posts in this series

1. Welcome Back Video
2. Introduction
3. Malthusian Populations
4. Logistic Populations
5. Logistic Populations II
6. Deviations from Equilibrium
7. r, R, and Bifurcations
8. Quasiperiodicity and Chaos

9. Chaotic Stability
10. Environmental Variation: Expectations and Averages
11. Nonlinearity and Inequality
12. States, Transitions and Extinction
13. Regime Shifts I

The Grand Banks of Newfoundland.

The Atlantic cod, Gadus morhua, has been the foundation of one of the world’s major fisheries for several centuries, with the Grand Banks off Newfoundland (Fig. 1) being amongst the most productive fisheries in the world. Figure 2 (below) shows the estimated population size of the Atlantic cod on the southern Grand Banks from the years 1959 to 2005 (Power et al., 2010), where G. morhua has historically been the most prominent component of that productive fishery. Cod populations, however, declined across the North Atlantic during the second half of the 20^th century, most notably in the northwestern Atlantic. Several factors might have played roles, including warming ocean temperatures and a resurgence of the predatory grey seal across its historic range after implementation of protection from hunting (Neuenhoff et al., 2019). There is little doubt, however, that over-exploitation by commercial fisheries has been one of, if not the most effective driver of the decline. The Grand Banks population initially increased steadily during the monitored period, reaching a maximum in 1966. Thereafter it declined significantly until 1976, after which it appeared to stabilize, before beginning a steady decline in 1985. Fishing mortality of older individuals (> 6 years old) meanwhile fluctuated, peaking in 1975 and again in 1991. Change point analysis, which is used to detect changes in the statistical distribution of data within a time series, suggests that the population underwent significant shifts in 1971, 1985 and 1993. Each time, the mean population sizes of the intervals defined by those shifts descended through transient phases to significantly lower sizes. The first transition, around 1971, was preceded by an interval of highly variable population size, yet those sizes all exceeded population size from 1971 onward. The period from 1975-1985 was characterized by reduced population size and low variability, but another change occurred in 1985, and by 1993 the population size had stabilized at abysmally low numbers, marking the end of the commercially viable fishery.

Estimated population size (connected line) and fishery catch size (red) for the period 1959-2005. Arrows show times of presumed regime shifts, as identified by change point analysis.

It seems reasonable to hypothesize that each interval between the change point transitions represents a stable state or regime of the population, with fishing mortality thus driving or contributing to transitions between multiple alternative states (Fig. 2). The relationship between fishing and population size is relatively straightforward. Initially, an increase of total catch in the late 1960’s followed an increase of population size, but then declined as population size itself began a steep decline in 1967. However, although population size continued to decline, catch size again increased in 1971, coincident with the time marked by the change point analysis as the first transition to a state of smaller population size. Catch size subsequently followed the decline of population size, reaching a minimum during 1978, after which it began to increase again, presumably in response to the relatively “stable” population. Population size increased after 1980, reaching a new maximum in 1985, but then after a sharp increase of catch size, began its decline to the low numbers at the turn of the century.

A phase map (Fig. 3) captures this journey of potential alternative stable states and transitions, and reveals two general types of regime shifts. First, the initial transition to the second state that persisted from the late 1970s to 1985 was likely both precipitated and maintained by fishing pressure. The continued decline of catch size between 1971 and 1978 might have in fact facilitated some recovery of population size. This is the first type of regime shift and the separation of states—an external driver is capable of moving the system between states, and of maintaining the system in at least one of those states. The basic dynamics of this type of regime shift can be understood in terms of external parameters. The second type of shift, however, is less transparent, because it involves intrinsic properties and dynamics of the system. Look closely at the population trajectory from 1995 on, the last transition of the series. Catch size is negligible over a period of ten years, yet there is no sign of population rebound. If, as claimed earlier, population size is driven by catch size, why didn’t the population recover, and what kept it in the final, most recent attractor or state?

Phase map of cod population size, plotting consecutive years against each other. Blue trajectories show intervals of presumed population stability, i.e., stable states. Red trajectories show the pathways of transition between those states.

