Understanding the Mutational Landscape Model

This post started out as a wonky rant about why a particular high-profile study of laboratory adaptation was mis-framed as though it were a validation of the mutational landscape model of Orr and Gillespie (see Orr, 2003), when in fact the specific innovations of that theory were either rejected, or not tested critically.  As I continued ranting, I realized that there was quite a bit to say that is educational, and I contemplated that the reason for the original mis-framing is that this is an unfamiliar area, such that even the experts are confused— which means that there is a value to explaining things.

The crux of the matter is that the Gillespie-Orr “mutational landscape” model has some innovations, but also draws on other concepts and older work.  We’ll start with these older foundations.

Origin-fixation dynamics in sequence space

First, the mutational landscape model draws on origin-fixation dynamics, proposed in 1969 by Kimura and Maruyama, and by King and Jukes (see McCandlish and Stoltzfus for an exhaustive review, or my blog on The surprising case of origin-fixation models).

In origin-fixation models, evolution is seen as a simple 2-step process of the introduction of a new allele, and its subsequent fixation (image).  2_step_cartoonThe rate of change is then characterized as a product of 2 factors, the rate of mutational origin (introduction) of new alleles of a particular type, and the probability that a new allele of that type will reach fixation.  Under some general assumptions, this product is equal to the rate of an origin-fixation process when it reaches steady state.

Probably the most famous origin-fixation model is K = 4Nus, which uses 2s (Haldane, 1927) for the probability of fixation of a beneficial allele, and 2Nu (diploids) for the rate of mutational origin.  Thus K = 4Nus is the expected rate of changes when we are considering types of beneficial alleles that arise by mutation at rate u, and have a selective advantage s.  But we can adapt origin-fixation dynamics to other cases, including neutral and deleterious changes. If we were applying origin-fixation dynamics to meiotic bursts, or to phage bursts, in which the same mutational event gives rise immediately to multiple copies (prior to selection), we would use a probability of fixation that takes this multiplicity into account.

In passing, note that origin-fixation models appeared in 1969, and we haven’t always viewed evolution this way.  The architects of the Modern Synthesis rejected this view— and if you don’t believe that, read The Shift to Mutationism is Documented in Our Language or The Buffet and the Sushi Conveyor.   They saw evolution as more of an ongoing process of “shifting gene frequencies” in a super-abundant “gene pool” (image).  1_step_cartoon Mutation merely supplies variation to the “gene pool”, which is kept full of variation.  The contribution of mutation is trivial.   The available variation is constantly mixed up by recombination, represented by the egg-beaters in the figure.  When the environment changes, selection results in a new distribution of allele frequencies, and that’s “evolution”— shifting gene frequencies to a new optimum in response to a change in conditions.

This is probably too geeky to mention, but from a theoretical perspective, an origin-fixation model might mean 2 different things.  It might be an aggregate rate of change across many sites, or the rate applied to a sequence of changes at a single locus.  The mathematical derivation, the underlying assumptions, and the legitimate uses are different under these two conditions, as pointed out by McCandlish and Stoltzfus.  The early models of King, et al were aggregate-rate models, while  Gillespie, (1983) was the first to derive a sequential-fixations model.

Second, the mutational landscape model draws on Maynard Smith’s (1970) concept of evolution as discrete stepwise movement in a discrete “sequence space”.  More specifically, it draws on the rarely articulated locality assumption by which we say that a step is limited to mutational “neighbors” of a sequence that differ by one simple mutation, rather than the entire universe of sequences.  The justification for this assumption is that double-mutants, for instance, will arise in proportion to the square of the mutation rate, which is a very small number, so that we can ignore them.  Instead, we can think of the evolutionary process as accessing only a local part of the universe of sequences, which shifts with each step it takes. In order for adaptive evolution to happen, there must be fitter genotypes in the neighborhood.

This is an important concept, and we ought to have a name for it.  I call it the “evolutionary horizon”, because we can’t see beyond the horizon, and the horizon changes as we move.  horizonNote two things about this idea.  The first is that this is a modeling assumption, not a feature of reality.  Mutations that change 2 sites at once actually occur, and presumably they sometimes contribute to evolution.  The second thing to note is that we could choose to define the horizon however we want, e.g., we could include single and double changes, but not triple ones.   In practice, the mutational neighbors of a sequence are always defined as the sequences that differ by just 1 residue.

