Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales



Stasis: A population of mollusks is experiencing stasis, living, dying, and getting fossilized every few hundred thousand years. Little observable evolution seems to be occurring judging from these fossils. From Evolution 101.

Suzanne Estes and Steven J Arnold. The American Naturalist 169: 227-244. Resolving the paradox of stasis: models with stabilizing selection explain evolutionary divergence on all timescales

Lynsey McInnes

Lynsey McInnes


The last time I read this paper was when I was complaining that all the macroevolutionary analyses I was attempting to conduct were kind of crap and far-fetched. Someone recommended this paper to me as a great example of an elegant, meaningful analysis of a heterogeneous dataset with a surprisingly simple outcome. I liked it then, but it made me despair even more about the state of my exclusively macroevolutionary analyses even more.

Now that I’ve jumped ship and am trying to find my way within the field of population genetics (with a lot of exposure to quantitative genetics), I like this paper even more. But enough angst from me. What about the paper itself? The authors quickly assume that stabilising selection is the general explanation for the extensive amounts of stasis observed in temporal datasets of a variety of phenotypes and set about attempting to find what kinds of models of phenotypic evolution can generate observed datasets.

This paper is a beautiful example of an attempt to cut to the chase of a bunch of models floating around in the literature using a set-up that makes just the right amount of simplifying assumptions for a tractable answer to emerge. Estes & Arnold find that the best model of the evolution of phenotypic means (where ‘stasis’ appears to be the norm) is one of tracking a fitness optimum that can move within fixed limits. They do this by seeing what quantitative genetics model fits best to a dataset of phenotypic mean changes across one to over a million generations (so, anagenetic rather than cladogenetic/splitting evolution). As an aside, I love that their analysis could be distilled as – does our elegant QG model generate points that fit within an ellipse around our data, or not. Genius!

Their set-up allows them to dismiss the common Brownian motion model (see Will’s post below) as well as the punctuational peak shift model in favour of a model that fits nicely with Simpson’s model of adaptive zones. Phew. This is a pleasing outcome for me as it sits comfortably with a lot of macro-scale analyses (using totally different data) that often find reasonably-sized clades filling up niche space to a certain point and then not really increasing in disparity or diversity until they jump over to new empty niche space (of course, there are counter examples left, right and centre). The matching results are convincing and underline further how naïve models of trait evolution are really quite unhelpful.

The data here consists of phenotypic means through time rather than across lineages at one time point (the typical format for macroevolutionary trait evolution datasets). I wonder how you could conduct a similar meta-analysis on such data? (Related tests have been done on individual traits like body size using the Ornstein-Uhlenbeck model of bounded evolution). I wonder if the signal Este & Arnold obtain is because they include phenotypic change across time-scales (from a single to millions of generations). Their best fitting model fits the amount of change observable at these vastly different time scales (i.e., massive change on a short-time scale that irons out into ‘stasis’ at macroevolutionary time-scales). Is it possible and/or interesting to attempt this kind of analysis across lineages? What do I even mean by this?

Taking a possibly more useful track – how can this result influence how we set up and test our cross lineage trait evolution studies? Can it be used to create more useful null models?

Most of my interest in thinking of stasis in phenotypic evolution comes from thinking about and observing phylogenetic niche conservatism (really just the narrow-sense niche encompassing abiotic environmental variables). The literature is replete with purported examples of strong evidence of PNC, but pretty bare on the process of keeping a niche axis conserved. I like this paper as it demonstrates to us how stabilising selection can generate the right amount of evolution observed at different time-scales. My favoured next step would be to add in some ecology to find out the mechanisms that prevent a lineage’s niche (or elements/axes within) from wandering amok?

Apologies for the rambling nature of this point. I’d be very keen to hear what others thought of it and how this result could be used to inform future analyses, particularly at the macro scale.

Will Pearse

Will Pearse

Too few papers draw links between models of evolution among and within species (phylogenetics vs. quantitative genetics to my mind). Lynsey is doing just that, so I’m not surprised she picked this paper this week! I liked it, if only (but not just) for its excellent summary of a lot of quantitative genetic ground.

