Paul Erdős was a prolific Hungarian mathematician who spent much of the later part of his career traveling to visit collaborators around the world. According to his Wikipedia biography,

Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathematicians. Erdős’s prolific output with co-authors prompted the creation of the Erdős number, the number of steps in the shortest path between a mathematician and Erdős in terms of co-authorships.

Or, to quote from Stephen Heard’s recent post on Erdős:

Paul Erdős (1913-1996) was a Hungarian mathematician who published somewhere around 1,500 papers (in mostly pure-math fields including set theory and number theory) and had somewhere around 500 coauthors. He was a fascinating figure, and his biography

is a great read. He was famous both for brilliance and for broad collaboration. Those two things in combination inspired mathematicians to invent the Erdős number as a metric of their collaborative closeness to Erdős. Here’s how it works: Erdős’s own Erdős number is E = 0; those who have coauthored research papers with Erdős have E = 1; those who have coauthored with an E = 1 scientist have, as a result, E=2, and so on.The Man Who Loved Only Numbers

Stephen’s Erdős number is a very impressive 3. And, since I’ve coauthored a paper with Stephen, that means mine is 4, which I think it pretty neat. (That’s the same as Stephen Hawking’s!)

Right after reading Stephen’s post (or, more accurately, Jeremy’s link to Stephen’s post), I visited the University of Florida to give a seminar, hosted by Bob Holt. When I got my schedule ahead of time from Bob, it included a couple of people who are not at the University of Florida, but who are/were there visiting Bob. That was sort of surprising, but not very, as Bob is someone who has collaborated with lots of people – as just one indicator, I remember as a grad student hearing that Bob Holt and Andy Dobson were the two people who were involved in by far the most NCEAS working groups. Given the breadth of topics Bob has worked on, as well as the strength of his contributions, it’s not surprising that lots of people visit him to work on things.

This combination of events got me wondering: is there anyone in ecology who compares to Erdős in terms of being prolific and exceptionally well-connected (in terms of collaborations)?

I think Bob Holt is a great candidate. According to Google Scholar, he has 446 papers. By my count, he has had 574 different coauthors! (You can check the list I assembled here.) Should we have the Holt number in ecology*, or can you come up with someone who is even more connected to other ecologists?

*Clearly this could be expanded to a Holt-Erdős number, a Holt-Erdős-Bacon number, etc. Thanks to Hao Ye, I know that Bob Holt has an Erdős number of 4, so my Holt-Erdős number is 6. (Updated to fix error — I originally said 8, but my Holt number is 2, so I don’t know why I wrote 8!)

I guess Anders Pape Møller could be high in such ranking 😉

I would hope the ecological equivalent of Erdos would not have a retraction for misconduct.

https://dynamicecology.wordpress.com/2011/11/03/is-scientific-misconduct-especially-rare-in-ecology-and-evolution/

Bob is indeed a good nomination. So, of course, because I should be working on the talk I’m giving later this morning, instead I’m calculating my Holt number. Which is no more than 3 (I published with Anurag Agrawal, who published with Peter Kotanen, who published with Bob Holt). It seems like I ought to be able to do better, but it’s actually more challenging to track a Holt number than and Erdos number, as there’s no simple automated tool (the American Mathematical Society’s tool uses a journal database that doesn’t capture ecology well). Maybe someone else who is supposed to be working on a talk could write an app that scrapes Google Scholar?

There are some tools for finding Collaborative Distance, although it often depends on the source of the data for the collaboration graph used.

See here for some examples that may or may not work for you:

https://academia.stackexchange.com/questions/13120/are-there-any-online-tools-to-calculate-academic-collaboration-distance-i-e-a

Steve, you did a presentation with me as a co-author at ESA a few years ago, and I’ve collaborated with Bob. Perhaps that would give you a 2? Of course you could just write up that presentation and publish it… 🙂

Godsoe, W., Jankowski, J., Holt, R.D. and Gravel, D., 2017. Integrating Biogeography with Contemporary Niche Theory. Trends in ecology & evolution, 32(7), pp.488-499.

I will admit that for many reasons I regret not writing that work up and publishing with you as coauthor. The effect on my Holt-Erdos number is now one of them (because I’m not sure using a copresentation is fair game). But not the only!