Putting these 2 pieces together, we can formulate a model of stepwise evolution with predictable dynamics.

mut_landscape_numberline Making this into a simulation of evolution is easy using the kind of number line shown at left. Each segment represents a possible mutation-fixation event from the starting sequence.  For instance, we can change the “A” nucleotide that begins the sequence to “T”, “C” or “G”.  The length of each segment is proportional to the origin-fixation probability for that change (where the probability is computed from the instantaneous rate).  To pick the next step in evolution, we simply pick a random point on the number line. Then, we have to update the horizon— recompute the numberline with the new set of 1-mutant neighbors.

Where do we get the actual values for mutation and fixation?  One way to do it is by drawing from some random distribution.  I did this in a 2006 simulation study. I wasn’t doing anything special.  It seemed very obvious at the time.

rokyta_fitnesses

(Table 1 from Rokyta, et al)

Surprisingly, researchers almost never measure actual mutation and selection values for relevant mutants.  One exception is the important study by Rokyta, et al (2005), who repeatedly carried out 1-step adaptation using bacteriophage phiX174.  The selection coefficients for each of the 11 beneficial changes observed in replicate experiments are shown in the rightmost column, with the mutants ranked from highest to lowest selection coefficient.  Notice that the genotype that recurred most often (see the “Number” column) was not the alternative genotype with the highest fitness, but the 4th-most-fit alternative, which happened to be favored by a considerable bias in mutation. Rokyta, et al didn’t actually measure specific rates for each mutation, but simply estimated average rates for different classes of nucleotide mutation based on an evolutionary model.

Then Rokyta, et al. developed a model of origin-fixation dynamics using the estimated mutation rates, the measured selection coefficients, and a term for the probability of fixation customized to account for the way that phages grow. This model fit the data very well, as I’ll show in a figure below (panel C in the final figure).

The mutational landscape model

Given all of that, you might ask, what does the mutational landscape model do?

This is where the specific innovations of Orr and Gillespie come in.  Just putting together origin-fixation dynamics and an evolutionary horizon doesn’t get us very far, because we can’t actually predict anything without filling in something concrete about the parameters, and that is a huge unknown.  What if we don’t have that?  Furthermore, although Rokyta, et al implicitly assumed a horizon in the sense that they ignored mutations too rare to appear in their study, they never tackled the question of how the horizon shifts with each step, because they only took one step.  What if we want to do an extended adaptive walk?  How will we know what is the distribution of fitnesses for the new set of neighbors, and how it relates to the previous distribution?  In the simulation model that I mentioned previously, I used an abstract “NK” model of the fitness of a protein sequence that allowed me to specify the fitness of every possible sequence with a relatively small number of randomly assigned parameter values.

Gillespie and Orr were aiming to do something more clever than that.  Theoreticians want to find ways to show something interesting just from applying basic principles, without having to use case-specific values for empirical parameters.  After all, if we insert the numbers from one particular experimental system, then we are making a model just for that system.

rokyta_fig1

(Figure 1 of Rokyta, et al, explaining EVT)

The first innovation of Orr and Gillespie is to apply extreme value theory (EVT) in a way that offers predictions even if we haven’t measured the s values or assumed a specific model.  If we assume that the current genotype is already highly adapted, this is tantamount to assuming it is in the tail end of a fitness distribution.  EVT applies to the tail ends of distributions, even if we don’t know the specific shape of the distribution, which is very useful.  Specifically, EVT tells us something about the relative sizes of s as we go from one rank to the next among the top-ranked genotypes: the distribution of fitness intervals is exponential.  This leads to very specific predictions about the probability of jumping from rank r to some higher rank r’, including a fascinating invariance property where the expected upward jump in the fitness ranking is the same no matter where we are in the ranking.  Namely, if the rank of the current genotype is j (i.e., j – 1 genotypes are better), we will jump to rank (j + 2)/4.

That’s fascinating, but what are we going to do with that information?  I suspect the idea of a fitness rank previously appeared nowhere in the history of experimental biology, because rank isn’t a measurement one takes anywhere other than the racetrack.  But remember that we would like a theory for an adaptive walk, not just 1-step adaptation.  If we jump from j to k = (j + 2)/4, then from k to m = (k + 2)/4, and so on, we could develop a theory for the trajectory of fitness increases during an adaptive walk, and for the length of an adaptive walk— for how many steps we are likely to take before we can’t climb anymore.

Figure 5.3 from Gillespie’s 1991 book. Each iteration has a number-line showing the higher-fitness genotypes accessible on the evolutionary horizon (fitness increases going to the right). At iteration #1, there are 4 more-fit genotypes. In the final iteration, there are no more-fit genotypes accessible, but there is a non-accessible more-fit genotype that was accessible at iteration #2.