The authors make reference to how, under a Brownian motion model, noise increases through time. This is a good point that’s often missed – I’ve brought this up to comparative biologists in the past, and they often retort that the signal of Brownian motion is never lost. This is very true, but if the noise  is so large that is swamps the signal (look at figure 1 in this), then what’s the point? Drawing broad generalisations, I think this reflects how most biologists are taught statistics; we’re taught that bias is always a bad thing (beware a biased predictor! bad!) whereas machine learning people are fine absorbing a little bit of bias if the precision is sufficiently increased (intro chapter of this excellent book). Yes, under Brownian motion the central tendency doesn’t change, but the precision of your prediction is tiny because so much error is introduced given sufficient time. Thus we can still make inferences about the deep past, but sometimes we might do better asking a different question.

Which brings me to the different models that were tested, many of which are ~two decades old, which is awesome in every sense of the word. A lot of people are scrambling to build ever-more complicated models that incorporate more and more detail, and yet more are turning to methods like Approximate Bayesian Computation as the only way to fit such complex models. This paper shows that might not be needed: they/Lande simplify by taking polynomial approximations of difficult equations, and then work with those. I’m a huge fan of non-linear interactions, but even these can (under certain conditions) be linearised and approximated to draw inferences about biology. The authors go to some pains to talk about whether some of these models could be fitted to phylogenetic data (some already are); were we to make such simplifications I really can’t see why these, and even more complex models, couldn’t be.

In passing, it’s interesting that they view models of DNA evolution in phylogenetics as successfully integrated and all fine and dandy. I really don’t – I think we need to start taking into account geography, and I occasionally see someone talk about ways to integrate directional selection into phylogenetics which sounds fantastic. I shudder when I consider how many phylogenies are built using loci under incredibly strong directional selection, like rbcL and matK (I do it!), and in so doing violate so many of the assumptions phylogenetics is based on.


The ecological dynamics of clade diversification and community assembly

Mark McPeek. The American Naturalist 172: E270-E284. The ecological dynamics of clade diversification and community assembly

Blue damselfly; McPeek has studied damselflies extensively. Taken by Umberto Salvagnin (via Wikimedia).

Blue damselfly; McPeek has studied damselflies extensively. Taken by Umberto Salvagnin (via Wikimedia).

Lynsey McInnes

Lynsey McInnes

I picked this paper because I remember reading it when it came out and being taken in by McPeek’s approach. It felt like he had built up a pile of phylogenies with negative gammas (a metric mired in controversy, but that’s for another post) and then he decided he should find out whether more or less feasible processes of ecological or non-ecological divergence generate similar distributions of gamma values.

A short background note: Pybus & Harvey’s gamma purports to detect ‘slowdowns’ in diversification by quantifying the pattern of nodes in a reconstructed phylogeny. In brief, if nodes cluster near the root of the tree, gamma is negative and this indicates that diversification has slowed as we approach the present. Positive gammas could suggest that diversification has sped up as we approach the present, but inference is complicated because of the signal left by extinction, such that a positive gamma does not unambiguously support a particular pattern. Since publication of McPeek’s paper there has been a swath of further papers documenting problems with the metric, probably the no.1 being that you get one gamma value per tree so the results will be dependent on what scope of clade you have chosen as to whether you can detect a clean slowdown or not. Again, this is not a post about the ins and outs of gamma.

Rolling with the assumption that gamma can provide a useful summary of the distribution of nodes in your tree, it can be used, as here, to quantify the different branch lengths attainable under different diversification scenarios. Regular readers will know I have a soft spot for simulation studies, so could anticipate that I liked McPeek’s setup here. Basically, he wanted to find out whether if, he enforced ecological divergence upon speciation, trees are produced that show signs of slowdowns in diversification (as ecological gradients are filled in). And this was indeed what he found. Some might argue that you get out what you put in, and presumably this is true to some extent. But I still found it a neat and tidy finding.

