Monday, October 31, 2011

Magic traits, muggle traits and squib traits

Speciation is a tricky business. Let's consider ecological speciation [1], a broad term for speciation that is the result of adaptation to different environments. The idea here is that 1) different environments generate divergent selective pressures on organisms, 2) this divergent selection causes divergent adaptations to the different environments, and 3) this divergent adaptation then leads to reproductive isolation, by various mechanisms. (The different "environments" might be in different places, at least partially geographically isolated from each other, or they might actually be different habitats or niches in a single place, such as different plants in a single meadow that plant-eating insects might adapt to eating; I'm going to gloss over this "allopatry" versus "sympatry" distinction here since it isn't particularly important to the points I'm going to discuss.)

Here's a specific empirical example: one of Darwin's finches, the Medium Ground Finch (Geospiza fortis) of the Galápagos (Fig. 1; discussed more in the previous post on this blog). We'll consider these birds as an example of "speciation in progress," but of course this means that it might not be an example of speciation at all – the early stages of divergence observed in this system may never "run to completion" and produce two fully distinct species. But because speciation is a process, it's best understood by looking at it as it's happening; by the time it's complete, much of the evidence regarding exactly how the process unfolded has vanished.

Figure 1. The Medium Ground Finch (Geospiza fortis), showing a
small-beaked individual (left) and a large-beaked individual (right).
Photo courtesy of De Léon, L.F.

To make a long story short, and glossing over many important details (see that previous blog entry and [1-4] for further discussion and cites), in the Galápagos there are small seeds and large seeds. The finches eat the seeds, and their beak size matters for this purpose because a large beak can generate more bite force than a small beak. So small-beaked birds are better suited to cracking small seeds, and large-beaked birds are better suited to cracking large seeds. The environment, by offering up these two seed types, is therefore applying divergent selection to the finches, and the finches, obediently following Darwin, have diverged adaptively: there are small-beaked morphs and large-beaked morphs, and the phenotypic distribution is bimodal, meaning there are relatively few medium-beaked morphs.

So that's great. Divergent selection, divergent adaptation – speciation? Not so fast. The problem is that sexual species, like these finches, mate, and when they mate, their offspring inherit chromosomes from both parents, which leads (in the typical case) to intermediate phenotypes. In other words, when a big-beaked finch mates with a small-beaked finch, their hybrid offspring will tend to be medium-beaked. So sexual reproduction pulls a population back together, opposing the diversifying force of divergent selection. This is the reason why the most commonly used definition of "species," the "biological species concept," defines "species" as being (mostly) reproductively isolated; if you're not reproductively isolated, then there's always the possibility that your incipient diversity will collapse back into a single phenotype due to mating.

How can this problem be overcome? This is the third and final step of ecological speciation, as I set it out at the beginning of the post: divergent adaptation must somehow lead to reproductive isolation. The finches seem to manage this: in some populations, there are relatively few medium-beaked morphs. There are lots of ways in which this can be achieved, and that's really what I want to talk about in this blog entry. Back in 2004, Sergey Gavrilets coined the term "magic trait" in a now-famous passage:
In the models considered so far in this chapter, speciation requires the establishment of correlations between the DS [divergent/disruptive selection] alleles and the NM [non-random mating] alleles. This requirement disappears if the same set of loci pleiotropically control both the trait subject to DS and the trait used in mating, or if the same trait underlies both processes... In this section, I consider several models, which I call magic trait models, describing such situations. [2, p. 368; emphasis in original]
This passage actually refers to exactly the problem discussed above. In order to speciate, you need to diverge in the alleles that are under divergent selection – the "DS alleles." You also need to establish non-random mating somehow, so that the small-beaked guys don't mate with the big-beaked guys; in the models being discussed by Gavrilets, this is achieved by diverging in "NM alleles" that affect mate choice (for example, one NM allele might be expressed as a preference to mate with small-beaked finches, and another NM allele might be expressed as a preference to mate with large-beaked finches). Finally, for this to result in speciation, there must be the "establishment of correlations" between these two types of divergence: the non-random mating must be aligned with respect to the trait under divergent selection. It does you no good to diverge into groups that prefer small versus large beaks, if what the population is actually diverging in ecologically is red plumage versus blue plumage. Similarly, it does you no good if the individuals with small beaks end up with the allele coding for preference for large beaks, and vice versa. That's the problem in a nutshell: how to establish this correlation between DS alleles and NM alleles ("linkage disequilibrium" is the technical term).

