Overpopulation? No problem!


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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.

Reining in the Red Queen


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(The Victorian Web)

Geerat Vermeij and I just published a new paper in Paleobiology, entitled ” Reining in the Red Queen: The dynamics of adaptation and extinction re-examined.” The paper is partly a follow-up to my earlier paper on the Red Queens Hypothesis, reported previously in these posts (here and here), and partly the result of a discussion started between Vermeij and myself while attending the workshop that resulted in this paper on state transitions in the global biosphere. Here we argue that some of the fundamental assumptions of the hypothesis are flawed and that it therefore likely holds only under restricted circumstances. The full reference and abstract follow.

Vermeij, G. J. and P. D. Roopnarine. 2013. Reining in the Red Queen: The dynamics of adaptation and extinction re-examined. Paleobiology 39:560-575.


One of the most enduring evolutionary metaphors is Van Valen’s (1973) Red Queen. According to this metaphor, as one species in a community adapts by becoming better able to acquire and defend resources, species with which it interacts are adversely affected. If those other species do not continuously adapt to compensate for this biotically caused deterioration, they will be driven to extinction. Continuous adaptation of all species in a community prevents any single species from gaining a long-term advantage; this amounts to the Red Queen running in place. We have critically examined the assumptions on which the Red Queen metaphor was founded. We argue that the Red Queen embodies three demonstrably false assumptions: (1) evolutionary adaptation is continuous; (2) organisms are important agents of extinction; and (3) evolution is a zero-sum process in which living things divide up an unchanging quantity of resources. Changes in the selective regime need not always elicit adaptation, because most organisms function adequately under many ‘‘suboptimal’’ conditions and often compensate by demonstrating adaptive flexibility. Likewise, ecosystems are organized in such a way that they tend to be robust and capable of absorbing invasions and extinctions, at least up to a point. With a simple evolutionary game involving three species, we show that Red Queen dynamics (continuous adaptation by all interacting species) apply in only a very small minority of possible outcomes. Importantly, cooperation and facilitation among species enable competitors to increase ecosystem productivity and therefore to enlarge the pool and turnover of resources. The Red Queen reigns only under a few unusual circumstances.

Simulating a Tragedy of the Commons II – Indirect cost



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

Two users, in a meadow...

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
c_{i}(t) = \frac{1}{N} \left [ R(t) - R(t+1)\right ]
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.

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 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.

Simulating a Tragedy of the Commons I


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TOC_sim1I introduced a recent paper, in the previous post, on the Tragedy of the Commons. The paper is published in Sustainability, an open access paper and is therefore available to everyone. One bit that I did not include in the paper, however, is the code that I used for the simulations therein. On the suggestion of a friend, I’ll publish them here in a series of posts. (Thanks Mauro)

The simulations are very simple, being based on difference equations, and were all coded in Octave. The code is not pretty, but I cleaned it up and added some comments. If you have questions, just drop me a comment on the blog. This first simulation is of a basic tragedy involving two users, and corresponds to Figures 1B-C in the paper. A resource is simulated to a steady state based on a Ricker model, for 100 steps, and then users begin to utilize it. They increase their utilization per time step at a steady rate (acceleration of utilization is constant), and the simulation is run until the resource is exhausted. The basic output of resource, one user’s benefit, and total utilization, are plotted in the figure here. The equations simulated are outlined in the excerpt from pg. 754 of the paper:
We now introduce a term to represent consumption or utilization by our human TOC agents.
\begin{aligned}  R(t) &=& R(t)e^{r\left ( 1-\frac{R(t)}{K} \right )} - U(t)R(t) \nonumber \\  & \Rightarrow & R(t)\left [ e^{r\left ( 1-\frac{R(t)}{K} \right )} - U(t)\right ]  \end{aligned}
where U(t) is the total fraction of R utilized by human users at time t, and ranges from 0 to 1. The term in square brackets on the right hand side of the equation is the modified growth rate of R. The resource is stable when this term is positive or zero, that is, the rate of resource renewal exceeds or is equal to utilization. Since U is the total standardized utilization rate of all users, it may be expanded to
0 \leq U(t) = \sum_{i=1}^{N}u_{i}(t) \leq 1
where there are N users and u_{i}(t) is the standardized utilization rate of the i^{th} user at time t. The benefit gained from utilization is modelled as
\begin{aligned}  b_{i}(t) &=& f_{i}u_{i}(t)R(t)\nonumber \\  B(t) &=& R(t)\sum_{i=1}^{N}f_{i}u_{i}  \end{aligned}
where b_{i} is the benefit to user i, f is a factor that converts resources utilized into another commodity, for example converting harvested food to energy or currency, and B is the total benefit to all users.