Now its time to go off on a tangent. Don’t get me wrong, I like this paper and appreciate this kind of study. I really believe that many clades are probably subject to slowdowns as they diversify and this might often be because they have filled some limited set of ecological niches and additional species are formed by geographic isolation without ecological divergence or some other mechanism like sexual selection or filling the niche of a species that has gone extinct. I just wonder how easy or indeed, possible, it is to detect the signal of this diversification trajectory on phylogenies. Perhaps the pattern emergent at the ‘evolutionary’ timescale is rough enough that slowdowns or equilibrial diversity dynamics are detectable and ‘real’ and the more haphazard activities occurring at ecological timescales will always be evened out and undetectable and this is OK. I’m also intrigued by methods that work ‘the other way’ and take massive phylogenies and try to delimit more restricted clades that somehow obey these slowdown patterns. It often seems like taxonomists’ brains have worked in similar ways and genera and families conform to these delimitations. Which is actually pretty cool.

In short, I am mesmerised by broad-scale patterns in phylogenies and often buy into the current trend of assigning ecological explanations to them. In some sense, ecological and evolutionary processes are all part of one continuum so must impact each other, but how often have we made ourselves believe that something more than just random spliting processes are at play. I’ve currently turned my back on macro-scale analyses, but will always have a soft spot for finding out how these crazy, very clearly real, patterns are generated and why.

Will Pearse

Will Pearse

This paper is the scientific equivalent of Samuel L  Jackson in Snakes on a Plane; an old-school “I just sat down and thought” kind of paper, and I like it. It’s probably the best example of how a simulation study can be insightful, starting with some fundamental observations from empirical data, and making a model just complicated enough to derive insight.

McPeek’s reviewer raises a very good point: what does it mean for the fossil record if his simulations shows we get species appearing and then rapidly disappearing? This reminds me strongly of raceme phylogenies, although I think it’s an open question whether these short-lived species would ever be so abundant as to swamp out the main ‘trunk’ of the tree of life. That said, most people would agree speciation is rarely instantaneous, and the shape of the simulated phylogenies would probably be different if a species only became a true species after a delay (à la protracted speciation), even if those proto-species were still ecologically different from one-another.  It makes me wonder the extent to which the diversity on Earth right now is comprised of these side-shoots, and how many of these species (ignore our influence for a moment) will be around in a few million years.

I also enjoyed the discussion of variation in structure among clades. There is no reason to assume that models of evolution are constant across a clade simply because, in the present, a researcher has decided that a particular group forms coherent ecological assemblages. As always, I’m convinced that different ecological processes should be operating in clades that have undergone different kinds of evolutionary processes, but drawing a distinction between ecology and evolution is somewhat arbitrary. The power of McPeek’s approach is that there is no disconnect between the two: in his models, evolution is just ecology over-and-over-again, and examining the two simultaneously must ultimately be the best approach.

There is one caveat to this. Many (and McPeek notes this) are quick to point out that we may never be able to estimate extinction and speciation rates using phylogenies. There are very, very few cases where the fossil record is as rich as we would like, and a molecular phylogeny necessarily misses extinct species. While modelling exercises like this are fantastically useful, I am somewhat skeptical that we can ever reliably fit models this complex to real data; of course that doesn’t mean we shouldn’t try!

A ‘synthetic’ review of a year of PEGE


Conifer phylogeny from Willamette Biology
Conifer phylogeny from Willamette Biology’s photostream

Lynsey McInnes

Lynsey McInnes

We’ve come to the end of a year of PEGE! Well done us! We only skipped one week in the whole year (and it was the week in which I got married) and we managed 16 guest posters. It’s been an entertaining year. Will and I set up PEGE mostly as an excuse to keep in regular contact with each other, to ensure we regularly checked the literature and to learn how to write something more or less thoughtful in a short timeframe (for me, within the length of the train journey from Stirling to Edinburgh). I think we succeeded in all three.

A secondary aim was to get an online discussion going along the lines of a journal club. In this, we did less well. Although we know that the site got substantial traffic (from our fanatical checking of site stats), few people commented. From perusing other blogs, I think this is a hard thing to get going and we’re not going to beat ourselves up about it. I know I read other blogs, more or less regularly, and have never commented on a single one. It’s enough for us if a paper we have highlighted or a comment we have made has impacted someone’s research in any which way. I know that writing these posts has had a positive impact on the way I think about my own research and the links between what I do and am interested in and what else is going on in the PEGE world.

