Reactionary fringe meets mutation-biased adaptation. 7. Going forward

This the last of a series of posts by Arlin Stoltzfus on the role of mutation as a dispositional factor in evolution. Arlin has established that the role of mutation in evolution is much more important than most people realize. He has also built a strong case for the influence of mutation bias. How should we incorporate these concepts into modern evolutionary theory?

Click on the links in the box (below) to see the other posts in the series.

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Reactionary fringe meets mutation-biased adaptation.
7. Going forward
by Arlin Stoltzfus
Haldane (1922) argued that, because mutation is a weak pressure easily overcome by selection, the potential for biases in variation to influence evolution depends on neutral evolution or high mutation rates. This theory, like the Modern Synthesis of 1959, depends on the assumption that evolution begins with pre-existing variation. By contrast, when evolution depends on the introduction of new variants, mutational and developmental biases in variation may impose biases on evolution, without requiring neutral evolution or high mutation rates.

Reactionary fringe meets mutation-biased adaptation
Introduction
1. The empirical case
2. Some objections addressed
3. The causes and consequences of biases in the introduction process
4. What makes this new?
5. Beyond the "Synthesis" debate
    -Thinking about theories
    -Modern Synthesis of 1959
    -How history is distorted
    -Taking neo-Darwinism
      seriously
    -Synthesis apologetics
6. What "limits" adaptation?
7. Going forwardTo distinguish these theories-- both compatible with mutational biases on non-adaptive evolution-- requires systematic data on the mutations underlying adaptation. Such data are now emerging, and recent analyses show that modest quantitative biases, e.g., transition-transversion bias, impose biases on the course of adaptation, so that the changes involved in adaptation are enriched for mutationally likely changes.

The reactionary response to this discovery in TREE's hatchet piece is to argue-- predictably-- that there is nothing new here.

We have reviewed the facts of history that refute this position. First, if we examine the contents of our theoretical toolbox, we find an explicit century-old mathematical basis for arguing against the efficacy of biases in variation, while the explicit basis to argue for their efficacy emerges only in 2001. Second, as we discovered earlier, when the issue of variation-biased evolution arises, leading thinkers such as Haldane, Fisher, Wright, Huxley, Ford, Simpson, Stebbins, Maynard Smith, et al (1985), and Gould invoke the opposing-pressures argument to undermine the notion of variation-biased evolution.

Yet, the significance of a new idea depends, not on how thoroughly it contradicts the past, but on how it shapes the future. How does rethinking the role of biases in variation help us to understand major features of evolution? How does it link disparate observations and build bridges between fields? How much can human health be improved by taking mutation biases into account when designing evolution-resistant treatments for pathogens and cancer? What opportunities for research emerge from considering this new idea?

Basic theory_A

The formal mathematical theory_A underlying the claims we have been exploring is thin, and would benefit from expansion. The simple model simulated by Yampolsky and Stoltzfus (2001) has obvious analytical solutions in 2 special cases corresponding to the sushi conveyor and the buffet. In the limiting case as u → 0 with N fixed (where u = u₁ + u₂), the result is an absorbing Markov chain whose behavior follows origin-fixation dynamics. In the limiting case as N → ∞ with u fixed, we enter the buffet regime, which may be represented with a set of coupled differential equations whose behavior typically dictates that the fittest type asymptotically approaches a frequency near 1.

If evolution usually occurs in an intermediate regime, as seems likely, these results are not precisely relevant. For the "concurrent mutations" regime, the problem might be addressed following Desai and Fisher (2007) (see also Jain, et al. 2011).

Beyond that, there are many other conditions to address: more complex genetic structures and fitness landscapes, diverse demographics, and variable environments.

Why develop such a body of theory? To answer this question, consider the example of dN / dS, the normalized ratio of non-synonymous to synonymous changes. This metric can be estimated for any species (animal, plant, virus, etc), for any class of protein-coding genes, and even for any branch of a tree, using only a small amount of data. The expectation of pure neutral evolution (e.g., in a pseudogene) is dN / dS = 1; dN / dS < 1 indicates purifying selection.

Thus, dN / dS is easily measured, widely applicable, and informative about the conditions of evolution (subject to complications, e.g., Mugal, et al., 2014 or Spielman and Wilke, 2015).

Now, imagine a metric E_B for the efficiency of biases in variation to impose a corresponding bias on evolution, with a range from 0 (no effect) to 1, meaning that a B-fold bias has a B-fold effect. If transition-transversion bias in mutation is known, E_B can be estimated for any category of gene, using a modest amount of comparative sequence data.

In the future, researchers will measure E_B for various species (Drosophila, E. coli, mouse, etc), and will compare E_B across categories, e.g., structural vs. regulatory changes, or fast-evolving vs. slow-evolving genes. For instance, the magnitudes of evolutionary biases observed in the studies discussed previously suggest that E_B is between 1 / 2 and 1.

Such results will create demand for a body of theory to interpret E_B. Clearly, we expect E_B = 1 for the origin-fixation (sushi conveyor) regime, and E_B ~ 0 for adaptation in the buffet regime. The simulations of Yampolsky and Stoltzfus indicate that E_B > 0 is expected well outside the origin-fixation regime. But most measured values of E_B, presumably, will be between 0 and 1. This is why we need a body of theory that addresses a range of conditions.