The barrier to solving that theory is solving the evolutionary horizon problem.  Every time we take a step, the horizon shifts— some points disappear from view, and others appear (Figure).  We might be the 15th most-fit genotype, but at any step, only a subset of the 14 better genotypes will be accessible, and this subset changes with each step: this condition is precisely what Gillespie (1984) means by the phrase “the mutational landscape” (see Figure).  In his 1983 paper, he just assumes that all the higher-fitness mutants are accessible throughout the walk.  Gillespie’s 1984 paper entitled “Molecular Evolution over the Mutational Landscape” tackles the changing horizon explicitly.  He doesn’t solve it analytically, but uses simulations.  I won’t explain his approach, which I don’t fully understand.  Analytical solutions appeared in later work by Jain and Seetharaman, 2011 (thanks to Dave McCandlish for pointing this out).

The third and fourth key innovations are to (3) ignore differences in u and (4) treat the chances of evolution as a linear function of s, based on Haldane’s 2s.  In origin-fixation dynamics, the chance of a particular step is based on a simple product: rate of origin multiplied by probability of fixation.  Orr’s model relates the chances of an evolutionary step entirely to the probability of fixation, assuming that u is uniform. Then, using 2s for the probability of fixation means that the chance of picking a mutant with fitness si is simply si / sum(s) where the sum is over all mutants (the factor of 2 cancels out because its the same for every mutant).  Then, by applying EVT to the distribution of s, the model allows predictions based solely on the current rank.

A test of the mutational landscape model?

As noted earlier, this post started as a rant about a study that was mis-framed as though it were some kind of validation of Orr’s model.  In fact, that study is Rokyta, et al., described above.  Indeed, Rokyta, et al.  tested Orr’s predictions, as shown in the left-most panel in the figure below.  The predictions (grey bars) decrease smoothly because they are based, not on the actual measured fitness values shown above, but merely on the ranking.  The starting genotype is ranked #10, and all the predictions of Orr’s model follow from that single fact, which is what makes the model cool!

Rokyta_fig2

(Figure 2 of Rokyta, et al. A: fit of data to Orr’s model. B: fit of data to an origin-fixation model using non-uniform mutation rates. C: fit of data to origin-fixation model with non-uniform mutation and probability of fixation adjusted to fit phage biology more precisely. The right model is significantly better than the left model.)

If they did a test, what’s my objection?  Yes, Rokyta, et al. turned the crank on Orr’s model and got predictions out, and did a goodness-of-fit test comparing observations to predictions.  But, to test the mutational landscape model properly, you have to turn the crank at least 2 full turns to get the mojo working.  Remember, what Gillespie means by “evolution over the mutational landscape” is literally the way evolution navigates the change in accessibility of higher-fitness genotypes due to the shifting evolutionary horizon.  That doesn’t come into play in 1-step adaptation.  You have to take at least 2 steps.  Claiming to test the mutational landscape model with data on 1-step adaptation is like claiming to test a new model for long-range weather predictions using data from only 1 day.

The second problem is that Rokyta, et al respond to the relatively poor fit of Orr’s model by successively discarding every unique feature.  The next thing to go was the assumption of uniform mutation.  As I noted earlier, there are strong mutation biases at work.  So, in the middle panel of the figure above, they present a prediction that depends on EVT and assumes Haldane’s 2s, but rejects the uniform mutation rate.  In their best model (right panel) they have discarded all 4 assumptions.  They have measured the fitnesses (Table 1, above), and they aren’t a great fit to an exponential, so they just use these instead of the theory.  Haldane’s 2s only works for small values of s like 0.01 or 0.003, but the actual measured fitnesses go from 0.11 to 0.39!  Rokyta, et al provide a more appropriate probability of fixation developed by theoretician Lindi Wahl that also takes into account the context of phage (burst-based) replication.  To summarize,

Assumption 1 of the MLM.  The exponential distribution of fitness among the top-ranked genotypes is tested, but not tested critically, because the data are not sufficient to distinguish different distributions.

Assumption 2 of the MLM.  Gillespie’s “mutational landscape” strategy— his model for how the changing horizon cuts off previous choices and offers a new set of choices at each step— isn’t tested because Rokyta’s study is of 1-step walks.

Assumption 3 of the MLM.  The assumption that the probability of a step is not dependent on u, on the grounds that u is uniform or inconsequential, is rejected, because u is non-uniform and consequential.

Assumption 4 of the MLM. The assumption that we can rely on Haldane’s 2s is rejected, for 2 different reasons explained earlier.

