Revisiting Colwell and Lees 2000

In a paper published in Trends in Ecology & Evolution in 2000, Robert Colwell and David Lees reviewed the conceptual and empirical literature on the influence of the “mid-domain effect” – geometric constraints in geographic patterns of species richness caused by physiological and physiographical boundaries. Sixteen years after the paper was published, I asked Robert Colwell about the motivation to write this paper, his collaboration with David Lees and what we have learnt since about the mid-domain effect.

Citation: Colwell, R. K., & Lees, D. C. (2000). The mid-domain effect: geometric constraints on the geography of species richness. Trends in ecology & evolution, 15(2), 70-76.

Date of interview: 26th September 2016 (on Skype)

Note: Robert Colwell thanks David Lees for helping him remember several details provided here

Hari Sridhar: I want to start by asking you about your motivation for this particular paper. By looking at your publications and at the references cited in this paper I realized that there are four or five other papers that sort of form the basis for this one. In the second paragraph you say: “…something fundamental has, until recently, been almost completely ignored: the geometry of species ranges in relation to geographical   boundaries.” You talk about a few simulation examples and a couple of analytical null models. So I wanted to ask you what, at this point in 2000, was the motivation to write this particular paper.

RC: This all started in 1993. I was sitting in my living room and thinking about a paper I was reviewing, by Klaus Rhode, on Rapoport’s rule, and how to analyse data for Rapoport’s rule, and there were two ways to do it. You know about Rapoport’s rule right?


HS: Yes.

RC: One way is just to make what we call “Stevens plots,” the way George Stevens originally did it, which was to plot mean range size at points evenly spaced over a latitudinal gradient. The problem with that approach is that you keep re-sampling the wide ranging species, and so wide-ranging species contribute disproportionately. The other way to do it is one point per species on a range-midpoint plot. Rhode was thinking about that, and I started thinking about it, and I realized that the range-midpoint plot has very interesting properties that had nothing to do with Rapoport’s rule. From that I came up with the idea for the paper with George Hurtt in 1994, called “Non-biological gradients in species richness…”. That’s the MDE (Mid-Domain Effect) part of the title, although the effect was not called that yet. The second part of the title, “…and a spurious Rapoport effect” and the second part of the paper, explains how undersampling can produce a false Rapoport effect. Actually the second part is what first inspired the paper. Nowadays I suppose I would write this as two papers, because people do that, but I tend to write longer papers. Anyway, you can read that paper sometime if you want, but that’s where it all started. George Hurtt was a grad student in my department at Connecticut and I got George interested in it and then we started doing some programming together. (I’ve been programming since 1965, when we used punch-cards and mainframe computers.) George was also interested in null models and so on, so anyway, we started messing around with it and ended up writing this paper. Initially, it was rejected by the American Naturalist because the Subject Editor felt it was – are you ready for this? – “too novel”! Too heretical, too disturbing somehow. And I thought, well, that’s a really great compliment, but I don’t think they should reject it for that reason. So I actually wrote to the editor, Mark Rausher, and complained. Fortunately, Mark re-assigned it to a different subject editor and it eventually got accepted. But it has indeed caused a lot of trouble! Anyway, between 1994 and 1999, I did nothing further with MDE. As I sometimes tell people, I believed that MDE was important, but only on alternate Thursday afternoons, during those years! I wasn’t too sure whether it was just a geometric fantasy or something that could apply to the real world. But eventually, several things happened that motivated me. Carsten Rahbek, who was then a grad student with Gary Graves at the Smithsonian doing his dissertation on South American bird macroecology and biogeography, stumbled on my paper and read it. I didn’t know him at the time. He ended up concluding that if you take out the effect of area, then there’s a mid-elevation richness peak in South American birds—which has been reconfirmed many times since. But that was news then, because if you just looked at the total number of species by elevation…well, there’s this thing called the Amazon Basin, which is rather large in area compared to the little narrow strip on the map that represents the steep eastern Andean slope! So without correcting for that area affect—I mean its basic form, the species-area curve—you would never see this mid-elevation peak. So Carsten was pretty excited about that and sent me a draft of his paper, which appeared in Am Nat in 1997. Pineda and Caswell applied the model to bathymetric gradients of diversity in 1998, and Mike Willig and Kate Lyons developed an analytical MDE model based on the binomial distribution, published the same year.