In that passage, Gavrilets gave a solution as well: establishing that correlation is much easier if the loci under divergent selection and the loci that affect non-random mating are one and the same. Then divergent adaptation leads inevitably to non-random mating that allows the divergence to be maintained. It's like magic! (Fig. 2)

Figure 2. Magic, performed in this case by Harry Potter.

But there are several things about this definition that are hard to pin down, and so confusion reigned o'er the land until Servedio et al. bravely stepped into the fray [3]. In their much-needed paper, they clarify this definition in several important respects. First of all, there's the confusion over whether a magic trait is a phenotypic trait, as commonly imagined with reference to traits like beak size (and there are many other examples; see [3]), or whether it's actually a "magic gene" that governs such a trait, or perhaps even a set of "magic genes" (note Gavrilets' use of the word "loci," plural). I'll let you read [3] to see how they handled this hot potato. Second of all, there was a thorny problem regarding exactly which sorts of traits would be considered "magic" and which would not. Servedio et al. resolved this by defining two types of magic traits, "automatic" and "classic," which I'll explain with reference, again, to G. fortis.

Consider a large-beaked finch and a small-beaked finch that mate and have a medium-beaked baby finch (aww, isn't it cute?): that baby finch is the problem, and it must be eliminated. How to eliminate it?  (I am speaking loosely for rhetorical purposes; I mean that it must be eliminated if divergence is to proceed, but of course G. fortis is not planning all this, nor is evolution guided somehow towards a goal of speciation.) One mechanism is via selection against that hybrid. If there are no medium-sized seeds in the system, then our medium-beaked bird will probably be outcompeted, will have low fitness, and will be relatively likely to die before reproducing. Through this mechanism, beak size is an "automatic magic trait"; reproductive isolation occurs, via selection against hybrids, as an automatic consequence of beak size being under divergent selection. There are other mechanisms by which magic traits can be automatic, involving spatial or temporal isolation, habitat choice, and some kinds of pollinator-related dynamics; see [3] for more details.

The other way that this undesirable baby bird can be eliminated (again, speaking loosely) is by not having it in the first place, through mate choice. If small-beaked finches prefer to mate with other small-beaked finches, and large-beaked finches prefer to mate with other large-beaked finches, then fewer hybrids will be produced (perhaps even none). And in fact, G. fortis does seem to mate assortatively, small with small and large with large, both because of a visual preference based on beak size, and because of imprinting on parental song, which, because beak size affects song, leads to a preference for mates with a beak size similar to one's own. This (both of these mechanisms of assortative mating based on beak size) makes beak size also a "classic" magic trait, by the definition of Servedio et al. The key distinction is that the non-random mating here is not inevitable or automatic; even with beak size under divergent selection, there is no a priori reason to think that that will lead to assortative mating. Instead, a separate genetic mechanism of some kind must be in place that establishes the rules that make it work, a mechanism that produces behaviors such as "I prefer to mate with males that have large beaks" or "I prefer to mate with males that sing a song like the one I heard my father sing when I was a baby." (I am here glossing over a further complication, between one-allele and two-allele mechanisms; see [3] and Felsenstein 1981). Once those rules, saying in one way or another "use beak size as a male mating cue," are set up (and they may have been set up in an ancestral species, long before G. fortis evolved), beak size acts as a magic trait; but since the use of beak size as a mating cue depends on that separate, external mechanism, it can be broken down, so it is not "automatic," it is "classic."

So far so good. Now our finches are 1) under divergent selection, 2) they exhibit adaptive divergence in response, and 3) they can preserve that adaptive divergence, to at least some extent, because the trait that is diverging, beak size, also "magically" produces assortative mating through both an automatic mechanism (selection against medium-beaked hybrids) and two classic mechanisms (female preference for particular beak sizes, and female preference for songs similar to the parental song they imprinted on). So... speciation? Again, not so fast.

The problem is that there are still various ambiguities and problems surrounding the "magic trait" definition, and so I and four co-authors wrote a letter to TREE [4] in response to Servedio et al. (and Servedio et al. replied [5]). Let's look at these difficulties, continuing with G. fortis as our example (see [4] for cites in support).