The code follows, and can be executed by running it in an interactive Octave session. Please be aware that WordPress has somewhat limited options for formatting code. I’ve used Matlab formatting here, but wrapped lines might not be obvious. Single lines are all terminated with a semicolon, “;”, so just look out for those.

#initial resource level
R0 = 1;
R = zeros(1,2);
R(1, 1) = 1;
R(1, 2) = 1;
#carrying capacity
K = 50;
#intrinsic growth rate r
r = 1.5;

#There are 2 users
#initial acceleration of utilization
du0 = 1.05;
#individual user parameters, users 1 and 2
#initialize arrays
u1 = zeros(1,2);
u2 = zeros(1,2);
b1 = zeros(1,2);
b2 = zeros(1,2);
u1(1,1) = 1;
#initial utilization rate
u1(1,2) = .001;
#conversion factor of resource to benefit
f1 = 1;
b1(1,1) = 1;
b1(1,2) = 0;
u2(1,1) = 1;
#initial utilization rate
u2(1,2) = .001;
#conversion factor of resource to benefit
f2 = 1;
b2(1,1) = 1;
b2(1,2) = 0;
U = zeros(1,2);
U(1,1) = 1;
#total utilization
U(1,2) = b1(1,2) + b2(1,2);
du = zeros(1,2);
du(1,1) = 0;
du(1,2) = du0;


for count2 = 2:100
  R(count2, 1) = count2;
  R(count2, 2) = R(count2-1, 2) * (exp(r*(1-(R(count2-1, 2)/K))));
  u1(count2, 1) = count2;
  u1(count2, 2) = u1(1,2);
  u2(count2, 1) = count2;
  u2(count2, 2) = u2(1,2);
  du(count2,1) = count2;
  du(count2,2) = du0;

for count1 = 101:265
  R(count1, 1) = count1;
  #modified Ricker model with utilization
  R(count1, 2) = R(count1-1, 2) * (exp(r*(1-(R(count1-1, 2)/K))) - (u1(count1-1,2)+u2(count1-1,2)));
  u1(count1, 1) = count1;
  #increase utilization
  u1(count1, 2) = u1(count1-1, 2) * du(count1-1,2);
  #benefits (equal for both users in this case)
  b1(count1, 1) = count1;
  b1(count1, 2) = f1 * u1(count1-1, 2) * R(count1-1, 2);
  b2(count1, 1) = count1;
  b2(count1, 2) = f2 * u2(count1-1, 2) * R(count1-1, 2);
  u2(count1, 1) = count1;
  u2(count1, 2) = u2(count1-1, 2) * du(count1-1,2);
  #total benefits
  U(count1, 1) = count1;
  U(count1, 2) = b1(count1, 2) + b2(count1, 2);
  du(count1,1) = count1;
  du(count1,2) = du(count1-1,2);

Ecology and the Tragedy of the Commons


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Well, it’s been quite some time since the last post, but I’ve been busy! This post is just a short notice of a new paper, just published today. The paper is part of a special issue on the Tragedy of the Commons in the journal Sustainability. My paper takes a comparative look at the Tragedy in ecological communities and human societies, and the potential of human mutualisms for avoiding tragedies. The situation is not a very hopeful one, however, given our ever-growing human population. Hardin did note this in his original essay. Finally, this paper was inspired by an earlier paper by myself and Ken Angielczyk.