But the thing that really got me interested in MDE again was David Lees and colleagues’ paper in 1999 about Madagascan butterflies and other creatures there. Lees is a butterfly guy and the biodiversity patterns of the mycalesine butterfly clade is the big news in that paper, though he also did lemurs and a bunch of other things that they happened to have latitudinal ranges for. David found these amazing fits for an MDE model for the latitudinal and elevational gradients in butterflies and other rainforest-biome creatures in Madagascar, and he worked to develop mathematical expressions for the pattern. David was also the first to separate short and long range species, and to note that the constraint is stronger—though I had guessed at this—the larger the range the more geometrically constrained it is, because you can’t slide a long pencil back and forth in the pencil box very much, so that species with large ranges have more of a signature of MDE than species with small geographical ranges. That was very clear from the results of the Madagascar study. I didn’t know David Lees then. I eventually met David, for a single afternoon, in 2000. Anyway, until then, this was all by email. We decided to write this paper and I queried the TREE editor as to whether that would be something they’d be interested in, and they said Yes. So that whole paper happened because David Lees had actually applied MDE to something interesting in an unusual, and to my eye, extremely convincing way, and it made me a believer in my own theory, to see what David and colleagues did with it in their 1999 paper. That’s how that started. The math in the 2000 TREE paper is mostly David’s, though I had already proved to myself that Lyons and Willig’s approach to MDE was mathematically identical to one of the models in my paper with Hurtt. David did the heavy lifting on the math parts of Boxes 2 and 3 of the TREE. (Should I just ramble or do you want to ask me more?)


HS: Go ahead. I’ll stop you if I want to ask you a question.

RC: Alright, thank you, Hari. So I have had some heretical ideas in the past, not to do with MDE, but to do with some other things, for example, sympatric speciation and group selection. I’m fond of heresies, frankly, and I’m always sceptical of orthodoxies, because they sort of feed on themselves, I think. So, I thought, well, I’d made some discoveries in those two areas, which had nothing to do with each other or with MDE, but they were both heretical and I didn’t push them enough; I just thought the meritocracy of science would reveal that my work and David Wilson‘s work, and the papers we wrote together on group selection, would win out because it’s true and right. Not true; very naive of me. You have to do politics in science. You have to go out there, peddling heresy to the orthodox, and you have to work on it, and keep after it, and not get discouraged and not be shut up by people who don’t want to hear about it. So by 2000 I knew these things, and I said, okay, I am going to write this paper with David Lees in a way that’s provocative, that’s none the less honest, and then, unless someone convinces me it is wrong, stick with it and not give up on this idea, because I think it’s important. Nowadays, we talk about drivers of this and that; well, MDE is about constraints, and constraints are always there and are often overlooked by people more interested in drivers. So that’s sort of the philosophical side of it. And indeed, I got a lot of trouble for that paper, even some extremely antagonistic and even patronizing emails from certain people (e.g., Brad Hawkins wrote, “You have an intellectual attachment to your idea going back at least to 1994, and old habits die hard.”) The problem was that it was about that time, the turn of the millennium, when certain folks interested in solving the latitudinal gradient problem thought that they had finally solved it as an energy-water balance analysis. That was it, that problem was finally solved, and then this guy comes in and says, “Ah, but what about geometry and geometric constraints?” They didn’t like that. Anyway, you’ve read some of the later papers; I guess you know the actors: Brad Hawkins, Fernando Zapata, David Currie, and Jeremy Kerr, if you interview them, they would say they are convinced that MDE is dead, that they did it, they did the deed, and MDE is no longer a problem for the field. Well, they’re wrong about that. It’s alive, and as Nick Gotelli would say, just read the papers. I don’t know if you’ve seen our 2016 paper on MDE and mid-point attractors?


