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Wednesday, July 03, 2019

Reactionary fringe meets mutation-biased adaptation. 4. What makes this new?

This is the fifth in a series of guest posts by Arlin Stoltzfus on the role of mutation as a dispositional factor in evolution.

Reactionary fringe meets mutation-biased adaptation. 4. What makes this new?
by Arlin Stoltzfus

Scientists value novelty because it signifies untapped potential: a new idea has not been interrogated, applied, and extended. The more novel an idea, the greater its potential to re-shape our discourse and advance our understanding beyond the well tried ideas of the past.

Reactionary fringe meets mutation-biased adaptation

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
Because theories shape thinking, the newness of a theory can be evaluated empirically by considering whether or not the reasoning actually used by scientists reflects the theory. To evaluate the newness of the theory that X causes Y, one considers how scientists address the consequences of X, the causes of Y, or the relation of X to Y. In regard to the role of biases in variation in evolution, we can expect the reasoning of scientists to be exposed when they consider: (1) the bottom-up question of what are the implications of differences in rates for different types of mutations, (2) the high-level question of what factors impart tendencies to evolution, or (3) any pattern, or any conjecture, suggesting an alignment between evolutionary tendencies and internal variational tendencies.

Note that this issue of novelty is not the same as the issue of academic priority. If a new theory is found tomorrow in an overlooked 1929 paper from Muller, then Muller has priority, but this finding would not change the past 90 years of evolutionary discourse.

In this post, we consider the reasoning used by evolutionary biologists to address the consequentiality of mutational or developmental biases in variation.

The opposing-pressures theory

Why do genetic diseases persist, rather than being eliminated by selection? Fisher and Haldane addressed this issue, deriving the famous mutation-selection balance equation: selection pushes down the frequency of a deleterious allele, while recurrent mutation pushes it up. In large populations, the allele reaches an equilibrium frequency (in the simplest case) of f ~ u / s, where s is the fitness disadvantage. Because u << s, f is small, much closer to 0 than to 1.

From this, Haldane and Fisher argued more generally that tendencies of variation typically can not cause evolutionary tendencies, because mutation rates are too small to overcome the opposing pressure of selection (Ch. 1 of Fisher, 1930, Haldane, 1933; see also Haldane, 1927, Wright, 1931).

For instance, before quoting Fisher's argument directly, Gould summarizes:
Since orthogenesis can only operate when mutation pressure becomes high enough to act as an agent of evolutionary change, empirical data on low mutation rates sound the death-knell of internalism.
- Gould (2002), The Structure of Evolutionary Theory, p. 510
Indeed, according to Provine (1978; see "Eliminating Competing Theories"), this argument played an important role in establishing the Modern Synthesis, by eliminating alternative theories of internal variational tendencies, e.g., Stoltzfus (2019) notes the opposing-pressures argument in works of Ford, Simpson, Mayr and Huxley (1942), who invokes it when considering possible causes of trends:
"For no rate of hereditary change hitherto observed in nature would have any evolutionary effect in the teeth of even the slightest degree of adverse selection. Either mutation-rates many times higher than any as yet detected must be sometimes operative, or else the observed results can be far better accounted for by selection. (p. 56)
This theory of opposing pressures presented a challenge to Maynard Smith, et al. (1985) in their seminal "developmental constraints" article:
[The issue] is whether biases on the production of variant phenotypes (i.e., developmental constraints) such as those just illustrated, cause evolutionary trends or patterns. Since the classic work of Fisher (1930) and Haldane (1932) established the weakness of directional mutation as compared to selection, it has been generally held that directional bias in variation will not produce evolutionary change in the face of opposing selection. This position deserves reexamination. For one thing, our examples (like many discussed during the last twenty years - e.g., White, 1965; Cox and Yanofsky, 1967) concern biased variation in the genetic mechanism itself. If such directed variation accumulates-- as the results regarding DNA quantity and chromosome numbers suggest-- one obtains a very effective evolutionary ratchet. For another, such directional biases may not stand in contradiction to the Fisher-Haldane point of view: within reasonable limits, neither the increase in cellular DNA content nor that in chromosome number is known to have deleterious effects at the organismic level.
The authors argue that intrinsic mutational biases may be effective under neutral evolution, as Haldane (1927) concluded, though he found the idea unimportant. Indeed, neutrality is a special case, not the general justification needed by evo-devo. Thus, Reeve and Sherman (1993) invoke the opposing-pressures argument when they criticize Maynard Smith, et al. for failing to provide a mechanism (p. 21, "why couldn't selection suppress an 'easily generated physicochemical process'").