Here’s a link to the paper, as well as the abstract.

Roopnarine, P. Ecology and the Tragedy of the Commons. Sustainability 2013, 5, 749-773.


This paper develops mathematical models of the tragedy of the commons analogous to ecological models of resource consumption. Tragedies differ fundamentally from predator–prey relationships in nature because human consumers of a resource are rarely controlled solely by that resource. Tragedies do occur, however, at the level of the ecosystem, where multiple species interactions are involved. Human resource systems are converging rapidly toward ecosystem-type systems as the number of exploited resources increase, raising the probability of system-wide tragedies in the human world. Nevertheless, common interests exclusive of exploited commons provide feasible options for avoiding tragedy in a converged world.

Of elections, polls and tragedies

This blog might seem an odd place to find a piece related to the recent U.S. presidential election, were it not for the fact that one of the highlights of the electoral drama was the polling scene and all those wonderful data. Many of you, numbers geeks like me no doubt, probably followed one or more of the excellent polls analyses online as the whole thing unfolded. Prominent among those were the analytical poll aggregators, my favourites being Nate Silver’s FiveThirtyEight, Votamatic, and the Princeton Election Consortium. The sheer audacious accuracy of those folks was a stinging indictment of political punditry, basically handing the talking heads Algorithms, Statistics, and Science. For those of you not familiar with what I’m talking about here, the numbers guys basically took the data being gathered by the armies of pollsters out there, and algorithmically decided what they meant.

And the pundits weren’t the only ones left lying about on the battlefield. If any of you were following the polls, the swings, disagreements and discrepancies left many of us scratching our heads sometimes. What one earth was wrong with them?! I certainly do not have an answer, but apparently some of the pollsters do. Frank Newport, Editor-in-Chief of the seriously (but apparently not fatally) wounded Gallup Poll offered up an explanation, which you can read in it’s totality here. He makes three main points (as far as I can discern). First, Gallup’s poll does not try to determine the winner of the election. It’s actual objective is to assess the popular vote. Okay, but then it is rather pointless in a republic based on an electoral college. No harm done, but I’ll scratch them off my RSS feed in 2016. Second, the political campaign game really has changed, what with the invention of these things called cell phones and social networks. They promise to get caught up before the next election. Third, and this is the one that I really want to address here, Newport backhandedly slams the aggregators as parasites, but he couches it in a somewhat clever reference to the Tragedy of the Commons. Okay, my turn to get analytical.

The Tragedy of the Commons, based on Garrett Hardin’s ground breaking 1968 essay published in Science, makes a simple argument: In a situation where a resource has multiple rational users, actions that benefit an individual can bring ruin to all. For example, consider a group of herdsmen. It seems reasonable that when he is able to, a herdsman will add another goat to his flock. The benefits of the additional goat are to the herdsman only, but because all herdsmen share a common pasture, the costs are distributed to all. This is quite a favourable arrangement for all the herdsmen, except for the fact that as herd sizes increase the quality of the pasture declines until it can no longer support any goats. Ruin to all. Newport, who refers to the concept as the Law of the Commons, claims that the statisticians are operating under a reverse tragedy. His argument is that you have these polling companies out there, such as Gallup, who are doing their business as best as they can, but by releasing their results the parasitic statisticians can then aggregate multiple datasets, crunch the numbers, and come up with a better answer than any single pollster could. In other words, and here’s the reverse, each pollster incurs all its own costs while distributing the benefits to all. Good point, right? No, not so fast, and here’s why.