HS: No, I haven’t.

RC: Okay, I’d like you to look at that, if you don’t mind, and you might enjoy it. It’s in Ecology Letters, the cover article in the September, 2016, issue. I  think it’s the next big step in mid-domain effect. I found a way to combine the constraints and the stochastic aspects of mid-domain effect, with what I call mid-point attractors. It’s a way of integrating drivers and constraints, but showing that, nonetheless, geometric constraints have an effect on the distributions. I had 20 co-authors. Except for Nick Gotelli and me, the rest are all data authors. That’s the latest thing on MDE. Okay, that’s my narrative about the last 25 years of MDE, since Colwell and Hurtt. Okay, ask me your questions.


HS: That is a really interesting back story. I want to ask you about the term “Mid-Domain Effect”. Was the 2000 TREE paper the first time you used this term?

RC: Yes. David and I had that a lot of fun talking about this and we decided it needed a name. He had given it a name in his 1999 paper; he called it the Périnet effect. What is Périnet? Périnet is the old French colonial name for a town in Madagascar—where I’ve now been; I went to Madagascar six years ago. Anyway, Périnet is the French colonial name (honoring an otherwise little-known French army engineer, whose full name was Marie Henri Zacharie Périnet) for this town that’s halfway between the north and south ends of the island and halfway between the sea level and the mountain top in the rainforest belt. So, for many groups, it is the point in the map of peak Malagasy diversity, a little red dot in the richness heat map, the supreme diversity point. So David called it the “Périnet effect”. But David’s partner at the time, Louise, was a restoration ecologist, also working in Madagascar. She was aghast that he would use the colonial name for this town and christen this effect with that name. She said he should use the Malagasy name. Well, most Malagasy place names start with ‘A’ and are about 20 or 30 letters long. Well this one was a bit shorter (Andasibe). Even the local name for the forest area (Analamazaotra)  wasn’t very euphonious, let us say. So we laughed about that for awhile, but he did back off and say that we can’t call it Périnet because Louise was right, and would kill David. We understood her argument, but Périnet is a short word whereas the Malagasy forest name was not. So we had to come up with something else. We tried a lot of different ideas and metaphors, and domain was already part of our thinking, and so that’s how it came up.


HS: Did all your communication with David Lees during this project happen over the phone?

RC: It was all email; we never had a phone call. I never spoke to him until I saw him in person in mid-2000, after the paper was done. So, one of my first really large collaborations was entirely by email, though I had some before that. I have many co-authors, but I have only met about two-thirds of them in person, often long after we have published together.


HS: I’d like to just step back a bit and ask you how you got interested in this topic. Looking at your publication profile, I see that interest in species diversity and the statistics around species diversity is there right from the beginning. Could you tell me about how you got interested in both of these and which came first?

RC: Well, I don’t know, maybe they came at the same time. When I was a graduate student at University of Michigan from 1965 to 69, my dissertation was on latitudinal and elevational diversity gradients of leaf litter arthropods. It was an experimental study that I did at three elevations in the US and three elevations in Costa Rica. Field experiments with rotting bananas and stuff like that. Anyway, there was a huge amount of data, which I welcomed, because I enjoy data. While in grad school, I took all the computer courses that were available. Also, statistics courses, because I figured I needed it to handle the massive dataset. So that’s how I sort of got interested in both at once. But species diversity patterns were just a fundamental interest from childhood. I grew up in the mountains of Colorado. We used to go hiking in the alpine zone, and my mom taught my sister and me how to collect and mount butterflies. That’s how I got started on insects. So, I guess it’s been there all along. My dissertation involved development of some novel statistics, which are now dead and buried, but they were useful then. Then there was this paper I wrote about predictability, in 1974, with some novel statistical methods, which I thought was dead and buried too, but it turns out it has a second life and people are using it to analyse seasonality (example). I was not properly trained as a statistician, but then I got introduced to Anne Chao 20 years ago. Anne is a phenomenal person whom you should interview someday about her famous 1987 paper, and its progeny. She was given an award by the Statistical Institute of Catalonia in 2016, recognizing the impact of that paper, which has been so influential. Linked to this award, Anne and I wrote a paper together for a journal called Statistics and Operations Research Transactions. Anyway, Anne’s a lovely person and we’ve worked together for many years now, often along with Nick Gotelli and sometimes with my wife, Robin Chazdon, also. I wouldn’t think of doing anything statistical without Anne. I’ve learned so much from her. She has basically given me private tutelage, over the years, on the kind of stats that she does. I’ve done some creative things with it myself, but usually by saying: Anne, I have this idea, what do you think of it? And she saying: Oh yeah, let’s try that.