Further tests for mutational effects

An obvious direction for future research is simply to extend the empirical work reviewed earlier, by assessing the effects of mutation bias for (1) a broader set of cases, and (2) other types of mutation bias, e.g., GC:AT bias, CpG bias, deletion:insertion bias, and so on. Note that transition bias is essentially orthogonal to selection (Stoltzfus and Norris, 2015), but this is not a safe assumption generally, e.g., we don't know whether 1-residue insertions in proteins are more conservative, less conservative, or about the same as 1-residue deletions.

That will be useful, but it will be even more valuable to focus efforts on (1) the distinctive implications listed by Stoltzfus (2019), and (2) implications with a potentially high impact.

For instance, the theory holds that the ability of mutation biases to influence evolution does not come from a mass-action pressure driving alleles to fixation, but from biases in the introduction process. From general theoretical considerations, as well as the simulation results of Yampolsky and Stoltzfus (2001), we expect that the power of selection to ensure that fitter alleles prevail will increase with uN. Therefore, it is important to examine cases of adaptation in which we expect uN > 1 (e.g., in resistance to anti-malarials per Anderson, et al. 2017). Note that we learned in part 6 that a scalar uN value is of limited use when values of s and u for the relevant mutants cover a wide range: a more general theory is needed.

Likewise, the theory says that, under limiting conditions, the bias in outcomes is a linear function of the bias in mutation. We should see proportionately stronger effects with stronger biases, e.g., a more thorough study might reveal a wide range of effects corresponding to a wide range of transition-transversion bias, from 1.2-fold in yeast, to more than 10-fold in viruses such as Hepatitis C.

Building bridges

The theory elaborated in Stoltzfus (2019) is not just about mutation bias, but also addresses developmental biases induced by the structure of a genotype-phenotype (GP) map-- an idea that has been discussed for decades, but not firmly established. However, it will be possible to evaluate this idea using molecular data on adaptation, because the genetic code is a GP map that induces biases in mutational connectivity.

Likewise, Stoltzfus (2019) proposes that the effects of network connectivity invoked in the self-organization literature implicitly reflect the action of biases in the introduction process, an effect that is invisible because of the way that models in that field lack separate parameters for origin and fixation. The way to expose these effects is to (1) parameterize mutation separately, and (2) experiment with different modes of mutation, including non-local (long-jump) mutation, and an artificial process normalized to remove differences in connectivity with mutant phenotypes.

Positive results would establish common interests across separate research fronts, and would make non-traditional concerns more understandable to theoretical population geneticists. A variety of arguments about internal factors in evolution regarding evolvability and self-organization assume implicitly that tendencies of variation are effectual in non-neutral evolution, i.e., this is the first-order principle underlying much thinking about higher-order principles. Therefore, establishing its empirical importance is fundamental.

Finally, note that ordinary mutational origination is only one flavor of introduction event. Events of introgression, lateral transfer or endosymbiosis can be events of introduction. When an organism lands on an island uninhabited by that species, this is an event of biogeographic introduction with highly predictable biases based on vagility, proximity of the source, prevailing winds and currents, etc.

The philosopher John Stuart Mill (1859) attributed the triumph of truth to an introduction bias:

"The real advantage which truth has, consists in this, that when an opinion is true, it may be extinguished once, twice, or many times, but in the course of ages there will generally be found persons to rediscover it, until some one of its reappearances falls on a time when from favourable circumstances it escapes persecution until it has made such head as to withstand all subsequent attempts to suppress it." (On Liberty, Ch. 2)

That is, the theory developed for evolutionary dynamics under biases in mutational introduction will have implications for other introduction-establishment processes.

Biomedical applications

Earlier in this series, I mentioned the results of Liu, et al., who aim to exploit the "survival of the likeliest" to improve drug design. Cancer researchers have begun to pay serious attention to effects of mutation rate, which has proven important in modeling prevalence, e.g., in the figure below, Cannataro, et al. 2018 present rankings of the top 25 effect sizes (right-facing bars) for lung adenocarcinoma (LUAD, left) and lung squamous cell (LUSC, right) carcinomas, along with mutation rates (left-facing bars).

The variants with the largest prevalence (tiny numbers on the ends of the left-facing bars-- see a bigger version here) are not the ones with the largest selection intensity, but the ones with the highest mutation rates. For instance, for the LUAD variants, the 5 most aggressive carcinomas are markedly more aggressive than the rest, but none are in the top 5 most prevalent carcinomas.

This is not my specialty, so I won't say much, other than that I look forward to hearing about new ways in which the arrival of the likeliest can be exploited to develop evolution-resistant therapies.

Concluding thoughts

Interestingly, one possible outcome of further theory_A development is the emergence of a qualitatively different conceptualization of issues. The verbal theory in Yampolsky and Stoltzfus (2001) and succeeding papers says literally that the effects of biases in variation are captured entirely in the introduction step, i.e., the single-generation jump in allele frequency from 0 to a non-zero value. Perhaps a more expansive analytical framework will suggest a new and different way to look at this, based on some new kinds of thinking, e.g., traveling waves.

To state this more broadly, my thinking has developed in a somewhat isolated way-- not by choice, but because the issue was not "on the radar" for other scientists until recently. Thus, the considerations above, presumably, are only the tip of the iceberg of novel thinking and research to be unleashed when more scientists turn their attention to this issue.

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