It was almost amusing how quickly it became apparent where Will’s and my interest lie. Regular readers can by now easily guess who wrote which post in an instance. I’ve found PEGE helpful in identifying my emerging interests and I hope to follow up some of these new found leads in my future research.

Apparently, I am super keen on intraspecific diversity and how it affects species’ responses to climate change, niche evolution and range movements. I am not a fan of community phylogenetics and can’t quite believe there is a good way to identify source pools for such analyses. I really like the idea of mesocosm experiments (although I
have no experience of them myself) and am prone to want to roll out any neat analysis on a particular study system to some sort of broad-scale comparative study. If only I had the cash and the expertise (and the time). Both Will and I are concerned with scale, the appropriate scale for various analyses (temporal and spatial), how scale affects the inferences possible and how, ultimately, a sound understanding of diversity patterns requires analyses across scales. Scale, scale, scale.

What’s up next for PEGE? We’ve decided to shake things up a little and to par down to fortnightly posts. In each, we will focus on a classic (we decide what constitutes a classic) paper from the PEGE world and hopefully spend a little more time (TWO train journeys) thinking about the paper and developing our thoughts. It’s been fun scanning the literature for new papers to discuss this year, but we often found ourselves choosing a paper based on an intriguing title and being disappointed by its content (bet you can guess which posts I’m referring to). Now we’ve had the chance to flex our commenting muscles, we’re going to try to put them to better use on ‘bigger’ papers.

Finally, thanks for reading. You know who you are. We’re hopeful that readers have enjoyed our posts and ever hopeful that our readership might grow alongside our comments column. Any tips to make PEGE better, suggestions for classics to discuss next year or requests to be a guest poster, just let us know.

Merry Christmas!

Will Pearse

Will Pearse

Wow, a whole year. I can hardly believe we’ve made it! Everything Lynsey has said is true; I’d just like to add I’m really grateful to everyone who’s read the blog. I’ve been lucky enough to talk with some of you at conferences, in comments beneath articles, and through email, and it’s always fun doing that. Thank you!

If, like I used to be, you’re skeptical of why something like PEGE is worthwhile, please believe me when I say this has been one of the most useful things I have ever done. It’s not just that this lets me constructively engage with scientists I could never otherwise hope to meet, it’s that my reading and writing skills have qualitatively improved. Every week for a year I have had to be constructively critical and engage positively with an article, then scribble out something that people will (hopefully!) find interesting. It makes you leaner, it makes you faster, and it makes you better.

If no one were reading PEGE it would be worth it for the impact its had on me alone. Many bloggers obsessively monitor site statistics – Lynsey and I are no different, but we haven’t actively sought-out more readers in the way I know others do. That’s not to say we haven’t engaged with people – we’ve replied to every comment, and I would like to think the diversity of our guest posters speaks for itself (thank you all!). I’m very happy with the audience we’ve built up (thank you again!) and if you’re thinking about setting up your own blog (do!) be reassured that you don’t have to dedicate hours every week to selling yourself on the Internet. Build it and they will come – but do make sure you email your friends!

As Lynsey said, we’re both obsessed about scale-dependency. Unlikely Lynsey, I like community phylogenetics – while I agree with her that defining source pools is tricky, I prefer to see it as a way of asking questions and don’t expect a single ‘answer’. Moreover, there’s more to community/eco-phylogenetics than source pools. Looking back through what we’ve chosen, I’m struck that there are a number of what I would call ‘case study’ papers, where there is a central story that verifies established theory and fleshes-out specific details for a particular system. Many say scientists are no longer interested in filling in the gaps with studies that have little conceptual novelty; I think it’s re-assuring that Lynsey and I have found so many excellent papers that do buck that trend. Maybe there’s hope yet!

Thanks again for reading, thanks again to all our guest posters, and thanks again Lynsey for writing, listening, and continuing to be my emotional supervisor. On to 2014!

Why abundant tropical tree species are phylogenetically old

Wang et al. PNAS 110(40): 16039-16043. Why abundant tropical tree species are phylogenetically old.