HS: Do you remember approximately how long it took you to write this paper? You said the motivation was the 1999 paper by Lees, and this paper was in 2000, so I’m guessing it didn’t take very long?

RC: Yes, we began after Lees’ 1999 paper. We did it quickly, and yeah it was fun, it was sort of a quick ride you know, and we didn’t have any trouble having it accepted, compared to what I had with the original paper, which was at first deemed “too novel” to be accepted!


HS: Did you write the first draft of this paper?

I did. David is a very British writer, which I say with my tongue in my cheek. He writes these long, beautifully constructed Darwinian sentences. You’ve read Darwin; they’re absolutely perfect grammatically, but stylistically very difficult to follow sometimes. So the writing style is mostly mine, and David happily acceded to that.


HS: Nick Gotelli, in his interview, said that, at that time, there was no ‘track changes’ in MS Word, so you used different colours to highlight sections that you edited. Was that the case with this paper as well?

RC: ‘Colorising’, we used to say. Yeah, I was surprised when I read that because I thought ‘track changes’ went back that far but maybe I’m wrong.


HS: You acknowledge a long list of people. Could we go over the list to discuss how you knew these people and how they contributed?

RC: I looked up the acknowledgments list and I can tell you that it’s a mix. Basically, we sent it out to everyone who had said anything or published anything on Colwell & Hurtt or on MDE, plus sceptical colleagues, for their advice. Some of them were David Lees’ colleagues, like Dick Vane-Wright, some were people neither of us knew like Jesús Pineda, and Mike Palmer, who is a plant ecologist, as well as some of my colleagues like Nick Gotelli and Gary Graves. A lot of people saw this. One of the most interesting was E.C. (Chris) Pielou, who was by then retired and living on Vancouver Island in a little cabin. I had to send her a draft, by old-fashioned postal mail. But I wanted to ask her because of her deep and vast knowledge mathematical and theoretical ecology. I asked her if she thought this was a novel idea or had it been thought of before, particularly because she had a paper on the distribution of algae along coasts, a one-dimensional MDE-type model, and had come up with the same binomial model for that. I’ve known her since the seventies, so I wrote to her and said, Chris, surely you guys noticed that if you shuffle these latitudinal ranges along or take samples from this distribution you get a richness peak. She said, actually, they hadn’t noticed that! I wanted to make sure we weren’t claiming novelty for something that everyone has known forever. And none of the people we wrote to could give me an example of an earlier discovery of MDE.


HS: You have already said a little about this – did this paper have a smooth ride through peer-review at TREE?

RC: Yeah, I don’t remember it being a big problem. I haven’t looked at the reviews for a long time, but I don’t remember them being particularly difficult to deal with. I’ve had papers that were very hard to deal with it, but this wasn’t one of them.


HS: At the time when it was published, how was it received in academia and in the popular press?

RC: Yeah well, I don’t think we did a very good job of getting this into the media. People didn’t do that much, you know, in 2000. There was no social network, I mean it was sort of vaguely there, but no Facebook or Twitter or any of that stuff. But in those days, there was an incredible demand for hard copy reprints, and we quickly ran out. The reactions were mostly from people who had published in this field, and some of them did not like it. Kevin Gaston and his students and postdocs were extremely upset by it. As I mentioned earlier, there were some rather personal, patronizing attacks as well, from some others, but my friends supported me through it. It was very hard for me, to tell you the truth. I’m not used to personal attacks, but Carsten Rahbek and Nick Gotelli were my steadfast supporters and co-authors, and we wrote two papers defending MDEs, in Am Nat in 2004 and 2005. They still think MDE is worthwhile. As I said, Nick’s a key co-author on this new paper on midpoint attractors that I really think takes it another step further.