Conclusion

I’m not objecting so much to what Rokyta, et al wrote, and I’m certainly not objecting to what they did— it’s a fine study, and one that advanced the field.  I’m mainly objecting to the way this study is cited by pretty much everyone else in the field, as though it were a critical test that validates Orr’s approach.  That just isn’t supported by the results.  You can’t really test the mutational landscape model with 1-step walks.  Furthermore, the results of Rokyta, et al led them away from  the unique assumptions of the model.  Their revised model just applies origin-fixation dynamics in a realistic way suited to their experimental system— which has strong mutation biases and special fixation dynamics— and without any of the innovations that Orr and Gillespie reference when they refer to “the mutational landscape model.”

Constructive neutral evolution on Sandwalk

The interesting things at Sandwalk always seem to happen when I’m not looking.  On Sunday, while I was out west taking the offspring to start university at UBC, Larry Moran posted a blog on Constructive Neutral Evolution that has elicited almost 200 comments.  Alas, many of the comments are not particularly useful, as Sandwalk is home to an ongoing pseudoscientific debate on intelligent design.

The one point that I would like to make about CNE is that it was not proposed as some kind of law or tendency (i.e., not like “Biology’s First Law” of McShea and Brandon).  Some other people treat CNE as the manifestation or the realization of some kind of intrinsic tendency to complexification. If this were the case, then examples of reductive evolution (e.g., cases involving viruses and intracellular parasites) would raise a question about the generality of the idea.  Obviously evolutionary change occurs in both reductive and constructive modes.  Bateson and Haldane each speculated that reductive evolution would be common because it is so easy to accomplish.

From my perspective, CNE is not a theory about a general tendency of evolution.  Instead it is a schema for generating specific testable hypotheses of local complexification.

One also can imagine a mode of Reductive Neutral Evolution in which simplification occurs. It is simply a matter of the local position of the system relative to the spectrum of mutational possibilities.

 

The buffet and the sushi conveyor

The return of mutationism to mainstream evolutionary biology is evident in the way mainstream articles now describe the role of mutation in evolution, in our reliance on mathematical models that evoke a mutationist view, and in evo-devo research programs that focus on identifying causative major-effect mutations.

This shift has happened in a kind of sub-conscious way, without commentary or reflection.  I’ll comment below on the reasons for that.

My main purpose here is to contrast way that the neo-Darwinian and mutationist views refer implicitly to two different regimes of population genetics evoked in two styles of self-service restaurant: the buffet and the sushi conveyor.

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Why the “four fundamental forces” view is mistaken

Over at Sandwalk, Larry Moran posted some interesting bits rrom his molecular evolution class exam, including a passage from Mike Lynch arguing for his claim that “nothing in evolution makes sense except in the light of population genetics”.  In this passage, which I’ll quote below, Lynch says that evolution is governed by 4 fundamental forces.

The idea that evolution is governed by population-genetic “forces” is common but fundamentally mistaken.  I wish we could just put this to rest.

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The range of rates for different genetic types of mutations

To understand the potential role of mutation in evolution, it is important to understand the enormous range of rates for different types of mutations. If one ignores this, and thinks of “the mutation rate” as a single number, or if one divides mutation into point mutations with a characteristic rate, and other mutations that are ignored, one is going to miss out on how rates of mutation determine what kinds of changes are more or less common in evolution.  It would be like allowing a concept of fitness, then subverting its utility by distinguishing only two values, viable and inviable. [1]

mut_rate_numberline

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The shift to mutationism is documented in our language

Last year Sahotra Sarkar published a paper that got me thinking.  His piece entitled “The Genomic Challenge to Adaptationism” focused on the writings of Lynch & Koonin, arguing that molecular studies continue to present a major challenge to the received view of evolution, by suggesting that “non-adaptive processes dominate genome architecture evolution”.

The idea that molecular studies are bringing about a gradual but profound shift in how we understand evolution is something I’ve considered for a long time.  It reminds me of the urban myth about boiling a frog, to the effect that the frog will not notice the change if you bring it on slowly enough.  Molecular results on evolution have been emerging slowly and steadily since the late 1950s.  Initially these results were shunted into a separate stream of “molecular evolution” (with its own journals and conferences), but over time, they have been merged into the mainstream, leading to the impression that molecular results can’t possibly have any revolutionary implications.