  1. Gallup is a business, not a non-profit organization. If they were the only polling company, they would still distribute their data/results in order to earn income. Their distribution of benefits therefore feeds back into the company, but the worry now is that the quality of the product is questionable.
  2. The collective data of the pollsters is a commons, but for the aggregators only, because they are the only ones partaking of the aggregated data. It is therefore difficult to argue that any harm is being done to Gallup if they are simply dumping grass out there for someone else’s goats.
  3. In fact, if Newport and friends were smart, they would take his analogy seriously and run with it. Treat the data as a commons indeed and partake of the benefits. It is clear that the analytic methods being applied to aggregated data are vastly superior to the singular reports of any particular pollster. Rather than damaging polling, I think that Silver and others have demonstrated that there actually is a good data signal in there.

Therefore, if Gallup and others are serious about providing insight, they would each take advantage of all the data, conduct proper analyses, and produce useful results. Then the reversal of the tragedy would indeed be complete: the actions of the individual bring success to all! Oh, but I forgot something: They weren’t interested in the outcome of the election. Never mind.

p.s. You can read one of our food web-related arguments on the Tragedy here:

Roopnarine, P. D. and K. D. Angielczyk. 2012. The evolutionary palaeoecology of species and the tragedy of the commons. Biology Letters 8:147-150. DOI:10.1098/rsbl.2011.0662

One more time: Why model?


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A wonderful statement by Jay Melosh in a recent interview with Physics Today. It really underscores the approach of much of the research presented in this blog; just replace “physics” with “biology” or “ecology”. And while Melosh is a master of planetary geology and hence the history of the Solar System, we’re dealing here with evolution and the histories of species and ecosystems. Okay, here’s the quote:

Computer modeling, of course, plays a big role in evaluating the consequences of different hypotheses, which we then compare to observations. While the physics of an individual process may be simple, Nature is messy and computers are one of our principal tools for combining simple processes into the complex fabrics necessary to mimic observations and thus either validate or refute different hypotheses about what we see.

PNAS: Late Cretaceous restructuring of terrestrial communities facilitated the End-Cretaceous mass extinction in North America


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That’s the title of our new paper, hot off the PNAS press. This study was a lot of fun, because it combines my food web work with one of the best known events in the fossil record. The lead author is Jonathan Mitchell, a graduate student at the University of Chicago. Jon became familiar with the food web work via Ken Angielczyk at the Field Museum, also in Chicago, a former post-doctoral researcher in my lab and close collaborator.  Jon wondered what Late Cretaceous, dinosaur-bearing communities would look like when subjected to CEG perturbations (just search this blog for info. on CEG!), and presented his results two years ago at the Annual Meeting of the Geological Society of America. The results were so intriguing that we decided then to explore the question in much greater detail, and ask what sorts of community and ecosystem changes unfolded in the years before the Chicxulub impact, and what role they might have played in the subsequent extinctions. And here are the results! I will list the full reference below, and you can obtain a complete copy of the paper from PNAS (sorry, not open access). Also, here are links to some news websites that have covered the paper, as well as the paper’s abstract. Enjoy!

EurekAlert, Science Daily, Science Codex

Jonathan S. Mitchell, Peter D. Roopnarine, and Kenneth D. Angielczyk. Late Cretaceous restructuring of terrestrial communities facilitated the End-Cretaceous mass extinction in North America. PNAS, October 29, 2012


The sudden environmental catastrophe in the wake of the end-
Cretaceous asteroid impact had drastic effects that rippled through
animal communities. To explore how these effects may have been
exacerbated by prior ecological changes, we used a food-web
model to simulate the effects of primary productivity disruptions,
such as those predicted to result from an asteroid impact, on ten
Campanian and seven Maastrichtian terrestrial localities in North
America. Our analysis documents that a shift in trophic structure
between Campanian and Maastrichtian communities in North
America led Maastrichtian communities to experience more second-
ary extinction at lower levels of primary production shutdown and
possess a lower collapse threshold than Campanian communities.
Of particular note is the fact that changes in dinosaur richness had
a negative impact on the robustness of Maastrichtian ecosystems
against environmental perturbations. Therefore, earlier ecological
restructuring may have exacerbated the impact and severity of the
end-Cretaceous extinction, at least in North America.


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