As I said, I was determined not to give in when people didn’t like it, because I did that a couple of times in my career and later regretted it. So, I’m glad I stood my ground. I’ve been stubborn about defending it, hopefully in sensible ways. The corner that they tried to push us into was to say, since it doesn’t explain everything, it explains nothing—as if it were Popperian hypothesis to be falsified, not a contribution among many to a multi-causal phenomenon, to be evaluated in a model-selection framework—a constraint within which mechanistic forces can act. But we never said that MDE explains everything. David Lees and I simply said that an MDE is unavoidable in any range-based null model for richness patterns within a bounded domain. The paper really challenged people to think what they meant by a biodiversity hotspot or a hotspot of richness, by getting people to look at null models for what patterns were expected for a hotspot, simply by chance. It had little explanatory power for patterns of narrow range size endemism, which are arguably the really interesting patterns people should be looking at, for a host of reasons. As we wrote in the Abstract of our 2000 paper, “The question is not whether geometry affects such patterns, but by how much”. “How much” might even be close to zero in some cases. In fact it is close to zero for a number of situations.


HS: There was also one formal exchange in the journal itself, do you remember that?

RC: Yes, it was by Bokma and Mönkkönen in the 7/7/2000 issue of TREE. We had a useful exchange with them regarding the prospects and challenges of two-dimensional geometric constraints models. A year later, Walter Jetz and Carsten Rahbek solved the problem elegantly, with their “spreading dye”, two-dimensional MDE model.


HS: In 2016, you published another paper (the midpoint attractors paper), which follows up on the 2000 paper. It’s now been 19 years since that first paper was published. If you were to think back about the paper itself and considering what’s happened since then, would you change the paper in any way? Or would you say all that you said then still holds true more or less in the same way?

RC: I can’t think of anything in the 2000 paper with David Lees that I would change. Would I change the tone? Would it make any difference if it were less assertive? Maybe it would have made a difference, maybe it would have pushed people’s buttons less, but I’m not sure. I don’t have any regrets about it. And I don’t know of any technical errors in it. I credit David Lees for that. He’s very careful and very clever with the math and so on.


HS: I want to spend some time discussing some specific sections of the paper. At the end of Box 3 you say “No analytical version of this particular model has yet appeared”, referring to the second constrained geometric null model. Is that still the case?

RC: Okay, at that time there was no analytical version, and I don’t think it has ever been done. David Lees said he didn’t know how to do it and that it would be pretty difficult. So I said okay let’s not, but I’m sure it could be done by somebody. That box is David’s work basically.


HS: And then on the same page you talk about the different kinds of boundaries and how they may vary in their potential to limit species distributions.  You say that defining, quantifying, or even ranking barrier resistance is likely to remain a challenge because the effectiveness of boundaries depends greatly on the temporal scale on which they are considered and on the phylogenetic constraints. Is that still the case, i.e. does defining and quantifying boundaries remain one of the main challenges in this kind of work?

RC: Absolutely.  I peer-reviewed a paper by Marcell Peters and colleagues, published in 2016 in Nature Communications. It’s an elevational study of many different taxa on Mount Kilimanjaro. Mount Kilimanjaro sits in the Serengeti plains at 700 meters. They applied MDE and, lo and behold, it didn’t work very well on those data. And they say, well we’re going to use the base of the mountain as a hard boundary. Yeah, but there’s this huge area affect, from the vast basal plains, reaching part way up the dry side of the mountain. But they treat Mt. Kilimanjaro like it was isolated, like an island the sea. I objected to that, but they insisted they should be able to do that, and they concluded that the steady decrease in richness with elevation on the mountain was driven by temperature, which everywhere on earth declines with elevation. That’s the kind of problem we were describing there. Yeah, it’s an elevation boundary, and certainly very different down on the plains, because Kilimanjaro’s a very young mountain, less than 3 million years old, but should that be a hard boundary or not?  That’s hard to answer. That’s why I like the ocean, because there are no trees down there. It’s difficult, and the question is, should we consider physiological limits as domain limits, as well? My favourite example of that is the hard freeze line in North America, which exactly limits the northern range limit for palms. Apparently, palms were unable to invent any way to deal with hard freeze. You can grow a palm there, but it won’t flower or fruit. It’s tricky.