Frog on a saucepan. Image from wikipedia (http://en.wikipedia.org/wiki/Boiling_frog)

Frog on a saucepan. Image from wikipedia (http://en.wikipedia.org/wiki/Boiling_frog)

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Why size matters: Saltationism, creativity, and the reign of the DiNOs

Debates on “gradualism” in evolutionary biology address the size distribution of evolutionary changes.  The classical Darwinian position, better described as “infinitesimalism”, holds that evolutionary change is smooth in the sense of being composed of an abundance of infinitesimals (not one infinitesimal at a time, but a blending flow of infinitesimals).   The alternative is that evolution sometimes involves “saltations” or jumps, i.e., distinctive and discrete steps.  The dispute between these two positions has been a subject of acrimony at various times in the 20th century, with several minor skirmishes, and a larger battle with at least one genuine casualty (image).

Walter Frank Rafael Weldon (public domain image from wikipedia). Legend has it that Weldon ignored an advancing illness and worked himself to death trying to disprove the relevance of Mendelism in natural inheritance.

Walter Frank Rafael Weldon (public domain image from wikipedia).  Weldon ignored an advancing illness and worked himself to death (1906) poring over breeding records in an attempt to cast doubt on discrete inheritance.  Along with Pearson and other “biometricians”, Weldon held to Darwin’s non-Mendelian view combining gradual hereditary fluctuations with blending inheritance.

Today, over a decade into the 21st century, we have abundant evidence for saltations, yet the term is virtually unknown, and we still seem to invoke selection under the assumption of gradualism.  Are we saltationists, or not?  I’m going to offer 3 answers below.

But first, we need to review why the issue is important for evolutionary theory.

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Revolt of the clay: updated evidence

In a previous post called “The revolt of the clay“, I described four different ways to think about the role of variation as a process with a predictably non-random impact on the outcome of evolution.  The main point was to draw attention to my favorite idea, about biases in the introduction of variation as a source of orientation or direction, and to provide a list of what (IMHO) represents the best evidence for this idea.  I gave anecdotes from four categories of evidence

  • mutation-biased laboratory adaptation
  • mutation-biased parallel adaptation in nature
  • recurrent evolution of genomic features
  • miscellaneous evo-devo cases such as worm sperm

With the publication of a study by Couce, et al., 2015 (a team of researchers from Spain, France and Germany), the first category just got stronger.   Couce, et al did an experiment that I’ve been trying to talk experimentalists into doing for a long time: they directly compared the spectrum of lab-evolved changes between two strains with a known difference in mutation spectrum.

In brief, they exposed 576 different lines of E. coli to a dose of cefotaxime that started well below the MIC and doubled every 2 days for 12 iterations. The evolved lines fell into 6 groups depending on 3 choices of genetic background— wild-type, mutH, or mutT—  and 2 choices of target gene copy number— just 1 copy of the TEM-1 gene, or an extra ~18 plasmid copies.

The ultimate dose of antibiotic was so extreme that most of the lines went extinct.  The figure shows how many of the 96 lines (for each condition) remain viable at a given concentration.

couce_fig1

The mutators were chosen because they have different spectra.  The “red” mutator (mutH) greatly elevates the rate of G –> A transitions, and also elevates A –> G transitions.  The “blue” mutator (mutT) elevates A –> C transversions.  The figure above indicates that the blue mutator fared slightly better.  A much stronger effect is that the lines with multiple copies of the TEM-1 gene did better.  Very few single-copy strains survived the highest doses of antibiotic.

The authors then did some phenotypic characterization that led them to suspect that it was not just the TEM-1 gene, but other genes that were important in adaptation.  In particular, they suspected the gene for PBP3, which is a direct target of cefotaxime.

They sequenced the genes for TEM-1 and PBP3 from a large sample of the surviving strains above, with results shown in this figure:

couce_fig3

The left panel, i.e., figure 3a, shows that evolved strains of mutH (red), mutT (blue), and wild-type (black) sometimes have one of the well-known mutants in the TEM-1 gene encoding beta-lactamase.   The predominance of red means that more mutH strains evolved the familiar TEM-1 mutations, which makes sense because these mutations happen to be the G–>A and A–>G transitions favored by mutH.

Panel 3b, which refers to mutants in the gene encoding PBP3, is a bit complicated.   As before, the histogram bars are colored based on the background in which the particular mutation listed on the x axis is fixed.  However, rather than showing all the lines together in one histogram, they are arranged into 3 different histograms depending on whether the mutational pathway matches the pathways preferred by mutT (left sub-panel), by mutH (center sub-panel), or neither (right sub-panel).  For instance, blue appears in 16 columns, so there are 16 different mutant PBP3 types that evolved in mutT backgrounds, and 14 of them are in the left sub-panel indicating mutT-favored mutational pathways.  Red appears in 18 columns, 15 corresponding to mutH-favored pathways.