References
Neuenhoff, R. D., Swain, D. P., Cox, S. P., McAllister, M. K., Trites, A. W., Walters, C. J., and Ham-mill, M. O. (2019). Continued decline of a collapsed population of Atlantic cod (Gadus morhua) due to predation-driven Allee effects. Canadian Journal of Fisheries and Aquatic Sciences, 76(1):168–184.

Power, D., Morgan, J., Murphy, E., Brattey, J., and Healey, B. (2010). An assessment of the cod stock in NAFO divisions 3NO. Northwest Atlantic Fisheries Organization SCR Doc, 10:42.

Pyron’s Puzzling Post Piece

Tags

Alexander Pyron, Conservation, ecology, environment, evolution, extinction, science

(Peter Roopnarine)

Alexander Pyron, a professor of biology at George Washington University, recently wrote an inflammatory op-ed for the Washington Post, entitled “We don’t need to save endangered species. Extinction is part of evolution.” The post outraged many, among them an awful lot of scientists. Needless to say, the piece is a seriously misguided bit of poor reasoning and inaccurate science, particularly with regards to extinction. Myself and colleague Luiz Rocha, also at the California Academy of Sciences, wrote our own response, published several days ago in bioGraphic. Regardless of your opinion on species conservation, Pyron’s article cannot be used as the basis for sound argument, because it is a collection of fundamentally flawed arguments. You can read our own reasoning here: Betting on Conservation.

The image, by the way, shows the fossilized burrows of tiny marine snails in sediments dating to about 250 million years ago. The fossils are from a geological exposure in the mountains of Hubei, China, and is some of the earliest evidence there of the biosphere struggling back from the devastating end Permian mass extinction of 251 million years ago. There are no guarantees in the History of Life.

I’ve edited this post to add a little addendum: While I disagree strongly with Pyron’s opinions, I cannot agree with or support the personal attacks which have been leveled against him by others. The core power of rationalism and modern science is open and free discourse. I think that his science in this case is wrong, and I disagree with his moral stance, but I would not place this in the same category of, for example, charlatan climate change deniers who have alternative and exploitative agendas. So let’s keep the discussion civil.

An update on the Deepwater Horizon spill

Remember the Deepwater Horizon drilling disaster? It’s been a few years now. This video is a brief update on some of our research on how the spill might have affected, and may still be affecting oysters off the coasts of Louisiana, Alabama and Florida. This has been very slow and difficult work, mostly because we have been monitoring the oysters for several years, and have had to develop protocols for the tissue analyses. But it is now moving toward publication.

Specimen collecting and cherry picking

Tags

biodiversity, california academy of sciences, endangered species, extinction, specimen collecting

In a recent opinion piece in Slate, Ben Minteer of Arizona State University continues to raise questions of the ethical legitimacy of collecting specimens for biological research. Minteer maintains that the risk to species, where population sizes might be small enough so that collecting represents a probabilistic extinction threat, outweighs the benefits to science and conservation. Unfortunately, Minteer is expressing an opinion, not the results of a carefully weighed and conducted analysis of data or facts. This is best highlighted by his example of the recent re-discovery of a species of New Guinea bat. Minteer states, “No scientist or conservationist today would deny the importance and value of describing a new species or confirming the return of one thought lost to extinction. But scientists also have a powerful ethical responsibility to minimize any and all adverse ecological impacts of their work.” Would that the world be so easily navigated. Today there are larger threats looming to biodiversity than at any time in the past 66 million years, and every one of those threats is the result of human actions. The threat of negative ecological impacts by scientists who are trying to document, explain and ultimately sustain what remains of the natural world pales hugely when compared to the threats of habitat destruction, the over-exploitation of species, and climate change. We will face very difficult decisions in the coming decades, and information is our friend, not our enemy.