HS: On the last page of the paper you say that “the geometric theory of species richness generates a specific and highly testable prediction: that wide-ranging species or higher taxa within a regional assemblage are considerably more likely to show patterns in accordance with geometric theory than narrow-ranging taxa”. Has subsequent work found support for this pattern?

RC: Yeah, this prediction has proven almost 100 per cent correct. There’s a 2007 paper by Rob Dunn, Christy McCain and Nate Sanders that reviews it. The paper’s got some writing problems and people have misinterpreted it, but it does find strong support for this prediction. Unfortunately, I wasn’t involved in the paper at all; I would have written it a little differently. But they basically showed that, over and over, that that’s the case.


HS: I want to ask you a little bit about the impact of the paper. It’s been cited over 900 times. Do you have a sense of what it usually gets cited for?

RC: Interesting. I haven’t read all 900 papers of course. But I will tell you another anecdote that will amuse you, because of your interest in such things. In 1971, Doug Futuyma and I published a paper—Colwell and Futuyma—measuring niche breadth. That paper has been cited nearly 1700 times. Back in the day (from 1977 to 1993), Current Contents, the ancestor of ISI, used to publish commentaries on what they began to call “Citation Classics”. Anyway, they declared our 1971 paper a Citation Classic when it got up to a mere 165 citations. They wrote to me and said they hoped I would prepare a commentary on this paper, to be published in the weekly print edition (remember, no internet!) of Current Contents. The question they asked is the sort of thing you asked—why do you think this paper has been cited so many times? Good question. So I actually went back and did random sampling. I haphazardly sampled the 160+papers and checked about half of them. To my astonishment and dismay, about 5% of the papers that cited Colwell and Futuyma in the References Cited section didn’t cite it in the text! The only theory I could come up with – you have to understand this was before citation managers, before personal computers, and people were writing their papers on typewriters with drafts and carbon paper and mailing everything by post—the only thing I could conclude was that, apparently, Colwell & Futuyma 1971 is the sort of paper you cite in the first draft and later eliminate because there’s not enough space, but forget to take it out of the citations. So, indeed, over the years it became sort of an obligatory citation—anytime, anybody mentioned niche breadth they would cite Colwell & Futuyma 1971; they never read it or anything. But we didn’t invent the term, Dick Levins did, in his 1968 book. So it was very amusing to see that, but it’s still cited somewhat the same way, and not very many people ever used the math in it and the statistics that we invented.

Anyway, so who knows why papers get cited, but there is this habit, you have to cite something, you look up what’s the most cited thing about this subject and cite that one. That’s not a very scholarly way to do things but a lot of people do that sort of obligatory citation. Anyway, so why is Colwell and Lees 2000 cited a lot? Well, I think it’s cited by people that hate it and people that love it. I don’t know what the proportions are. I am very curious to know whether this new approach will have any fans among the previous haters of MDE. I hope so. I’m hoping that David Currie will like it, despite a very silly (and technically flawed) reductio ad absurdum attack on MDE on Madagascar by Jeremy Kerr and Currie in 2006, which David Lees and I resoundingly put to rest in a rebuttal the following year. Currie has called for “new models of geometric/spatial effects on richness” that integrate geometric constaints with environmental effects. That’s exactly what the midpoint attractor paper does, so I’m curious to see what he thinks.


HS: In the 16 years since the paper was published have you ever read it again?