Importantly, the density in the columns doesn’t overlap much: nearly all of the blueness is in the left histogram (~50/52), and nearly all the redness is in the center histogram (~26/31).  This means that evolved mutT strains overwhelmingly carried mutations favored by the mutT mutators, and likewise for mutH strains and mutH mutators.  If adaptation were unaffected by tendencies of mutation, as the architects of the Modern Synthesis believed, then the colors would be randomly scrambled between the 3 histograms.  Because it is not, we know that the regime of mutation imposes a predictable bias on the spectrum of adaptive changes.

The main weakness of the paper, perhaps, is that they did not do reconstructions to show causative mutations.  Instead they make plausibility arguments based on having seen some of these in other studies of laboratory or clinical resistance.  I think the paper is pretty strong in spite of this.   Recurrence of a mutation in independent lines is a very strong sign that it is causative, whereas singletons might be hitch-hikers with no causative significance.    Yet if we were to eliminate the 17 non-recurring mutants, we would still have a striking contrast.  Of ~43 mutT mutants with recurrently fixed mutations, ~41 are for mutT-favored pathways; of the ~23 mutH mutants with recurrently fixed mutations, ~18 are for mutH-favored pathways.

Unfortunately, due to the language and framing of this paper, casual readers might not recognize that it is actually about mutation-biased adaptation.  The term “mutation bias” only occurs once, in the claim that “Mutational biases forcibly impose a high level of divergence at the molecular level.”  I’m not sure what that means.  What I would describe as “evolution biased by mutation” is described by Couce, et al as “limits to natural selection imposed by genetic constraints”.   Sometimes the language of my fellow evolutionists seems like a strange and foreign language to me.  But I digress.

To summarize, this work clearly establishes that 2 different mutator strains adapting to increasing antibiotic concentrations exhibit strikingly different spectra of evolved changes that match their mutation spectra, consistent with the a priori expectation of mutation-biased adaptation.

The revolt of the clay: an initial progress report

A “chance” encounter

Earlier this month I was contacted by a reporter writing a piece on the role of chance in evolution.   I responded that I didn’t work on that topic, but if he was interested in predictable non-randomness due to biases in variation, then I would be happy to talk.  We had a nice chat last Friday.

I’m only working on the role of “chance” in the sense that, in our field, referring to “chance” is a placemarker for the demise of an approach based implicitly on deterministic thinking— evolution proceeds to equilibrium, and everything turns out for the best, driven by selection.  This justifies the classic view that “the ultimate source of explanation in biology is the principle of natural selection” (Ayala, 1970).  Bruce Levin and colleagues mock this idea hilariously in the following passage from an actual research paper:

To be sure, the ascent and fixation of the earlier-occurring rather than the best-adapted genotypes due to this bottleneck-mutation rate mechanism is a non-equilibrium result. On Equilibrium Day deterministic processes will prevail and the best genotypes will inherit the earth (Levin, Perrot & Walker, 2000)

Wait, I’m still laughing.   (more…)

Conceptual frameworks and the problem of variation

Conceptual frameworks guide our thinking

Our efforts to understand the world depend on conceptual frameworks and are guided by metaphors.  We have lots of them.  I suspect that most are applied without awareness.  If I am approaching a messy problem for the first time, I might begin with the idea that there are various “factors” that contribute to a population of “outcomes”.  I would set about listing the factors and thinking about how to measure them and quantify their impact.  This would depend, of course, on how I defined the outcome and the factors.256px-New_York_City_Gridlock

Let’s take a messy problem, like the US congress.  How would we set about understanding this?   I often hear it said that congress is “broken”.  That has clear implications.  It suggests there was a time when congress was not broken, that there is some definable state of unbrokenness, and that we can return to it by “fixing” congress.  By contrast, if we said that congress is a cancer on the union, this would suggest that the remedy is to get rid of congress, not to fix it.

I also often hear that the problem is “gridlock”, invoking the metaphor of stalled traffic.  The implication here is that there should be some productive flow of operations and that it has been halted.  This metaphor is a bit more interesting, because it suggests that we might have to untangle things in order to restore flow, and then congress would pass more laws.  By contrast, this kind of suggestion is sometimes met with the response that the less congress does, the better off we are.   If this is our idea of “effectiveness”, then our analysis is going to be different.

