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.


About will.pearse
Ecology / evolutionary biologist

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

  1. Pingback: Friday links: valuing scientists vs. science, real stats vs. fake data, Pigliucci vs. Tyson, and more | Dynamic Ecology

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