First of all, it's hard to decide whether beak size in G. fortis is truly "magic" or not, even by the clarified definition of Servedio et al. In G. fortis, divergent selection is only present in some years (and only at some sites); in other years (or at other sites), particularly when seeds are plentiful and so competition is low, medium-beaked individuals seem to do fine. So the black-and-white requirement of a "trait under divergent selection" is fulfilled only some of the time; is that good enough or not? In our letter, we propose that the "magicness" of magic traits is really the result of a trait-environment interaction. Beak size is not a "magic trait" unless it is placed in an environment that subjects it to divergent selection. In other environments, it is a "muggle trait," a trait which influences non-random mating but which is not presently under divergent selection; if a muggle trait is subjected to divergent selection, it becomes a magic trait. "Muggle trait" is a term coined by Eva Kisdi following the Harry Potter terminology in which "muggles" are people that are non-magical (Fig. 3). Similarly, such "magic environments" are only magic for organisms with a beak size trait that is used as a mating cue. So there will be, then, a spatiotemporal mosaic of "magicness" in those spots where the trait and the environment come together. It doesn't really make sense to talk about a "magic trait" except with reference to the "magic environment" it is in.

Figure 3. Muggles (unidentified); note their
aposematic coloration, perhaps Batesian mimicry.

Whether beak size in G. fortis is magic is unknown for other reasons as well. The "automatic" part of the non-random mating, since it depends upon selection against hybrids, occurs only for some years/sites, as just explained. The "classic" aspects of non-random mating in G. fortis depend upon how consistently, through time and across space, beak size is used as a mating cue, and that has not been studied well enough to draw firm conclusions, to my knowledge; it may be, for example, that beak size is only important for mate choice in lean years. The requirement of pleiotropy is also on slightly shaky ground, although it's better established than other aspects. Beak size certainly seems to be the trait under divergent selection, and seems also to be the trait used as a mating cue, and so pleiotropy seems guaranteed (since beak size and beak size are the very same phenotypic trait). But the hypothesis that beak size is the true trait subject to both divergent selection and assortative mate choice (rather than a correlated trait) can only really be shown conclusively with manipulative experiments (altering beak size somehow and observing the effect on fitness and mate choice) that are impossible to conduct since the Darwin's finches are protected species; so pleiotropy is not conclusively proved.

So we can't actually say whether beak size is magic or not; indeed, we can't even say with certainty whether any of the three definitional requirements are satisfied, despite this being one of the most extensively studied species on the planet. But there's a problem in the other direction as well: it might be a little too easy to claim that beak size is magic. You see, the definition of "magic trait" says nothing about the magnitude of any of its requirements. Even the tiniest amount of "divergent selection" greater than zero suffices. Even the tiniest tendency towards "non-random mating" above panmixia suffices. And even the tiniest amount of pleiotropy suffices, too – one could imagine an organism for which nose length is under divergent selection, toenail growth rate is used as a mating cue, and these two traits are largely governed by independent loci, but there is one locus, perhaps a regulatory gene of some sort, that has a tiny pleiotropic effect on both. That regulatory gene would then be a "magic trait" despite its very small pleiotropic contribution to the two phenotypic traits in question. So the definition draws a line, but at a place that isn't really related to the function of the thing being defined.

There are lots of cases where we work with such definitions. The car up on cinderblocks in your neighbor's yard had its wheels taken off a couple years back, and its engine is probably rusted firmly together; but it's still a "car," even though it isn't usable as transportation (Fig. 4). On the other hand, we often choose not to use such definitions. The "biological species concept" (BSC) definition of "species," set out by Ernst Mayr, originally required complete reproductive isolation between species, because otherwise two putative species might collapse back into a single species, in a case of the random mating problem we've been discussing, writ large. But in later writing Mayr (and the rest of biology) backed off from that requirement, as it became clear that many species in nature actually do hybridize with other species to a limited extent, and thus the absolute definition would not draw a line in a useful place. Rather than trying to draw a new, arbitrary line regarding just how much hybridization is allowable, the working definition of the biological species concept now essentially allows a vague "you know it when you see it" amount of hybridization. Despite this vagueness, it has proved more useful than the old, absolute definition. (Similarly, if you asked your neighbor "Hey, can I borrow your car?" and he gave you the keys to the Chevy on blocks, you would probably be unhappy – and if this happened frequently, you might start considering a different definition for the word "car"!)

Figure 4. A car.

