Revisiting Abrams et al. 1993

In a paper published in Evolutionary Ecology in 1993, Peter Abrams, Hiroyuki Matsuda and Yasushi Harada developed models to examine adaptive change in continuous traits under different conditions, and show that they can result in both stable fitness minima and unstable fitness maxima. Abrams and colleagues also discuss real biological scenarios in which the adaptive process is likely to fail to maximise individual fitness. Twenty-three years after the paper was published, I asked Peter Abrams about his collaboration with Hiroyuki Matsuda, the origins of his interest in this topic and what we have learnt since about it.

Citation: Abrams, P. A., Matsuda, H., & Harada, Y. (1993). Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evolutionary Ecology, 7(5), 465-487.

Date of interview: Questions sent by email on 21st December 2016; responses received by email on 31st December 2016.


Hari Sridhar: I would like to start by asking you about the origins of this paper and the work presented in it. What was your motivation to do this particular piece of work, in relation to earlier research you had done on adaptive evolution of quantitative traits? Also, did you work on this paper and the Evolution paper (also in 1993 with the same co-authors) simultaneously?

Peter Abrams: This paper grew out of a number of earlier papers in the late 1980s.  Russell Lande had published a long series of papers that examined the dynamics of quantitative traits based on the Breeder’s Equation, and various authors’ studies of coevolution (including some of mine) had revealed that frequency dependent selection commonly arose from simple ecological interactions.  Some earlier papers of mine had (somewhat tangentially) examined the stability of dynamics of behavioural and evolutionary traits that changed according to the slope of the relationship between individual fitness and the trait.  In 1991, Hiroyuki Matsuda, a young theoretical biologist from Japan responded to an ad I had posted for a postdoctoral fellow.  I had met Matsuda several years before at a Joint US-Japan theoretical biology meeting in Honolulu.  He was already a mature scientist with a stable position, but was interested in spending a year in North America, and I was glad to have him use the fellowship money to allow this.  The idea to do an article on the relationship between stability and fitness maximization at evolutionary equilibria was his, and it was a topic he had worked on earlier with Yasushi Harada.  The paper took a long time to get published, and we wrote the shorter Evolution paper to include some closely related ideas that arose during the several re-writes of the main one that finally came out in Evolutionary Ecology Research.  Ironically, we submitted the original maximization/minimization article to Evolution.  It was also somewhat ironic that the evolutionarily stable minimum part of our results had been published in an appendix of a 1991 article in Evolution, that neither we nor the editor was aware of.


HS:  Stepping back a bit, could you tell us how you got interested in mathematical modelling of ecological and evolutionary processes, which has been the focus of your research throughout your career.

PA: I went into ecology because of a life-long interest in the natural world.  When I was six years old I intended to become an entomologist when I grew up.  My biological interests shifted as I matured, and I was attracted to modeling after taking a summer physics course at Cornell University after my junior year of high school.  I was inspired by the surge in mathematical approaches initiated by Robert MacArthur, and ended up doing my thesis on models of the limiting similarity of competitors.  Back in the early 70s, there was less of a division between ecology and evolution, and most theoreticians worked in both fields.


HS: Could you tell us, approximately, how long it took you to develop these ideas and write a first draft of the paper? How often (and where) did you and the other authors meet during this study?

PA: If I remember correctly, this was the first paper Matsuda and I started working on after he arrived in Minneapolis in September of 1991, and we had a first draft done by the end of the year.  However, as described under #1, it took quite a while before it was accepted.
HS: If you don’t mind, I would like to go over the names of people you acknowledge in the paper to find out a little more about who these people were, how you knew them and how they helped:

  1. J.W. Curtsinger
  2. O. Leimar
  3. C. Packer
  4. P. Taylor
  5. M. Taper
  6. B. Charlesworth
  7. J. Endler
  8. M. Kirkpatrick

PA: Two of these were editors who rejected the manuscript from other journals, two were reviewers, and three were colleagues at the University of Minnesota and Stockholm University.  I’d prefer not to give any more details.