Back to Minteer though. I think that his argument amounts to cherry picking and straw men. The reason for my position is best stated in a recent blog post by my colleague at the California Academy of Sciences, Dr. Jack Dumbacher. Jack explores the discovery of that very same bat picked by Minteer as an example, and he outlines very nicely the critical nature of the work. Please read his post. I’ll end here with an excerpt: “This study highlights the value of museum specimens in modern research, and the importance of taking specimens in modern field studies. Ironically, these studies were undertaken to assess the impacts of selective logging. The biggest threat to lowland forest in PNG is due to habitat loss from logging, mining, and oil palm conversion. One of the few things that might slow habitat loss is the fact that one little poorly known female bat was recently collected there.“

The legitimacy of collections for biological research

Tags

biodiversity, extinction

(copyright Python? via YouTube)

The April 18th issue of Science magazine included a piece by Ben Minteer of Arizona State University, and co-authors, “Avoiding (re)extinction“. The authors argued that the collection of specimens for biological research has, and may continue to place species at heightened risk of extinction, citing among other things stories such as the collection of the last remaining individuals of the Great Auk, as if those extinctions could be attributed to scientific collecting. The piece was very ill-conceived and poorly supported by evidence, basically constructing a straw man in the interest of argument (“But this is just contradiction.” “No it isn’t!”). Luiz Rocha, one of my colleagues here at the California Academy of Sciences, led a response which eventually involved 134 scientists hailing from 64 institutions around the world. Our response was published last week, also in Science. I cannot print any of the letters here, but I will include a link to our press summary.
SCIENTIFIC COLLECTIONS PLAY VITAL ROLE IN CONSERVATION BIOLOGY

Today is the Day of International Biodiversity

Tags

biodiversity, extinction, food webs

Today the UN and other organizations recognize the critical importance and threats to biodiversity around the world. The Species Alliance is recognizing the day by airing its documentary, Call of Life, on Free Speech TV (also streamed online). The documentary is followed by short interviews of myself (Peter Roopnarine), and Stuart Pimm. Please join if you can!

Overpopulation? No problem!

Tags

biodiversity, carrying capacity, human population, overpopulation, population growth

Giving Out Corn to the People, During a Season of Scarcity.”: Chinese officials engaged in famine relief. Detail of engraving by G. F. Sargent.

“Overpopulation is not the problem” goes a recent opinion piece in the New York Times by environmental geographer Erle Ellis. The core argument of the article seems to be that humans are unlikely to undermine ecosystems and ecosystem functions that sustain us. After reading the piece, however, I remain uncertain as to exactly which point the author wishes to prove. I question the article’s reasoning, (mis)representation of ecological concepts, and its historical interpretations.
 
Ellis launches his article by disputing any notions that disaster looms for humanity as our growing population threatens to exceed the Earth’s natural carrying capacity. His summary? “This is nonsense.” I agree, but only because the Earth’s natural carrying capacity is, in my opinion, a fuzzy and ill-conceived concept to begin with. I will point to a paper in Nature which I co-authored with a number of colleagues last year. There we argued that rapidly increasing human alteration of ecosystems, via species over-exploitation, landscape alteration, climate change and so on, threatens to push those ecosystems into a new functional state, most likely characterized by lower species richness and lessened ecosystem function. To the extent that humans depend on any of those species and functions, their loss will be felt. The notion of a finite carrying capacity for the planet is never emphasized in the article, however, because many of us involved do not believe that we have the necessary data to estimate that limit. Furthermore, arguments that ecosystems themselves represent an everlasting finite pie over which organisms must struggle are inconsistent with our record of the history of life on planet Earth. Geerat Vermeij and I make this very point in a recent article (see here). One view of life’s history reveals a stepwise increase in the quantity of energy fixed, transmitted and utilized by living organisms. So far not much to dispute with Ellis.
 