Conceptualizations of the role of variation

How do evolutionary biologists look at the problem of variation?  How do their metaphors or conceptual frameworks influence the kinds of questions that are being asked, and the kinds of answers that seem appropriate?

Here I’d like to examine— briefly but critically— some of the ways that the problem of variation is framed.

Manantenina bauxite

Bauxite, the main source of aluminum, is an unrefined (raw) ore that often contains iron oxides and clay (image from wikipedia)

Raw materials

The most common way of referring to variation is as “raw materials.”  What does it mean to be a raw material?   Picture in your mind some raw materials like a pile of wood pulp, a mound of sand, a field scattered with aluminum ore (image), a train car full of coal, and so on, and you begin to realize that this is a very evocative metaphor.  Raw materials are used in abundance and are “raw” in the sense of being unprocessed or unrefined. Wool is a raw material: wool processed and spun into cloth is a material, but not a raw material.

What is the role of raw materials?  Dobzhansky said that variation was like the raw material going into a factory.  What is the relation of raw materials to factory products?   Raw materials provide substance or mass, not form or direction.  Given a description of raw materials, we can’t really guess the factory product (image: mystery raw materials).  Raw materials are a “material” cause in the Aristotelean sense, providing substance and not form.  This is essential to the Darwinian view of variation: selection is an agent, like the potter that shapes the clay, while variation is a passive source of materials, like the clay.

User:Sjschen, Source: Self made, Some commonly used raw incense and incense making materials (from top down, left to right) Makko powder (抹香; Machilus thunbergii), Borneol camphor (Dryobalanops aromatica), Sumatra Benzoin (Styrax benzoin), Omani Frankincense (Boswellia sacra), Guggul (Commiphora wightii), Golden Frankincense (Boswellia papyrifera), Tolu balsam (Myroxylon balsamum), Somalian Myrrh (Commiphora myrrha), Labdanum (Cistus villosus), Opoponax (Commiphora opoponax), and white Indian Sandalwood powder (Santalum album) Date18 November 2006 (original upload date) Source Transferred from en.wikipedia; transferred to Commons by User:Trengarasu using CommonsHelper. AuthorOriginal uploader was Sjschen at en.wikipedia Permission (Reusing this file) CC-BY-SA-2.5,2.0,1.0; GFDL-WITH-DISCLAIMERS.

These are the raw materials for what manufactured product?  See note 1 for answers and credits

What kinds of questions does this conceptual framework suggest?  What kinds of answers?   If we think of variation as raw materials, we might ask questions about how much we have, or how much we need.  Raw materials are used in bulk, so our main questions will be about how much we have.

This reminds us of the framework of quantitative genetics.  In the classical idealization, variation has a mean of zero and a non-zero variance: variation has an amount, but not a direction.  Nevertheless, the multivariate generalization of quantitative genetics (Lande & Arnold) breaks the metaphor— in the multivariate case, selection and the G matrix jointly determine the multivariate direction of evolution.

Chance

The next most-common conceptual framing for talking about the role of variation is “chance”.  What do we mean by chance?  I have looked into this issue and its a huge mess.

By Steaphan Greene (Own work) [CC-BY-SA-3.0 or GFDL], via Wikimedia Commons

By Steaphan Greene [CC-BY-SA-3.0 or GFDL], via Wikimedia Commons


BTW, I have experienced several scientists pounding their chests and insisting that “chance” in science has a clear meaning that applies to variation, and that we all know what it is.  Nonsense.  The only concept related to chance and randomness that has a clear meaning is the concept of “stochastic”, from mathematics, and it is purely definitional.  A stochastic variable is a variable that may take on certain values.  For instance, we can represent the outcome of rolling a single die as a stochastic variable that takes on the values 1 to 6.  That is perfectly clear.

However, is the rolling of dice a matter of “chance”?  Are the outcomes “random”?  These are two different questions, and they are ontological (whereas “stochastic” is abstract, merely a definition).  Often “chance” can be related to Aristotle’s conception of chance as the confluence of independent causal streams.  To say that variation is a matter of “chance” is to say that it occurs independently of other stuff that we think is more important.  Among mathematicians, randomness is a concept about patterns, not causes or independence.  To say that variation is random is to say that it has no discernible pattern.

What kinds of questions or explanations are prompted by this framework?  One might say that it does not provide us with much guidance for doing research.  I would argue that it provides a very strong negative guidance: don’t study variation, because it is just a matter of chance.