A direct re-examination of the opposing-pressures argument did not occur until Yampolsky and Stoltzfus (2001) considered whether, and under what conditions, biases in the generation of variation might have a direct influence on the course of evolution.

We reviewed their results already in Part 3. Why did they reach a different conclusion than Haldane, Fisher, Wright, Ford, Huxley, Simpson, Mayr, Gould and others? The critical innovation is to stop thinking of mutation as a mass-action pressure that might cause large shifts in frequency, i.e., as a force comparable to selection or drift, and instead to consider the introduction process, a point process of allele origination.

The introduction process is not subject to the logic of opposing pressures: it can not be opposed by selection. For instance, suppose that some new alleles are introduced at a rate k << 1, so that the waiting time for the next event is 1 / k. If the next allele is deleterious, this does not cause its introduction to be delayed.

When the outcome of evolution depends on the introduction process, mutational and developmental biases in variation act as prior biases on the course of evolution. Under limiting conditions, a B-fold bias has a B-fold effect. This influence does not require neutral evolution or high mutation rates. Mutation in the guise of the introduction process has a completely different set of implications from mutation in the guise of a mass-action pressure on the frequency of an allele.

Evolution as shifting gene frequencies

Why did Haldane and Fisher draw a conclusion without considering this theory?  Why didn't Maynard Smith, et al. (1985) refute the opposing-pressures argument and justify the efficacy of developmental biases?  Why did it take 70 years for Yampolsky and Stoltzfus (2001) to explain why the original argument is not definitive, and to provide an alternative?

The answer relates to the theory of population-genetic forces. During this period, scientists reasoned about questions of evolutionary causation as if they could be resolved by reference to mass-action forces that shift a distribution of allele frequencies from one set of non-zero values to another.

Consider the case of a single locus. The first allelic selection model, Norton's model (Punnett, 1915), shows the change in frequencies for two alleles with different fitnesses: one frequency rises, another falls. The starting and ending populations have the same alleles in different proportions.

In the multi-locus context, the initial population has a distribution of allele frequencies tuned to the current environment, and when conditions change, the frequencies shift to a new optimum. The result (above) is the shifting-gene-frequencies theory of the Modern Synthesis of 1959 (see Stoltzfus, 2017): phenotypic change (left) is a smooth shift driven by selection; at the genetic level (center), frequencies of small-effect alleles at many loci (A1 vs. A2, B1 vs. B2, etc) are shifting simultaneously to a new optimum; the population moves in the interior of an allele-frequency space (right), without an introduction process.

By comparison, the first widely recognized model of sequential mutation-fixation events at a single locus, allowing a succession of fixed states, was Gillespie's (1983) model of beneficial mutations (see McCandlish and Stoltzfus, 2014). Aggregate models of origin-fixation events across infinitely many loci have been used since 1969, primarily to consider the fate of neutral or slightly deleterious mutations (McCandlish and Stoltzfus, 2014). Origin-fixation models are an invention of the molecular era.