Will Pearse

Will Pearse

I’ve really come to appreciate Neutral Theory. Great conceptual leaps have come from thinking neutrally, such that drift is something a generation of ecologists now take for granted as part of orthodox ecological theory. I think this paper is a perfect example of the exciting work that can come from predicting evolution from ecology, and it’s something Neutral Theory helps make possible.

That said, I have two (slightly snarcky) criticisms. The first is I don’t think ‘species age’ is necessarily the most useful thing to be working with because a lot of things go into species age, and so it doesn’t make for the best test of many models. For example, extinction of closely related species will increase species age – if your thirty closest relatives die, you look older. The second is using a phylogeny from Phylomatic to make predictions about close relatives, because such phylogenies tend to have less resolution among congeners and close relatives. You can see this problem in the horizontal lines in figure 2a – all the congenerics have the same age because they’re within the same polytomy.

More fundamentally and less snarkily, this paper makes me think about models of speciation. What would protracted speciation look like when plotted like this? Do we find these patterns with species that undergo frequent hybridisation, like oaks? I think one of the great strengths of Neutral Theory is it lets us make predictions about the shape of present-day phylogeny, and more papers like this that move from evolutionary process to ecology are only a good thing.

Lynsey McInnes

Lynsey McInnes

First, apologies for the delay in posting PEGE this week, my fault entirely.Now, onto the paper. This was Will’s pick this week (because he loves Barro Colorado Island) and I gamely went along with it. As ever, I spent less time with the paper than I should, but found it really thought-provoking, if a bit odd in places.I like neutral theory and neutral theory predictions. It appeals to the side of me that doesn’t intuitively know what the ecological differences are among species, I like that you can start from a point where there aren’t any. And it amuses me that a theory can rile people so badly. In addition, I love most studies that attempt to bridge across scales and believe that there is a lot to be done in this area using neutral theory. Sure, we’ve come a long way since Hubbell’s hastily added speciation mechanism in the original book, but I don’t think we’ve exhausted possibilities yet.

I’ve got a confession to make. I’ve long been intrigued by range size, but never got to grips with abundance (my macroecological background rearing its ugly head again). So, the intricacies of this analysis did elude me a bit, but basically the authors find that if they add variable speciation rates to an otherwise neutral model they recover the empirical positive correlation in species age and abundance found for some tropical trees. Without the addition, the relationship should be flat or humped depending on speciation mode (mutation- or fission-, both a bit dodgy). The authors do mention that abundant species are usually also large ranged, so I could perhaps sub in range size for abundance and feel more comfortable (but would likely piss someone off).

The authors discuss how the range size-age correlation is often explained by niche differences, large range species are ecological generalists and buffered from extinction from, e.g., climatic fluctuations. They suggest their neutral model is more parsimonious than invoking niche differences and put forward ways to test this. I have a feeling their model would fall down in the face of these tests. There is also the chicken and the egg issue that there is plenty of evidence that most (all?) large range species are (at least now) more generalist than small range species…they have to be just to occupy really large ranges.

So, there is something circular at looking at ages, abundances and ranges in a neutral setting. One somehow needs to look at species as they speciate (and then they are all young) and the hunt to find reasons why some species are old (bad/unwilling to speciate) and especially how some species are old AND large ranged/abundant seems to remain unanswered. Models such as those in this paper and related ones might be the way to go, but it is going to be hard to avoid circularity.

One other thing that is dodgy and difficult to get around is how to define a species’ age. We don’t often know what species budded off from which or whether a split was more ‘even’ and this impacts on what is ‘old’ or not. Resetting age at every node of a phylogeny seems a naive (but understandable) way to go about things (and lets not even get into what extinction does to these ages).

Oops, this came out as a bit of stream of consciousness. Great paper for mulling over and I welcome all attempts to bridge macro and micro, evolutionary and ecological scales of analysis. The world is not neutral, but it seems like there is a lot to be gained from starting from the premise that it is.

Eighty-three lineages that took over the world: a first review of terrestrial cosmopolitan tetrapods

Şerban Procheş and Syd Ramdhani. Journal of Biogeography (early access): DOI:10.1111/jbi.12125. Eighty-three lineages that took over the world: a first review of terrestrial cosmopolitan tetrapods.

