This is going to be a long post, so put it off for a lazy post-lunch lull, get yourself a cup of coffee, and prop your feet up on your favorite ottoman. You have been warned.
I recently participated in the
Helsinki Summer School on Mathematical Ecology and Evolution, which this year focused on the theory of speciation. The school was a part of the larger series of schools, workshops and conferences organized by
FROSpects, an ESF Research Networking Programme that has been doing a great job of supporting and promoting speciation research – I've attended several of their events in the past, such as the
Abisko Winter School in 2011 and the
Speciation 2010 conference in Austria, and they have had a big influence on my path as a graduate student. I'll talk about the Helsinki summer school in a moment, but first, I can't resist giving you a brief touristic interlude.
Since I've never been that far northeast in Europe before, I seized the opportunity and went for an overnight visit to St. Petersburg (only three and a half hours away by train!), which was fun but exhausting. The high point for me was seeing the iconic
Church on the Spilled Blood, which was every bit as spectacular in person as it is in photos:
The
Hermitage was amazing too, and could have taken up much, much more than the half-day I could give it. It was heartbreaking to have to hurry through rooms filled with works by Cézanne, Matisse, Van Gogh, Corot, Caravaggio, Gauguin, Pisarro, Degas, Renoir, Seurat, Vlaminck, Picasso... I will have to go back some day. They had great exhibits of ancient art and artifacts from around the world, too, which I enjoyed a lot, and tons of Middle Ages and Renaissance art that I mostly skipped due to lack of time. (I did suffer the tourist hordes to glimpse the two very famous
da Vincis there, though.)
One lovely thing about the Hermitage is that unlike many stuffy, arbitrarily restrictive museums, they mostly allow you to photograph their exhibits (but no flash, of course, since it can damage the art). The first photo below shows an example of the opulent interior of the museum, which was once a palace; the second shows a nifty Kandinsky that caught my eye; and the third shows a remarkable mask and breast collar for a horse, from around the 3rd-4th century B.C., from the Pazyryk culture of the Altai – a region in central Siberia that I had never even heard of before:
I got to spend a little time in Helsinki, too, on the way in and out, which was great. It has a beautiful downtown area with an open-air market, small side streets and lovely churches:
And also quite a remarkable island fortress called
Suomenlinna that you can explore, walking both on top of and inside of the walls and admiring the old cannons:
Amusingly, the name Suomenlinna is Finnish for "Finnish castle", while the Swedish name for the fortress, Sveaborg, is Swedish for "Swedish castle". (It was built by the Swedes in 1748, then was captured by the Russians in 1808 – but I don't know whether their name for it would translate to "Russian castle" – and then became Finnish when Finland became independent in 1917.)
The school was actually held, not in Helsinki, but in
Turku, another town in Finland to the west of Helsinki. I didn't have much time to see Turku – in part because I managed to crack a rib early in the summer school, attempting to play soccer one fine evening, which subsequently limited my mobility – but the
Turku cathedral dates back to the 13th century (although much of it was rebuilt after fires much more recently) and was quite groovy.
Well, I'm supposed to be talking about the summer school, aren't I! If I were Andrew, I would find a way to weave some quirk of my travel experiences together with musings about evolution to form a unified tapestry. Suomenlinna and the evolution of defenses against predation and parasitism? The Hermitage and the adaptive value (if any) of the human sense of aesthetics? But I am not feeling inspired, so please pardon the abrupt transition from tourism to biology.
The school had five main speakers: Sergei Gavrilets, Nick Barton, Sander van Doorn, Eva Kisdi, and Dan Bolnick. First, however, Mats Gyllenberg opened the school with a talk about competitive exclusion, limiting similarity, and coexistence; this is a central question for speciation theory, of course, whether coexistence occurs with secondary contact after divergence in allopatry, or is an ongoing issue as divergence proceeds in sympatry or parapatry. Ultimately, all life on our planet descends from one common ancestor, and yet that life has managed to subdivide the niche of "planet Earth" (which one could imagine being dominated by one extreme generalist species) into enough partitions to support the many millions of species now extant, finessing the
Principle of Competitive Exclusion in a myriad ways. The upshot of Gyllenberg's talk, which I believe was based upon work by Dieckmann, Metz, and Mesz̩na, was that coexistence of an infinite number of species is mathematically possible Рthe variety of biodiversity could be continuous, in other words, rather than divided into discrete packets that we call "species" Рbut that this result is not robust, and collapses into a finite number of discrete species subdividing the available dimensions of niche space given any sort of perturbation from stochasticity. Paraphrasing him, the messy realities of biology prevent the coexistence of infinitely many types.