Several theoreticians have described this limitation in stark terms, e.g., Yedid and Bell (2002) wrote
In the short term, natural selection merely sorts the variation already present in a population, whereas in the longer term genotypes quite different from any that were initially present evolve through the cumulation of new mutations. The first process is described by the mathematical theory of population genetics. However, this theory begins by defining a fixed set of genotypes and cannot provide a satisfactory analysis of the second process because it does not permit any genuinely new type to arise."
Likewise, Hartl and Taubes (1998) wrote
Almost every theoretical model in population genetics can be classified into one of two major types. In one type of model, mutations with stipulated selective effects are assumed to be present in the population as an initial condition . . . The second major type of models does allow mutations to occur at random intervals of time, but the mutations are assumed to be selectively neutral or nearly neutral."
Eshel and Feldman (2001) made a similar distinction:
We call short-term evolution the process by which natural selection, combined with reproduction (including recombination in the multilocus context), changes the relative frequencies among a fixed set of genotypes, resulting in a stable equilibrium, a cycle, or even chaotic behavior. Long-term evolution is the process of trial and error whereby the mutations that occur are tested, and if successful, invade the population, renewing the process of short-term evolution . . ." (p. 182)
They conclude that
Since the time of Fisher, an implicit working assumption in the quantitative study of evolutionary dynamics is that qualitative laws governing long-term evolution can be extrapolated from results obtained for the short-term process. We maintain that this extrapolation is not accurate. The two processes are qualitatively different from each other." (p. 163)


From 1927 until the end of the 20th century, leading thinkers addressed the potential for variation-biased evolution in discrete characters using the opposing-pressures theory. Maynard Smith, et al. (1985), whose authors included 3 eminent theoreticians (Maynard Smith, Lande and Kauffman), called for a re-examination of the opposing-pressures argument, but did not articulate an alternative. In The Origins of Order, Kauffman (1992) argued that the evolutionary exploration of genetic spaces leads to predictable properties that are not themselves selected, yet he offered no recognizable evolutionary cause to account for his "almost magical" references to self-organization (Fox, 1993).

During this period, evolutionary discourse lacked a theory of the biological causes, and population-genetic consequences, of biases in the introduction of variation. The theory summarized by Stoltzfus (2019) suggests that effects of network connectivity invoked in the literature of self-organization (e.g., Cowperthwaite and Ancel, 2007) are consequences of biases in the introduction of variation. Likewise, this theory would define the novelty of evo-devo as an emphasis on the previously misunderstood dispositional role of developmental biases in the introduction process.

This theory is not a truism. It is not necessarily true that evolution actually operates in a way that depends on biases in the introduction process. Even if evolution shows mutational biases, this is not necessarily due to biased dynamics of introduction. Even if biased dynamics of introduction are sometimes influential, they are not necessarily a primary cause of developmentally mediated effects, or of effects invoked in the self-organization literature.

A key prediction of this new theory is that the efficacy of biases in the introduction process does not require neutrality, absolute constraints, or high mutation rates. Instead, the course of adaptation may reflect modest quantitative biases in ordinary mutations.

Initial results confirm this key prediction. This is exciting.

What are the next steps? There are two kinds of challenges, scientific and meta-scientific. The scientific challenges are (1) to build out the theoretical infrastructure, and (2) seek empirical verification of implications.

The meta-scientific challenge is exemplified by TREE's hatchet piece. Because this new idea threatens orthodoxy, reactionary forces want to undermine it by blurring the issues, raising objections, and (paradoxically) trying to appropriate it. A successful distortion campaign will deter progress-- by stirring up doubts and by imposing social and professional costs on those who associate with claims of novelty--, thus preserving the authority of tradition for a bit longer.

I will return to scientific issues after addressing this meta-scientific challenge in the next series of posts.


  1. Empirical verification of mutation frequency biasing evolutionary outcome is already highly evident in the somatic evolution of cancer, where mutation rates (origination rates) vary over orders of magnitude and epistasis is present to such an extent that alternative trajectories are often irrevocably altered by fixation of initial mutations. The prevalence among patients of cancer driver mutations is a joint function of the mutation rate and the intensity of selection. See e.g.

  2. @Jeffrey_Townsend, thanks, I will add Cannataro, et al. to the empirical case for mutation-biased evolution described in

    This also refers to Liu, et al 2019, a very recent study showing effects of origination dynamics on drug-resistant tumor outgrowths in leukemia. Another study (MacLean, et al 2010) provides measured mutation rates showing a 50-fold range for nucleotide mutations in the same gene.

    In a later post, I will return to the issue of epistasis when I address theoretical objections in TREE's hatchet piece (, which argues that mutation-biased adaptation is unlikely and that the evidence is unconvincing.