He immediately runs into trouble though as he wades into human prehistory, first pointing out, albeit correctly, that humans have a deep history of innovation, both social and technological, of exceeding the capacity of natural ecosystems to support human populations. The problem with this point is that it is only part of the story. Human societies have historically altered the environments around them to do things such as increase food production. Unfortunately, there are many examples in which either the alterations themselves initiated a slow and inexorable decline or change of environmental properties detrimental to the societies themselves, or the societies exhausted local natural resources on which they were dependent. Simplistic, blanket statements such as Ellis’ overlook too many of the intricacies and contingencies of human history. For example, the rapid rise of the Athenian Empire in the 5th century BCE was driven in part by the massive exploitation of natural resources to fuel Athens’ lucrative silver mines, and later the instrument of Athenian power, her super navy. As the trees ran out, the Athenians looked elsewhere for timber, coming to rely heavily on the kingdom of Macedonia to the north. Should I continue? There’s more than food at stake.
 
Ellis’ second point, and we’re still early in the article, is that humans learned over generations, as “their preferred big game became rare or extinct”, to increase the range of species on which they depended. And where is the evidence supporting the notion that the extinction of big game resulted in an increasingly diverse diet? In fact, if one wished to make the tenuous argument that it led to the domestication of cattle, wheat and so on, then one would have to concede that rather than increasing our repertoire of game, humans have in fact come to rely on a rather small and specialized subset of species. And in societies that did not do so, well, I believe that we refer to them today as hunter gatherers and nobody is too worried about their exploding populations.
 
The argument continues on to outline our ancestors’ triumphant climb to planetary dominance, claiming along the way that the Earth’s carrying capacity for prehistoric societies was probably no more than 100 million. As an ecologist, I have no idea what that claim is supposed to mean. Is the author claiming that if hunter gatherer societies had reached a total population of 100 million, that they would then have run into limits? Why? What would have limited them? Food production from natural ecosystems? Carrying capacity is far more than the amount of food out there. Species population sizes, humans included, are limited by more than just available food. There are other factors, driven by increasing population density, such as the more rapid spread of diseases, reduction of living space, good times for predators and parasites, and so on. And that brings me to the crux of what bothers me so much about this article, and that is the belief that we can continue to grow the human population without accumulating negative consequences, without risking the onset of additional and perhaps unseen negative consequences, without any reliance upon or concern for services provided by ecosystems, and with a blind belief that we will always innovate our way forward to address growing needs.
 
Thomas Malthus’ theory of exponential population growth does not claim that “population growth tends to outrun the food supply”. Malthus pointed out that without constraint, populations will indeed grow exponentially, but that growth is limited ultimately by the means and ability of the population to provide for itself. This is an important distinction. The idea that population growth is a driver of productivity, ascribed by Ellis to the economist Ester Boserup, should be interpreted carefully. Ellis interprets it positively, implying that population growth somehow facilitates productivity. Another interpretation of course is that population growth is a forcing agent of increased productivity because it applies constant pressure towards starvation. The fact is that the global human population has been growing approximately exponential since the 19th century, and certainly no earlier than that. The fact that some civilizations have supported substantial populations in the past, such as China and the Indian sub-continent, is indeed testament to the ability of human societies to organize and innovate to promote food production and security. But one should never lose sight of the dependence on the environment. Just ask the last members of the Tang Dynasty, whose final collapse was precipitated by the combined calamity of a breakdown of central authority and severe famine. Or the poor harvests during the final years of the Roman Empire. The margin for error is slim. In fact the history of China, trotted out as an example of population and productivity growth striding hand in hand, is punctuated by catastrophic famines and their socio-political consequences.
 
I suppose one could argue that technology will save us. This is indeed a possibility, and our global population, which has nearly doubled in my lifetime alone, is a fairly well-fed one. Many of the famines in the past century were caused as much by, or perhaps more by a lack of food security stemming from socio-political causes rather than environmental destruction. But predicting the future is a risky business, and simply saying that we can increase land productivity with existing technologies, and thereby never worry about rapid population growth, seems naive to me. I concede that I could be wrong, but I think that a far more likely scenario, given current trends and thinking, is increasing population size coupled with increasing per capita consumption, unrelenting domestication of natural spaces to support human consumption, degraded natural systems, and a globally declining quality of life. I stand with Ellis and others in the call for more sustainable means of production, but it is clear to me that sustainability cannot be achieved without proper protection and stewardship of Earth’s ecosystems. Perhaps there will be no starvation, but that will come at the cost of a world so transformed as to make the walls of the petri dish a wee bit more tangible.