Sergei Gavrilets gave quite a fast-paced set of lectures (despite his laptop dying at the beginning of the school). He started with the history of population genetics and the earliest forays into mathematical modeling and theoretical speciation research. Then he discussed fitness landscapes of various kinds, evolution on them, peak shift models and the difficulty of getting across valleys, the Bateson-Dobzhansky-Muller model of neutral mutations leading to reproductive isolation due to epistatic interactions, and movement along "nearly neutral networks" on high-dimensional "holey adaptive landscapes." Much of this covered similar ground to his very important 2003 paper "Models of Speciation: What have we learned in 40 years?" Then he wrapped up with an overview of models of non-random mating and sympatric speciation, touching on the importance of a cost of choosiness in inhibiting the development of assortative mating. Little is known empirically about costs of choosiness, but this is a central consideration for speciation theory. Empiricists, take note!
Nick Barton walked us all through the rather intricate details of a remarkably powerful extension to population genetics that he has developed with Michael Turelli and Mark Kirkpatrick. This method allows the effects of dominance, epistasis, and linkage disequilibrium to be accounted for much more tractably than with more traditional methods. In many situations these effects can be ignored, because populations are often well-mixed (because selection is weak compared to recombination), and so selection acts chiefly on the marginal, additive effects of genes. Not so in speciation theory, however, because speciation typically implies strong selection, non-random mating, and mixing of populations between divergent habitats, all of which cause linkage disequilibrium, and because reproductive isolation is often based upon epistasis, and so forth. Indeed, he said that speciation might best be formally defined in terms of linkage disequilibrium; so clearly speciation theory must tackle the causes and consequences of that! In later talks Dr. Barton used his method to explore speciation in the Levene model, with reference to Felsenstein's classic 1981 "Santa Rosalia" paper, and then wrapped up with a survey of models of parapatric speciation and clines.
Sander van Doorn talked about the role of sexual selection in speciation. Dr. van Doorn is one of those speakers who is so eloquent that he makes very complex ideas seem simple... until, a few moments after he stops speaking, the illusion of perfect understanding that he had cast over you melts away. Sexual selection is a multifarious topic. There are cue traits and preference traits, ornaments and honest signals and nuptial gifts and parental investment, male-male competition and female choice, good-genes models and magic-trait models and Fisherian runaway sexual selection models. There is the problem of coexistence of ecologically identical species after speciation due to sexual selection, and the problem of the origin of variation in mating preferences. He surveyed a wide range of models touching upon these and other issues, and I'm not going to try to summarize it all except to say that it was very interesting and I look forward to a review paper from him covering the same ground!
Eva Kisdi gave a very clear and gentle introduction to adaptive dynamics, starting with the Levene model and the fine-tuning problem, then introducing the tools of adaptive dynamics from pairwise invasibility plots to the criteria for classifying singular points. One pithy statement that she made stuck with me: natural selection is usually called "the survival of the fittest", but when an evolutionary branching point is present, it instead selects for increasing diversity! Perhaps that nicely encapsulates why I find speciation theory fascinating. She walked us through a very cool proof of a method of determining the constraints on trade-off functions that will produce evolutionary branching in any given model – even models for which analytical results cannot be obtained. In later lectures, she showed how to do adaptive dynamics for sexual populations, and then applied that method to a magic trait model.
Finally, Dan Bolnick grounded the school with talks (and a workgroup that I participated in) on the interactions between theory and data. He started with a summary of what he thinks are the big questions in speciation research today, and summarized contributions from theorists and empiricists to those questions. I found this to be a very helpful clarification of the "big picture": why we were all gathered together in a classroom for a week to talk about speciation. He then took a step back and talked about how exactly theory and data can interact, what theory typically does for empirical work, what empirical work typically uses theory for, and the limitations inherent in those interactions. He proposed that there are four types of interaction. The first is that theory and empirical work can be "in the same room", sharing a biological context but not actually meeting or speaking to each other. Alternatively, work can be data-driven, with novel empirical findings driving new theory to explain what was observed, or theory-driven, with interesting theoretical findings pushing empirical investigation of questions that had not previously been examined. Most intimately, there can be a reciprocal interaction in which each prompts new work in the other, in a feedback loop between theoretical refinements and new experiments. He capped things off with a tale of
Tribolium, an insect that has been leading him and a postdoc in his lab on a wild goose chase through both theory and experiment, with a mysterious cliff-hanger ending that has yet to be resolved.