Cosmopolitan species... geddit? From Esquire magazine

Cosmopolitan species… geddit? From Esquire magazine

Will Pearse

Will Pearse

I really don’t know how I feel about this paper; I found the introduction the most interesting part because it introduced me to many things I never think about. The authors are asking why some species are found everywhere throughout the world, and they think up some pretty cool ways of looking at it. This seems very much like a first-pass at these ideas, and I’d be quite interested to see what more analyses these authors will do.

While many species are not cosmopolitan, their clade is – the authors use shrews as an example of a clade that is widespread, but the individual species within the clade are not. This paper examines how wide you have to make your definition of a clade to make it cosmopolitan; for instance, how many close relatives of the Arctic fox do we have to add before we have a widespread clade? I think looking at the number of species is much less interesting than looking at how old a clade has to be for it to be widespread. Moreover, if we know how widespread species are, can we reconstruct that as if it were (maybe it is) an ancestral state, and look at relationships between the evolution widespread-ed-ness and traits?

Their trait analysis says that flying things and big things are more cosmopolitan, which is essentially the same as saying that things that need more space (to hunt, to feed, etc.) cover a wider space. This in of itself is kind of interesting, because it makes me think about scaling. Large birds are at the top of the food chain, and as such they’re not so affected by individual aspects of ecology – they just need other birds or larger prey they can kill. They can spread across a number of ecoregions because the ecologically limiting factors for them are more abstract (some kind of bird, not just one kind of bird) and different to those for other species. Maybe there’s a relationship between trophic position and how widespread a species is.

Lynsey McInnes

Lynsey McInnes

I have mixed feelings about this paper, just like Will. It definitely felt like a first pass exploration, with lots of potential for extensions and I am totally happy to overlook some misgivings on the approach the authors took in exchange for their presenting an interesting and most definitely overlooked side to macroecological patterns.

I’ve thought a little about cosmopolitan/widespread species mostly with respect to dispersal ability. While the authors suggest good dispersal ability helps generate cosmopolitan taxa, I’d be inclined to take a more careful look at dispersal ability and what we mean by it. A good ‘disperser’ (let’s loosely define that as a species that can move ‘far’) can get to far-flung areas, but will this action produce one cosmopolitan taxon or lots of restricted range taxa? This will of course depend on other intrinsic traits, the nature of the environments the dispersed lineages find themselves in, the frequency of dispersal (continuing gene flow preventing divergence). While it feels logical that species that can reach a large area are the most likely to have large ranges, I think we also have to think long-term (evolutionary time?) to really understand how dispersal relates to distributions.

The above paragraph also relates to the authors’ attempt to define cosmopolitan with respect to single species but also w.r.t. multiple species (i.e., how many lineages do we need to make a cosmopolitan taxon?). This was an interesting element of the paper and I felt the authors could have pursued this line of reasoning more thoroughly. ‘What is a species’ is of course a controversial subject and one I won’t go into here, but, when it comes down to it, most of us are happy to recognise a ‘species’ as a special unit such that a single species cosmopolitan taxon is much more striking than a multi-species one (requiring different traits perhaps, and strong population connectivity). One route to untangling this conundrum might be to look at species’ ages. Are all single-species cosmopolitan taxa really young, and just en route to splitting up into multiple species? I imagine yes in many cases, but probably not all. What about this subset? How do they manage it? Of course, we need robust phylogenies for this. Damn.

The authors were also keen to relate their analyses back to invasion biology and there are clear parallels here. It would be fun to do analyses on cosmopolitan/non-cosmopolitan species and on invasive/non-invasive species concomitantly and see if the same set of traits (or indeed species) come up. Are cosmopolitan species already pests? Will they become so? Do we need to separate out old and young species? Do we need to pay particular attention to restricted-range species in the paths of invading cosmopolitans.

In passing, some of the discussion in this paper reminded me of this work by Purvis et al. looking at mammals on the edge of trait space. Without re-reading the paper, I think I recall the authors finding ‘weird’ species are able to make it when they occupy ‘weird’ niches. They might not diversify, but they can persist and persist because there’s nothing else like them. Are old cosmopolitan species also weird?

In short, an imperfect, but thought-provoking paper. I’d like to see these questions being pursued further in other groups and from different angles.

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