Field of Science

Both robust and evolvable

ResearchBlogging.orgWhen the environment is stable, it's good to be robust against mutations. This is because all mutations in an adapted organism will be deleterious or neutral.

When the environment changes, being robust against mutations means that it is more difficult to adapt, so being robust is not good. This is because robust organisms have a hard time finding the mutations that lead to phenotypic change.

These two truisms are the basis for the suspicion that organisms that are mutational robust are less adaptable.

I an recent paper in Nature, Mutational robustness can facilitate adaptation, authors Draghi, Parsons, Wagner, and Plotkin demonstrate how this is not always true, contrary to the simple expectation. Being robust sometimes leads to higher evolvability.

Evolvability [wiki]
Evolvability is one of these relatively new notions is evolutionary biology. The idea is that different populations (at any level) have an unequal ability to evolve. Some will be better able to respond to the changes in the environment that necessitate phenotypic change. The better able a population is to generate new, beneficial, heritable phenotypic change, the more evolvable it is.

Note that Günter Wagner is sort of the godfather of evolvability, which by default makes you pay attention. (Don't confuse with Andreas Wagner, no relation, except Andreas was a student of Günter, and works on similar things.)

They investigate this problem using a very straightforward computational simulation, and compare the results with a not so straightforward mathematical model developed for the purpose. I will explain the former, and ignore the latter, except to say they find perfect agreement between the two.

Their model has just five easy parameters:

N - number of individuals in the population
P - number of possible phenotypes
K - number of phenotypes accessible by a single mutation from a given genotype
q - the probability that a mutation is neutral
μ - the probability that an offspring will have a new genotype (aka mutation rate)

P, K and μ describes the mutational neighborhood of each individual. If K=5 and q=0.4, then part of the network of genotypes could look like this:

The nodes represent different genotypes, and the colors are different phenotypes. If you are a red phenotype, there is a 40% chance that a mutation will produce a different genotype with the same phenotype. Under one of the assumptions made in the paper, all other phenotypes are lethal, meaning that if your offspring is blue, purple or green in the figure, then they don't survive. Life's hard, if you even get the chance.

They let the population evolve under the Moran model, which just means that every time-step one individual is chosen at random to have a offspring that then replaces one individual chosen at random (may be the parent). First they let the simulation run until the population has equilibrated on the neutral network of viable genotypes. The population thus spreads out over the network of different genotypes but identical phenotypes.

Once this equilibrium has been reached, they randomly choose just one other phenotype not on the neutral network to be the goal of adaptation (i.e. one non-red color), and then let the simulation go until an offspring finds this genotype. The adaptation time, the time from creating the goal genotype until it is found, τΔ, is their ad hoc measure of evolvability. Shorter time means higher evolvability.

The first expectation is that the more robust organisms are, the harder it will be for them to find the new genotype. In this experiment we would thus expect τΔ to be larger for more robust organisms, i.e. the larger q is.

However, what they find is that adaptation time is only a monotonic function of q when K=P, i.e. when the mutational neighborhood of each genotype is all possible phenotypes. In this case the goal phenotype can be reached with one mutation from any genotype. Thus, the more of the genotypes that are neutral (same phenotype), the higher the chance that a mutation will not find the goal phenotype with each mutation. In the figure below, this is the red curve, showing that adaptation time increases the more robust the organisms are, and that organisms with no robustness (q=0) are most evolvable.

But, when K is smaller than P, so each genotype is connected to fewer of the total number of phenotypes, then the shortest adaptation times are for q>0, or an intermediate amount of robustness. The smaller K/P is, the larger the optimal amount of robustness is (the minimum adaptation time shifts to the right as K/P decreases).

What they don't discuss in the article is how for any level of robustness, the most evolvable organisms are those with a higher K/P ratio. In other words, whatever q is, the larger the fraction of the total number of phenotypes that are accessible by a single mutation, the shorter the average adaptation time will be. I then wonder if the K/P ratio is something that organisms can evolve to optimize as well. Obviously K=P is highly unrealistic - expecting all phenotypes to be one mutation away would be idiotic, but perhaps it is a variable that selection could act on?

This is a very nice result, neatly delivered, and very nice to know. But...

Why is it in Nature, is what I want to ask? The abstract begins this way:
Robustness seems to be the opposite of evolvability. If phenotypes are robust against mutation, we might expect that a population will have difficulty adapting to an environmental change, as several studies have suggested[1, 2, 3, 4]. However, other studies contend that robust organisms are more adaptable[5, 6, 7, 8].
That is, while four studies have suggested the naïve expectation, four others contend that robustness does not need to mean less evolvable. This study then makes it clear that... well, what I just said, but given all the trouble that researchers have getting their manuscripts accepted in Nature, it seems odd that they would publish this one. For example, one paper from 2007 by Andreas Wagner, Robustness and evolvability: a paradox resolved, who writes this in the abstract:
I here resolve this tension [between robustness and evolvability] using RNA genotypes and their secondary structure phenotypes as a study system.


A consequence is that finite populations of sequences with a robust phenotype can access large amounts of phenotypic variation while spreading through a neutral network.
Sounds exactly the same to me.

But, I am thrilled whenever I see studies on evolutionary simulations published in Nature, because I hope to have something published there one day myself. Even if I have to do the math.

Draghi JA, Parsons TL, Wagner GP, & Plotkin JB (2010). Mutational robustness can facilitate adaptation. Nature, 463 (7279), 353-5 PMID: 20090752


  1. Thanks very much for your interest in our paper, and the really nice
    presentation of our results.

    I'm glad you mentioned Andreas's paper, since
    it was an important inspiration for our work, and it deserves to be
    widely read and appreciated. The principal difference between the two papers
    is that Andreas explored the RNA-folding landscape via computer simulation,
    whereas formulated and analytically solved a general population-genetic model (and also
    showed that the general model predicts the behavior of the RNA-folding landscape in particular).

    If you read it carefully, I think you might agree that Andreas' work doesn't
    fully resolve the paradox of robustness and evolvability: most importantly, the quantitative effect
    of robustness on the rate of adaptation in a population is not addressed. Andreas' paper makes an insightful distinction between "genotypic"
    robustness, which inhibits evolvability, and "phenotypic" robustness,
    which facilitates adaptation. However, these two concepts must be
    unified to predict the actual rate of adaption. This is the crucial
    step that we tried to tackle in our paper, and this step
    required grappling with stochastic population dynamics. By moving from
    a simulated, RNA-specific fitness landscape to a very general, abstract model,
    I think our work has helped to clarify the essential aspects of epistasis that influence adaptation. A general
    population-genetic model permitted a rigorous mathematical approach to
    these stochastic dynamics, and it allowed us to really test which
    elements of a fitness landscape truly determine the robustness-evolvability

    Simulations with RNA folding algorithms, by Andreas and many others,
    have produced some thought-provoking and exciting results. I hope our
    work will encourage others to appreciate these papers and to
    incorporate the resulting ideas into the long-standing mathematical framework
    used by population geneticists.

  2. Jeremy, thanks for the clarification. I haven't read Andreas' paper, except for the abstract. I will incorporate your comments into the journal club talk I will give on your paper next week. You're invited of course. It's in California, though.

    Are you working on something related now?


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