Other speakers touched upon the interaction between theory and data too:
- Dr. Gavrilets, for example, opined that the maturity of any scientific field can be assessed by its level of mathematical sophistication, and that evolutionary biology is therefore the most mature subfield of biology – a provocative claim! – and also quoted Haldane as saying that one should mistrust any verbal argument when an algebraic argument would instead be possible, and that skepticism is warranted whenever not enough facts are known to permit an algebraic argument from being formulated.
- Dr. Barton emphasized that he thinks there is a need to relate theory more to things that we can actually measure, and for empiricists to then actually measure those things. For example, adaptive dynamics predicts that populations will evolve towards stationary points and then often experience disruptive selection; this is an extremely important prediction, but it has not been tested. Can it be tested? If not, can the predictions of adaptive dynamics be framed somehow in a more testable way?
- Dr. van Doorn pointed out that in reality, a species can respond in many different ways to selection pressures: evolution of dominance, concentration of genetic variance at just a few loci (evolution of polymorphism), broadening their resource utilization curve, evolving sexual dimorphism, evolving plasticity... but because of the kind of models we build, with very little genetic flexibility or realism, we have little to say about when these different outcomes should be expected instead of speciation. Can we make better models? How can empirical data help us to do so?
- Dr. Kisdi, in her discussion of trade-offs, emphasized that so little is known empirically about the shape – or even the existence! – of trade-off functions in nature that theorists have more or less free rein to speculate in this area. In the workgroup that I participated in with Dr. Bolnick, we returned to this issue in more depth, and one of my fellow students, Pavel Payne, gave a brief presentation about what little is known about trade-offs in nature. How can we know so little about something so central? What can we can do improve this state of affairs? And are there ways that theorists could help what what must ultimately be an empirical project in this area?
For me, these discussions of the interaction between theory and data were the most thought-provoking part of the summer school, because they spoke to my developing identity as an evolutionary modeler. What does it mean to be a modeler? If your models are untestable, are you still doing biology, or are you doing pure mathematics? Is evolutionary modeling an undertaking whose primary aim is to inform and explain empirical work, or is it a field that stands on its own, and that does not necessarily need to be useful to empiricists to be worthwhile? Alternatively, if Dr. Gavrilets is right that it is the mathematical models that show the maturity of the field, then is empirical work in biology perhaps an undertaking whose primary aim should be to supply data, parameter values, and scenarios as fodder for modelers? Do theory and data have a mutualistic relationship, or a commensal relationship, or a competitive relationship – or is one perhaps even a parasite of the other? Is the "reciprocal interaction" between theory and data that Dr. Bolnick described the best way for the two to interact, or are other ways – even just being "in the same room" – just as good, or perhaps even better? There were as many answers to these sorts of questions as there were participants at the school, and that made for very rich and interesting discussions, to me.
I got to go with my friend in Helsinki to a traditional public wood-burning sauna (awesome!), and then several times I used the sauna at the convention center where the summer school was held, too. So I can definitively state that saunas are not only good in theory; I have confirmed this experimentally, and I have replicated my results several times in independent trials. This, I think, is the best of all possible outcomes of the interaction between theory and data. May all your research endeavors go so well.
And perhaps that's where I can find a thread to tie together my touristy travelogue with the summer school. Ultimately, for me, it is the real world that I wish to understand and explain. Reality is more beautiful than any mathematical model, to me, and mathematics is just one tool (albeit both a beautiful and useful one) to help us understand reality. No model would ever predict the Church on Spilled Blood. Ergo, tourist snaps of St. Petersburg. And on that note, let's shift back to the tourism to wrap things up!
At the end of the school, we spent the final evening in
Naantali, a charming little tourist trap on the coast. For some reason, Naantali is associated with the
Moomintrolls, a set of children's book characters, and there was Moomin-kitsch everywhere. I grew up reading the Moomin-books, though, so it was fun for me (and I now regret not buying something related to the
Hattifatteners, my favorite part of those books). We had a really yummy dinner at a local restaurant and enjoyed the views of the Baltic and the amazing
Archipelago Sea off the coast of Finland. Here's a Moomin-flag for the
Moomin World at Naantali, and then a shot of Dan Bolnick looking for (and finding!) stickleback in the waters of the Baltic, with the beginnings of the archipelago behind him:
The summer school was organized by Eva Kisdi and Tadeas Priklopil, who did a great job of making the event run smoothly. Thanks to Eva and Tadeas, to the lecturers who gave so much of their valuable time, to my fellow students for making it fun, and to FROSpects and the other organizations that made this school possible!
Participants at the summer school. (I'm the guy in the lower
right who is so white that he looks like he'd glow in the dark.)
Those who want more travel details and photos will eventually be able to find them on my photography website, cloudphotographic.com, but they won't be there for a couple of months, probably, and by then you will all have forgotten.