Another reason the original BSC definition of "species" was loosened was that it wasn't testable. How do you prove that two species positively, absolutely, never, ever, interbreed? That's unprovable, and so the definition, used strictly, was useless. Similarly, how do you prove that a given trait 1) is not subject to even the tiniest smidge of divergent selection, 2) absolutely never affects mate choice, and 3) is not governed, even to the tiniest degree, by pleiotropy at any locus? You could never prove such a proposition, for any trait, and so for all we know, every single trait in every single (sexual) organism is magic. In fact, that's not even an unreasonable thing to assert. I think it might even be true. So maybe that's a problem.

This starts to get at the heart of the problem: effect size. The effect size of a magic trait is "how much the trait contributed to the evolution of increased reproductive isolation" [3]; in other words, it is how important the magic trait actually is for speciation (or was, to be precise, since the definition is retrospective). The main point of our letter was to underline that this question of effect size is actually the important empirical question in need of investigation. "Magicness" may prove somewhat of a red herring, since, as described above, it's almost impossible to prove with certainty that a given trait is magic, and yet at the same time probably most or even all traits are in fact magic. We coined a term for the (perhaps very common) magic traits of very small effect: "squib traits." Like Kisdi's term "muggle trait," this comes from the Harry Potter world; a squib is a person who is born of magical parents, and who is magic in a non-useful sense (squibs can see Hogwarts, for example), but who cannot actually perform magic. A squib trait is like a Chevy on cinderblocks; it may be magic, but it ain't gonna take you anywhere (Figs. 4, 5).

Figure 5. A squib, Argus Filch, with his cat, Mrs. Norris.

Sadly, TREE nixed our coinage of "squib trait" (apparently there are still people somewhere who haven't read the Harry Potter books, and so the reference might be confusing :->), so we used the term "trivial magic trait" (versus "important magic trait") instead. Eva Kisdi's term "muggle trait" hasn't made it into the primary literature yet either. Bonus points to the first person who manages to get these terms into print!  :->

I've done a lot of arguing about the definition of "magic trait" here, because I think it's interesting and it leads the discussion through many important issues, but it's the definition we've got, and it may be as a good a definition as any other that anybody could have come up with. What we really wanted to emphasize with our letter is: the definition is what it is, but the important questions in speciation do not revolve around the distinctions at the line between magic and non-magic. Rather, the important questions are things like:
  • How can we measure or estimate the expected effect size of traits in nature, given that the definition of "effect size" is retrospective?
  • How common are magic traits of large effect size in nature, compared to traits that are either non-magic, or magic but of very small effect size (i.e. squibs)?
  • How often is speciation driven by magic traits of large effect size, as compared to other mechanisms in which the magicness of traits is not important? (And, to follow up on a point in [5], are there plausible mechanisms in which magic traits of relatively small effect size are still important to speciation? But – if there are, then aren't those magic traits, by definition, of large effect size?)
  • What drives the evolution of effect size itself; are there evolutionary mechanisms that tend to promote large effect sizes in magic traits, or were the magic traits of large effect size that we are beginning to find in some systems just produced by happenstance?
To illustrate the point here more forcefully, let's return one final time to Geospiza fortis. As biologists interested in speciation, what should we study about G. fortis to try to better understand the dynamics of the incipient speciation that may be occurring in that system? We could try to determine, once and for all, whether beak size is a magic trait, and if it is, to what extent it is "automatic" versus "classic." That would probably involve a great deal of hairsplitting work regarding the genetic basis of beak size, manipulative experiments to show how much of mate choice involves beak size per se versus correlated traits (and are those correlated traits pleiotropically linked to beak size, then?), replication across time and space to show exactly when and where beak size is and is not under disruptive selection and is or is not used as a mating cue, and so forth. In the end, we might be able to find an answer; and yet we still might not know much more than we know now about how beak size affects speciation. If instead we focus on effect size, we will find out so much more, because we'll be focusing on what really matters: to what extent beak size allows and even drives adaptive divergence and speciation, and how much of the adaptive radiation in Darwin's finches has been driven by beak size acting as a magic trait of large effect. Isn't that what we want to know?

Servedio et al., in their reply [5] to our letter, offer up some strong counterarguments to some of this, and remind the reader, in other cases, that they did give some consideration to these issues in their original paper (although not, we felt, enough consideration). But since this is my blog entry, and since it's already too long, I think I'll stop here, and let you, gentle reader, pursue the thread of argument further if you wish. And perhaps we can get a guest post from one of Servedio et al., to give you their own perspective!