Simulating a Tragedy of the Commons II – Indirect cost

Tags

Scientific models, tragedy of the commons

I continue the series on the Tragedy of the Commons, based on my recent paper in the journal Sustainability.

Two users, in a meadow…

A tragedy of the commons (TOC) is initiated when one or more users of a common, and unmanaged, resource increases its use of the resource. Because the resource is a commons, all the benefits of increased use accrue to that user alone but the cost to the resource is shared by all users. According to Hardin’s argument, other users are then compelled to increase their own use, presumably to maintain their levels of benefit. This argument is generally accepted by TOC studies, whether they are for or against Hardin’s suggestions of the frequency of TOC or his suggested solutions. If one takes a historical view of any particular TOC, however, then there must have been a point when total utilization by all the users was below the level of resource available and the amount being produced (remember, the resource is renewable!). The question then arises, why, if one user’s increased utilization does not affect your own benefit because of the plenitude of the resource, would you feel compelled to increase your own utilization? There are assuredly multiple, non-exclusive answers, including the ability of humans to forecast situations. In that case, you could perceive a future limitation of your own benefits, or potential for growth, and therefore engage in a somewhat competitive escalation of resource use. No matter, because benefits are still accrued by yourself only, while costs are distributed among all the users. This perceived, or indirect cost can be measured in terms of the developing model (see previous post) as

where c is the average cost to each user. Any reduction of the standing resource available is a positive cost, while increases are negative costs. A stable resource level means that no cost is incurred by any users. I illustrate the situation with the following cartoons:

One user increases his use of the meadow. The grey around the goats represents resource destruction or degradation.

The other user increases his own herd in response, further degrading the resource. Note, however, that there is still plenty of meadow available for herd expansion.

The situation changes significantly when total resource utilization reaches a point where individual user benefits cease to grow and actually begin to decline. Then, users are indeed compelled to increase use simply in order to maintain their current benefit. That is the classic TOC, but it leaves wanting the explanation for escalation of use prior to that point. I’ll take this up in the next post.

Coral reef food webs are out!

Tags

biodiversity, coral reef, corals, food webs, marine communities, real world networks, trophic guild

The first paper dealing with our Caribbean coral reef work is finally out. This paper is really just a detailed account of the data and webs compilation, but the data are now available to all. Enjoy!

Roopnarine, Peter D. and Rachel Hertog. 2013. Detailed Food Web Networks of Three Greater Antillean Coral Reef Systems: The Cayman Islands, Cuba, and Jamaica. Dataset Papers in Ecology, Vol. 2013, Article ID 857470, 9 pages.

Abstract: Food webs represent one of the most complex aspects of community biotic interactions. Complex food webs are represented as networks of interspecific interactions, where nodes represent species or groups of species, and links are predator-prey interactions. This paper presents reconstructions of coral reef food webs in three Greater Antillean regions of the Caribbean: the Cayman Islands, Cuba, and Jamaica. Though not taxonomically comprehensive, each food web nevertheless comprises producers and consumers, single-celled and multicellular organisms, and species foraging on reefs and adjacent seagrass beds. Species are grouped into trophic guilds if their prey and predator links are indistinguishable. The data list guilds, taxonomic composition, prey guilds/species, and predators. Primary producer and invertebrate richness are regionally uniform, but vertebrate richness varies on the basis of more detailed occurrence data. Each region comprises 169 primary producers, 513 protistan and invertebrate consumer species, and 159, 178, and 170 vertebrate species in the Cayman Islands, Cuba, and Jamaica, respectively. Caribbean coral reefs are among the world’s most endangered by anthropogenic activities. The datasets presented here will facilitate comparisons of historical and regional variation, the assessment of impacts of species loss and invasion, and the application of food webs to ecosystem analyses.