RC: Oh yeah, many times. For one thing people keep quoting it, so I want to see what they’re saying. But I also go back, especially to the boxes, just to make sure I understand how the different models are related and so on. Yeah, I’ve read it a few times. It’s not bad!


HS: And if you were to compare this paper to the papers you write today, like the Ecology Letters (midpoint attractor) paper for instance, do you find any striking differences in the way you write or organize papers?

RC: No, not really. I’ve always been an organized person who writes many, many drafts, and I’m very determined to write in unambiguous and simple language. That’s what I’ve always tried to do. People whom I co-author with learn to appreciate that, and even do it themselves in some cases.


HS: That’s what Nick Gotelli also said when I asked him about the Ecology Letters paper, that it’s always a pleasure to write a paper with you..

RC: That is very kind. Did you know that Shahid Naeem was my doctoral student?


HS: No, I didn’t. The first interview I did was with Shahid Naeem.

RC: Yeah, you did that in Bangalore. I didn’t know he was there. Shahid is a very, very dear friend and wonderful person. I think it is fair to say that Shahid learned a lot about writing from me. He would admit that himself. Most of my students would admit it.


HS: I asked Shahid Naeem if the Ecotron biodiversity-ecosystem function paper was his favourite, and he said, no, he liked his PhD work more.

RC: Yes, there were some wonderful papers, from his PhD dissertation. The same hands that create his marvellous artwork (I hope you know about that! (example; see p10)) allowed him to do some almost impossibly minute experimental manipulations in the field, to reveal the secrets of life in plant-held waters.


HS: That’s also my next question. Would you count this 2000 paper as one of your favourites, among the papers you’ve written?

RC: Yes, I would, I think. The Colwell & Hurtt paper’s got to be a favourite also. I have several favourites, including a paper in Science last year with Thiago Rangel  as lead author, the product of 5 years of work and interdisciplinary collaboration, which is many ways is a capstone achievement for me. We built a spatially explicit, mechanistic model that simulates the history of life on the South American continent, driven by modeled climates of the past 800,000 years. It was all done at level of geographical ranges of populations. We implemented adaptation, geographical range shifts, range fragmentation, speciation, long-distance dispersal, competition between species, and extinction, all with only 4 parameters. Amazingly, despite the geologically short time period and a complete absence of any target pattern, richness patterns emerged that closely resembled real-world patterns for birds, mammals, and plants—which, themselves, are quite similar to one another. The most ground-breaking feature of the study was that we were able to identify not only regions that emerged as “cradles” of speciation and “museums” of persistence, but for the first time, “graves” of extinction. But, maybe my most favourite paper of all is Colwell & Winkler 1984. Nick actually wrote a commentary about that paper for a compendium of classic papers in macroecology, for which Colwell and Winkler was chosen. That was one of the most creative collaborations I’ve ever had. It was with David Winkler, who is an ornithologist at Cornell now, but he was a grad student at Berkeley then. I was on the faculty at Berkeley for 20 years. David and I wrote that paper in, like, 3 days of intense creative collaboration. It was so much fun. Of course, there were revisions after that. I love that paper, and it introduced the term “null model” to biogeography for the first time at the historic Wakulla Springs meeting where I presented it orally (three years before the book with the paper was finally published). The term was quickly picked up. Another paper I love, which I wrote just by myself, was published in 2000, also in the American Naturalist, about Rensch’s rule. That paper took me 20 years to write! I was very pleased it won the President’s Award (selected by the President of ASN) for being the best paper in the journal that year. It’s about evolution of sexual size dimorphism. I know you are interested in evolution of traits so you might enjoy looking at that sometime. It’s about mites and hummingbirds. For decades, I have studied these weird little hummingbird flower mites that ride on hummingbird bills. And a final favourite is the midpoint attractor paper I published in Ecology Letters. We’ll have to see if it stands the test of time but I’m very proud of it. Oh, and then I’m very proud of the Colwell, Chao, Gotelli et al. (2012) paper in Journal of Plant Ecology, tying together rarefaction and extrapolation curves in species richness patterns. That was actually supposed to be a short little note as “payment due” for getting invited to a conference in Guangzhou! Fangliang He had organized a conference in theoretical ecology in Guangzhou because he had a joint appointment there—he is normally in Alberta—and the agreement was, that if they paid your way there and fed you several Chinese banquets that you would write something for this journal. The journal was published by the Chinese plant ecology society for many years in Chinese, but around this time they got Oxford to pick it up and make it an English language journal. They needed to get the journal launched in English and the conference was a clever way of doing it. I was going to write a short note that would have been about one tenth of what the paper turned out to be, a note that had been rejected when Chang Xuan Mao and I, in 2004, published another paper in Ecology. We had tried to publish this second one, a companion paper, but it was rejected by none other than Fangliang He, himself, as Subject Editor! So I thought, this will be fun. I’ll take that rejected paper and Fangliang will have to publish it in this new journal, many years later! He agreed to that, but then I started thinking about some things Anne Chao had previously published. Anne and Nick had done a point estimator for extrapolation of species richness. I thought, well why not estimate it for every point and then connect it to the rarefaction curve and see if we can get confidence intervals? So I wrote to Anne, sent her a cartoon basically, and asked, “Anne, is there any way this would work?” She wrote back saying, well, it’s completely different mathematics to rarefy and to extrapolate and the confidence intervals are estimated in completely different ways, so I doubt very much it will look very good when you glue them together. But then she wrote back 48 hours later and said: “It works! Its seamless, it’s amazing!” So that’s how that paper came about, and it’s gone way beyond that now, with several papers that unify extrapolation and rarefaction. That was a hugely fun thing because it was Anne’s brilliant mathematical statistics making a silk purse out of the sow’s ear of my intuition, and it all came together and made something new.