Posted by: Benjamin C. Haller


1. Schluter, D. (2001). Ecology and the origin of species. Trends in Ecology and Evolution 16, 372-380, doi:10.1016/S0169-5347(01)02198-X

2. Gavrilets, S. (2004). Fitness Landscapes and the Origin of Species. Princeton University Press

3. Servedio, M.R., Van Doorn, G.S., Kopp, M., Frame, A.M., Nosil, P. (2011). Magic traits in speciation: 'magic' but not rare? Trends in Ecology and Evolution 26, 389-397, doi:10.1016/j.tree.2011.04.005

4. Haller, B.C., De Léon, L.F., Rolshausen, G., Gotanda, K.M., Hendry, A.P. (in press). Magic traits: distinguishing the important from the trivial. Trends in Ecology and Evolution, doi:10.1016/j.tree.2011.09.005

5. Servedio, M.R., Van Doorn, G.S., Kopp, M., Frame, A.M., Nosil, P. (in press). Magic traits, pleiotropy and effect sizes: a response to Haller et al. Trends in Ecology and Evolution, doi:10.1016/j.tree.2011.09.011

Supplemental data:

Figure S1. This is my nephew, who has a rather different
kind of magic trait action going on, as you can see. This
trait is hypothesized to be vulnerable to Kryptonite.
Happy Halloween, everybody!


  1. Hi Ben,

    I enjoyed reading your post on magic traits, and have some follow-up thoughts. I know, I know, you were hoping for a post from the Servedio camp. So I here I am as a substitute option, hopefully not as objectionable as Delores Umbridge was in her fleeting role as Professor of Defence Against the Dark Arts...

    First off, it's a real shame that TREE wouldn't let you publish your Harry Potter terminology. I was immediately reminded of a couple of classic publications that referred explicitly to Lewis Carroll characters: The experimental psychologist Frank Beach's 1950 paper "The Snark was a Boojum", and the ethologist Peter Klopfer's 1973 book "On Behavior: Instinct is a Cheshire Cat". Literary references applied to scientific papers can really help articulate a point with clarity and power ("squib traits"? awesome!). I've just been pondering again Dawkins' "The Selfish Gene", for upcoming lectures on kin selection, and I see that there are more gems to be mined from the Harry Potter canon. Are not genes that code adaptive traits a sort of horcrux, repositories of information that transcend the lives and fates of their bearers? Would I err in suggesting that principles of group selection guided the actions of the corrupted ministry of magic, as manifest in the series' final volumes?

    Second, I applaud the main point of your letter and blog post, which I read as a call to arms for further empirical study. But there are several content points that I think merit slight clarification or expansion. You do acknowledge that your post glosses over some important details, but some extra precision never hurts.

    -- When discussing the two morphs of the medium ground finch in our El Garrapatero studies, I wouldn't say that the environment offers up two seed types (large and small). The situation is actually a lot more complex than that, with dozens of food types available and consumed. Indeed, statistical analyses are showing us (in data yet to be published) that there are clusters of softer and harder seeds, consistent with the selection data. But a tight link between seeds and selection on beaks has yet to be established for this population.

    -- I find it premature to talk about spatial and temporal variation on selection against morph "hybrids", because we really only have those data for one site (El Garrapatero). Furthermore, at this site, while it seems likely that the selectively-disfavored intermediate birds were inter-morph hybrids, we unfortunately don't have pedigree data that could confirm that directly.

    -- In assessing the "classic" magic trait definition in Darwin's finches, there are several data sets published by the Grants in the 1990's that suggest quite strongly that vocal mating signals (songs) are the key reproductive isolation barrier in these birds. This inference is central to the discussion of ecological speciation, given that vocal divergence among incipient species occurs in part as a pleiotropic effect of adaptation and beak size evolution. For these last two reasons, the "classic" definition seems to me to hold sway over the "automatic" definition for the finches, at least for now, based on the data currently available.

    These observations lead me to the one statement in your post with which I heartily disagree, that this Darwin's finch is "one the most extensively studied species on the planet". That is a consistent but errant perception -- a cultural boggart? -- because in fact the number of empirical studies on this radiation is alarmingly small, taken within the broader context of the literature on ecology and evolution. So we circle back again to your prescient main point, the need for more empirical study.

    There is, of course, one other way we could enhance our study of ecological speciation. Anybody know the whereabouts of Hermoine's time turner?

    Jeff Podos

  2. Nice post Ben! Jeff I suggest for next expedition instead of mist nest we use broom sticks to catch finches. With a radar to avoid Opuntia cacti.


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