HS: How did you decide to submit this paper to Evolutionary Ecology? Would you remember if this paper had a relatively smooth ride through peer-review?

PA: It had a smooth ride at Evolutionary Ecology, which was then edited by Michael Rosenzweig.  However, it had been rejected at Evolution and American Naturalist before that.  The handling editor at American Naturalist even refused to send it out for review.  At the time, there were many fewer journals, and, after our first two rejections, Evolutionary Ecology was just about the only place we could have send an evolutionary theory paper that did not use explicit population genetic and still have much hope that biologists might pay attention to it.


HS: Would you remember how the paper was received when it was published? Did it attract a lot of attention?

PA: The early 1990s predated a lot of the more visible current mechanisms for a paper garnering attention (no social media, no Faculty of 1000, etc.)  This is one of a handful of articles of the ones I’ve published where one or more mathematical ecologists whom I had not met expressed their admiration of the paper to me within the first few years after it was published.


HS: This paper has been cited over 250 times. Do you have a sense of what it gets cited for, mostly?

PA: My feeling is that most of the citations deal with the ‘fitness minimization’ result because these equilibria constitute ‘evolutionary branching points’.  Thus, a larger number of people who later employed ‘Adaptive Dynamics’ to help understand evolutionary diversification cite this work.  The unstable maximum result was an outgrowth of Ilan Eshel‘s earlier work on continuously stable strategies, which still does not receive enough attention.


HS: How did this paper influence the future trajectory of your research, both in the short-term and the long-term?  

PA: This paper was one of many articles I ended up working on with Hiroyuki Matsuda which involved evolution of frequency dependent traits that influenced interspecific interactions.  Matsuda’s concept of ‘evolution to self-extinction’, also termed ‘evolutionary suicide’ grew out of this work.  The ultimate outcome of evolution involving a stable fitness minimum is still an empirically unsettled topic.  An article I was involved in that came out in TREE in 2006 (with Claus Rueffler as first author) suggested a range of possible outcomes (evolutionary branching, species invasion and others), but we still lack any comprehensive empirical review.


HS: Today, 23 years after the paper was published, could you reflect on where you stand with regard to its main message? Also, what would you see as this paper’s most important impact on the field?

PA: The main impact was to promote the study of evolution within an ecological context, something that was more fully developed by the eco-evo effects literature and the field of adaptive dynamics.


HS: In the paper you identify “ecological situations which seem most likely to result in stable fitness minima or unstable maxima”. Subsequent to this paper, how much empirical support have these ideas received, i.e. have examples been documented from the ecological contexts you identify?

PA: I have been disappointed that unstable maxima have been largely ignored.  However, this is understandable in that they would be very difficult to document.  Stable minima are widely thought to exist temporarily in the process of adaptive diversification, but conclusive documentation is relatively rare.


HS: You say that since John Endler‘s 1986 survey of Natural Selection, additional examples of disruptive selection on quantitative traits have been documented, but which are unexplained, and that it is not known if this phenomenon is common or reflects the scenario you describe. Today, do we have a better idea of the prevalence of disruptive selection in nature and its explanation?

PA: There have been some reviews, but they have not been very conclusive.  Troy Day and I tried unsuccessfully to start a research group at NCEAS to examine the empirical literature around 2000.  There is a need to develop a research program specifically to explore mechanisms in some of the observed cases of stable disruptive selection.


HS: In the 23 years since this paper was published, have you ever read it again? If yes, in what context? What strikes you most about it when you read it now?

PA: In rereading this, as well as other papers from the 1990s, I have been impressed that there actually has been considerable progress in understanding the evolution of ecologically important characters since that time.


HS: Would you count this as one of your favourites, among all the papers you have published?  

PA: Yes, this is one of my favorites, in a large part because it marked the beginning of a long, productive and enjoyable period of collaboration with Hiroyuki Matsuda.




Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s