HS: In six years it’s been cited over 1000 times

RC: Yeah, it’s the most cited paper in that journal, so far, and by a good margin, and it isn’t even really a plant ecology paper. They were very nice to us, I have to say. We said, well this paper is going to be quite a bit longer than we thought because we came up with this terrific idea, and Fangliang says, “Oh, don’t worry don’t worry, take as much space as you want.” When do you hear that from an editor, right? And then we said, well, we don’t know if we have the money for the colour Figures —they were charging an extra 500 pounds or something for colour figures. And Fangliang said, “Oh, that’s alright, we’ll pay for that.” But they got their money’s worth, we got our money’s worth, and it was all fun.


HS: What about Colwell & Coddington?

RC: Oh, sure yeah that was fun. That’s a biggie, 4700 citations so far. That’s what led to our collaboration with Anne. Jon Coddington discovered her 1984 paper in the literature, and that was sort of the basis of our collaboration. We sent a draft to Anne and she said, oh, you shouldn’t call these measures Chao1 and Chao2, I don’t need my name on this. We said, well too late! So yeah, that was the start of all my collaborations with Anne.


HS: This is my final question. What would you say to a student who is about to read this paper today? What do you think he or she should take away from this paper written 18 years ago, and would you add some caveats?

RC: That is a great question, Hari. You come up with some good ones. What would I say? I’d say, it’s still worth reading, for a start. I don’t think it’s been shown to be ‘wrong’ or unimportant. And there are still some, as you point out, unsolved questions. But I would also say, read this, but then read this, this and this and the other things that followed. I would also say go ahead and read it, but go back and read Colwell & Hurtt, too, because it’s all in there. I mean it’s a weird paper, but it’s only because it’s got that other part about the spurious Rapoport effect, which people ignore (but should not). I always do this with my students. In population genetics—what is the word I’m looking for, well you know, the coalescent? You are supposed to find out what the common ancestor is, based on all the current genes of living species in a clade. Well, that’s what I try to teach my students. When you come to an idea that you’re interested in, that you find appealing, that’s interesting, don’t just cite the last paper that was published on it. Figure out what the coalescent is, of that idea -where has it come from, what’s the origin of the idea, or the origins if there’s more than one.





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