My Holt number is 3, through several Holt coauthors. 😉

Across all ecologists, Is a plot of # coauthors (y) vs # of publications (x) scale-free 😉?

P.S. my Holt number is 2

DE certainly knows how to distract a guy…..! A quick check shows that my Holt number is 2 – Bob and I have both published with Jens-Christian Svenning.

As I mentioned in the comments to Steve’s post, folks might also wish to think about their Darwin number; Darwin published alone (exclusively?) so I that propose a suitable Darwin number would be how many handshakes you are from the great man. Via my PhD supervisors I can get back to David Lack > Julian Huxley > TH Huxley > Darwin, making my Darwin number 5. That must be beatable by someone?

Re: Darwin publishing alone, if memory serves one of his first papers–which later in life he “forgot” to include when listing his publications–was written with Fitzroy. It was a defense of the activities of Christian missionaries.

Yes, it’s listed here: https://en.wikipedia.org/wiki/Charles_Darwin_bibliography

Jens is quickly turning into a viable candidate to have his own separation number! (He is one of my connections to Holt as well).

Great post. Bob Holt is definitely the closest thing ecology has to Erdos. Although as far as I know Bob doesn’t bum around the world, showing up at people’s houses unannounced in the middle of the night and expecting to be cared for for weeks at a time. 🙂

Bob was the external member of my PhD committee, so I feel like my Holt number ought to be low. And it turns out it’s 2. Whew! 🙂

Yes, when I tweeted about this post idea, I noted that I meant Ecology’s version of Erdos in terms of having a big influence and being very well-connected, not in terms of having an itinerant lifestyle. 🙂

Via Twitter:

I approve, but solely because my Asner number (2, via J. Cavender-Bares or J. Gamon) is lower than my Holt number (3, via multiple paths)

Via Twitter:

Although I feel like I should have a Holt # of one (we’ve coauthored a paper that never got published), in the formal record, I have a Holt number of two but through at least 6 different people. Which just goes to show you picked the right person!

Yes, my Holt number is also 2, and also through a bunch of different people!

Much to my surprise, I am a 2. Me — de Mazancourt, Loreau — Holt. In retrospect this is not that surprising given how many people Claire and Michel have published with. I was just surprised given my relatively low number of papers.

Richard Shine, U Sydney, AU has 900 papers in professional journals and books.

He actually has more than 900; his website ends at 2016.

Here is Shine’s pub list and website

http://sydney.edu.au/science/biology/shine/publications/index.shtml

Correction: Steve Strogatz’s Holt # is 3. Via math sci net. Strogatz -> Edward Ott -> Ying-Cheng Lai -> Holt. So an Erdos-Holt-Bacon number of 7!

Steven Strogatz confirms!

Via Twitter, Tim Blackburn throws shade on everyone who doesn’t have a Holt Number of 1. 🙂

Meghan, how long did it take you to type up Bob Holt’s coauthor list? Or did you have some app that scraped the data for you?

I brute-forced it, after deciding that would take less time than figuring out how to automate it. I did it in little bits and pieces between other stuff, so I’m not sure how long it took overall.

That’s the secret to blogging, or a secret anyway. Get something out of scattered little bits of time you can’t use on much else. That’s how I’ve compiled the data on gender balance of recent ecology faculty hires.

This is way more fun than work.

My Holt number is 3 (Holt-Wardle-Aarssen-Laird, and perhaps via other paths); same as my Erdos number (Erdos-Shallit-Yazdani-Laird). Regrettably, I have no film credits, but if Strogatz’s Bacon number is 1 (from M. Holden’s comment above), then my Bacon number is no greater than 7 (as my Strogatz number is 6, according to https://mathscinet.ams.org/mathscinet/collaborationDistance.html).

By the way, Paul Erdos’ Holt number appears to be no greater than 4, again according to mathscinet.

Fun! So if you have a Holt or Erdos # of n. Then your Holt-erdos # can be no greater than 2n+4. As per your Bacon number, that’s done via films/tv, not papers ;), so you have to act in films with people to have one.