But the same doctrine has a very obvious application when we are constructing retrospective explanations.  If evolution took a particular path dependent on some mutations happening, then the path is a matter of “chance” because the mutations are a matter of chance.  We would say that evolution depends on “chance.”  This kind of empty statement is made routinely by way of interpreting Lenski’s experiments, for instance.

This framework also inspires skeptical questions, prompting folks to ask whether variation is really “chance”.  This skepticism has been constant since Darwin’s time.  But the claims of skeptics are relatively uninformative.  Saying that variation is not a matter of chance tells us very little about the nature of variation or its role in evolution.

Handcuffed hands (line drawing, original)

Constraints

According to the stereotype, at least, academics value freedom.  Who would have guessed that they would so willingly embrace the concept of “constraints”?

In this view, the role of variation is like the role of handcuffs, preventing someone from doing something they might otherwise do.  Variation constrains evolution.  Or sometimes, variation is said to constrain selection.

What kinds of hypotheses, research projects, or explanations does this framework of “constraints” suggest?

To show that a constraint exists, we would need to find a counter-example where it doesn’t.  So the constraints metaphor encourages us to look for changes that occur in one taxonomic context, but not another.  Once we find zero changes of a particular type in taxon A, and x changes in taxon B, we have to set about showing that the difference between zero and x is not simply sampling error, and that the cause of the difference is a lack of variation.

An unfinished bridge.  How do we know it is unfinished?  This image was originally posted to Flickr by David Jones at http://flickr.com/photos/45457437@N00/4430518713.

The Pat Tillman memorial bridge in a state of partial completion. How do we know it is incomplete?Originally posted to Flickr by David Jones http://flickr.com/photos/45457437@N00/4430518713.

For this reason, the image of handcuffs is perhaps misleading.   A better image would be a pie that is missing a slice, or perhaps an unfinished bridge (image).  The difference matters for 2 reasons.  First, handcuffs actually exist, and they prevent movement because they are made of solid metal.  By contrast, a “constraint” on variation is a lack of variation, a non-existent thing.  A constraint is not a cause: it is literally made of nothing and it is invoked to account for a non-event.   Second, how can nature be found lacking?  What does it mean to say that something is missing?  We are comfortable saying that a pie is missing a slice, because we are safe in assuming that the pie was made whole, and someone took a slice.  We say that the bridge is “missing a piece” because we know the intention is to convey vehicles from one side to another, which won’t be possible until the road-bed connects across the span.  We are comparing what we observe to some normative state in which the pie or the bridge is complete.

So what does it mean when we invoke “constraints” in a natural case?  Isn’t nature complete and whole already?  What is the normative state in which there are no “constraints”.  Apparently, when people invoke “constraints”, they have some ideal of infinite or abundant variation in the back of their minds.

We can do better than this

How do we think about the role of variation in evolution?  Above I reviewed some of the conceptual frameworks and metaphors that have guided thinking about the role of variation.

The architects of the Modern Synthesis argued literally that selection is like a creative agent— a writer, sculptor, composer, painter— that composes finished products out of the raw materials of words, clay, notes, pigment, etc.  They promoted a doctrine of “random mutation” that seemed to suggest mutation would turn out to be unimportant for anything of interest to us as biologists.

The “raw materials” metaphor is still quite dominant.  I see it frequently.  I would guess that it is invoked in thousands of publications every year.  I can’t recall seeing anyone question it, though I would argue that many of the publications that cite the “raw materials” doctrine are making claims that are inconsistent with what “raw materials” actually means.

A minor reaction to the Modern Synthesis position has been to argue that variation is not random.  As noted above, simply saying that mutation is non-random doesn’t get us very far, so advocates of this view (e.g., Shapiro) are trying to suggest other ways to think about the role of non-random variation.

For a time, the idea that “constraints” are important was a major theme of evo-devo.  One doesn’t hear it as much anymore.  I think the concept may have outlived its usefulness.

Notes

1.  According to Wikipedia, these are raw materials for making perfume, including (from top down, left to right) Makko powder (抹香; Machilus thunbergii), Borneol camphor (Dryobalanops aromatica), Sumatra Benzoin (Styrax benzoin), Omani Frankincense (Boswellia sacra), Guggul (Commiphora wightii), Golden Frankincense (Boswellia papyrifera), Tolu balsam (Myroxylon balsamum), Somalian Myrrh (Commiphora myrrha), Labdanum (Cistus villosus), Opoponax (Commiphora opoponax), and white Indian Sandalwood powder (Santalum album).  Image from user Sjschen, wikimedia commons, CC-BY-SA-2.5,2.0,1.0; GFDL-WITH-DISCLAIMERS.