Rich Lenski’s Holt-Bacon number will be tough to beat:

How anyone can calculate their Holt number:

Another person with a 2 for Holt number:

Relevant and arguably just as entertaining as the GDoc: https://academictree.org/evolution/tree.php?pid=64363

my H = 2

Despite how fun this post is, I’d perhaps argue that there is no equivalent to Erdos in ecology (at least that I know of). The average number of authors on a math paper is 2.1 and on an ecology paper is 5.7. The 1,500+ papers with 500+ coauthors is so beyond the tail of the distribution for mathematicians that it is incomprehensibly legendary (and he passed away in 1996 when average author lists were shorter) . Bob Holt is of course one of the most prolific authors in ecology with a truly astonishing number of collaborators, but there are probably a few superstar ecologists that have reasonably similar records if we were to exhaustively search for them.

I think an Erdos equivalent ecologist would need to have around 1,000 collaborators (500 * 5.7 / 2.1 = 1357). Is that too harsh of an equivalent Erdos requirement?

https://www.sciencedirect.com/science/article/pii/S2405844016322800#tbl0010

My paleontological (!) colleague Jessica Theodor matches my Holt number!

This raises the question of whether any paleontologist has a Holt number of 1. And the related question of who out of all people with Holt number N (N=1, 2,…) works in the field farthest removed from ecology.

I bet there’s somebody from somebody from particle physics or cultural anthropology or something who has a Holt number of 2. But is there anyone from a field far removed from ecology with a Holt number of 1? Meghan, can you answer this?

He’s definitely collaborated with theoretical physicists. Bob Holt has 2 papers in physics journals according to mathsci.net. They are particularly good candidates for producing some pretty distant coauthors (none of the co-authors would even be considered bio-theory folks). Physicists dabbling in math-ecology often produce fun quirky papers, sometimes they reinvent the wheel (or circumvent the wheel in an unclear way) but it’s nice to see some that work directly with ecologists. These will make it into my reading list.

Shulenburger, Luke; Lai, Ying-Cheng; Yalçınkaya, Tolga; Holt, Robert D. Controlling transient chaos to prevent species extinction. Phys. Lett. A 260 (1999), no. 1-2, 156–161.

Dhamala, Mukeshwar; Lai, Ying-Cheng; Holt, Robert D. How often are chaotic transients in spatially extended ecological systems? Phys. Lett. A 280 (2001), no. 5-6, 297–302. 92D40

My Holt number is 2.

Some other suggestions:

Robert Costanza has over 800 papers (according to GS) and is one of the key nodes in this cool network analysis of authorship in ecosystem services papers: https://www.sciencedirect.com/science/article/pii/S2212041612000034.

Teja Tscharntke (over 500 papers according to GS, and very well-connected in my broader field); David Lindenmayer (over 1000 papers according to GS).

Thanks to my article with 63 collaborators, including Manu and Teja, my Holt number is also 2. That’s at least 50-60 more people with Holt numbers of 2, as well. (A few collaborators, such as Claire Kremen, have a Holt number of 1.)

The article, for anyone interested (or who just wants to share my pain in entering all those authors into the manuscript system): “A global synthesis of the effects of diversified farming systems on arthropod diversity within fields and across agricultural landscapes,” http://onlinelibrary.wiley.com/doi/10.1111/gcb.13714/full

Might be interesting to compare Peter Reich’s network. Certainly has had many hundred coauthors, and an enthusiastic and positive and well-travelled collaborator, but via empirical more so than theoretical work.

He sits somewhere on the bridges between plant ecophys, biodiversity-ecosystem function, and “trait ecology”. So while there’d definitely be lots and lots of people with Reich numbers of 1-2, what’s not so clear is whether almost everyone in ecology would be within 3-4 links from him.

(Actually thinking about it more carefully now, there’d be some theoreticians of communities or populations or games with Reich number of 1, and they would link onward, so I think probably the coverage of ecology within 3-4 links of Peter might indeed be pretty comprehensive.)

just a footnote to elaborate a bit further — it’s not the volume of output that I’m thinking about for Peter, rather the different styles for being a really influential collaborator

If part of the Erdos analogy is number of different fields/sub-fields one has worked on, then I would think Simon Levin has to enter the conversation too.

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