The Haldane-Fisher “opposing pressures” argument against internal tendencies

In his magnum opus, Gould (2002) writes as follows, citing an argument from Fisher (1930):

“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” (p. 510).

The conclusion of this argument is that internalist theories — the kind of theories that attempt to explain evolutionary tendencies by referring to internal variational tendencies — are incompatible with population genetics because mutation rates are too small for the pressure of mutation to be an important causal force.

Provine (1978) identifies this argument as a key contribution of theoretical population genetics to the Modern Synthesis, anchoring its claim to have refuted all alternative theories.

Below I will explain the argument, why it is important today, and how it appears in evolutionary writing.

The argument

The mutation pressure theory, explained in much more detail in Bad Takes #2, appears most prominently as a strawman rejected by Haldane (1927, 1932, 1933) and Fisher (1930). That is, Haldane and Fisher did not advocate for the importance of evolution by mutation pressure, but presented an unworkable theory as a way to reject the idea, popular among critics of neo-Darwinism, that evolutionary tendencies may reflect internal variational tendencies.

Haldane and Fisher concluded that evolution by mutation pressure would be unlikely on the grounds that, because mutation rates are small, mutation is a weak pressure on allele frequencies, easily overcome by opposing selection. Haldane (1927) concluded specifically that this pressure would not be important except in the case of neutral characters or abnormally high mutation rates (image)

The conclusion of Haldane (1927)

The argument is hard to comprehend today because most of us think like mutationists and no longer accept the shifting-gene-frequencies theory central to classical thinking.

The way to understand the argument more sympathetically is to consider how, in the neo-Darwinian tradition, the focus on natural selection shapes conceptions of evolutionary causation in a very specific way: selection is taken as the paradigm of a cause, so that other evolutionary factors are treated as causal only to the extent that they look (somehow) like selection. For instance, drift and selection can both cause fixations, and so they are often contrasted as alternative evolutionary causes.

More generally, classical population genetics tends to treats causes of evolution as mass-action pressures that shift frequencies. The mutation-pressure argument treats mutation as a pressure that might drive alleles to prominence, i.e., to high frequencies.

That is, the way to understand Haldane’s treatment is that, if mutation-biased evolution is happening, this is because mutation is driving alleles to prominance against the opposing pressure of selection, so that either the mutation rate has to be very high, or selection has to be practically absent (i.e., neutrality). Fisher’s (1930) reasoning on the issue was similar to Haldane’s. From the observed smallness of mutation rates, he drew a sweeping conclusion to the effect that internalist theories are incompatible with population genetics.

Contemporary relevance

Subsequent work has partially undermined the narrow implications of the Haldane-Fisher argument, and completely undermined its broader application as a cudgel against internalism. Mutation pressure is rarely a reasonable cause of population transformation, because it would happen so slowly and take so long that other factors such as drift would intervene, as argued by Kimura (1980).

This means that we can reject Haldane’s narrow conclusion in the sense of suggesting that, when we see important effects of mutation in evolution, this must be due to high rates of mutation or to neutral evolution. Instead, we must also consider biases in origination.

Although the mutation pressure theory is useful mainly as a historically important strawman, it is not entirely irrelevant to evolution in nature. Consider the loss of a complex character encoded by many many genes: perhaps the total mutational target is so large that a population might reach a substantial frequency of loss of the character due to the mass effect of many mutational losses. The case studied by Masel and Maughan (2007) is exactly this kind of case in which evolution by mutation pressure is reasonable. In particular, the authors estimate an aggregate mutation rate of 0.003 for loss of a trait (sporulation) dependent on many loci, concluding that complex traits can be lost in a reasonable period of time due primarily to mutational degradation.

To reiterate, the main relevance of this argument today is historical and meta-scientific. First, it represents a historically influential fallacy. Recognizing that the argument cited by Gould above is a fallacy might cause us to pause and reflect on how conventional wisdom from famous thinkers citing other famous thinkers might have an improper grounding. Second, this is not just an arbitrary technical error, but reflects a substantive flaw in the Modern Synthesis view of causes and of evolutionary genetics, exposing the extent to which the argumentation of the architects of the Modern Synthesis was grounded in the shifting-gene-frequencies theory and, as such, was poorly grounded.

Examples

Haldane’s 1927 statement is given above. In 1933, he wrote as follows, again treating the role of mutation in the “trend” of evolution as a matter of mutation pressure (where Haldane uses k and p, we would today use something like s for selection coefficient and something like u for mutation rate).

p. 6.  “In general, mutation is a necessary but not sufficient cause of evolution.  Without mutation there would be no gene differences for natural selection to act upon.  But the actual evolutionary trend would seem usually to be determined by selection, for the following reason.  

A simple calculation shows that recurrent mutation (except of a gene so unstable as to be classifiable as multi-mutating) can not overcome selection of quite moderate intensity.  Consider two phenotypes whose relative fitnesses are in the ratios 1 and 1-k, that is to say, that on the average one leaves (1-k) times as many progeny as the other.  Then, if p is the probability that a gene mutates to a less fit allelomorph in the course of a life cycle, it has been shown (Haldane, 1932) that when k is small, the mutant gene will only spread through a small fraction of the population unless p is about as large as k or larger.  This is true whether the gene is dominant or recessive.” 

Fisher used much more dramatic language.

“For mutations to dominate the trend of evolution it is thus necessary to postulate mutation rates immensely greater than those which are known to occur.”

“The whole group of theories which ascribe to hypothetical physiological mechanisms, controlling the occurrence of mutations, a power of directing the course of evolution, must be set aside, once the blending theory of inheritance is abandoned. The sole surviving theory is that of Natural Selection”

Fisher (1930) The Genetical Theory of Natural Selection

Huxley and others were more strongly influenced by Fisher’s argument. Haldane’s conclusion is stated subtly.

“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 [apparent evolutionary trends] can be far better accounted for by selection.”  p. 56

“Of course, if mutation-rate were high enough to overbalance counter-selection, it would provide an orthogenetic mechanism of a kind.  However, as Fisher and others have shown, mutation rates of this intensity do not exist, or at least must be very rare. ”  p. 509

Huxley (1942), Evolution: the Modern Synthesis

“if ever it could have been thought that mutation is important in the control of evolution, it is impossible to think so now; for not only do we observe it to be so rare that it cannot compete with the forces of selection but we know this must inevitably be so.” p. 391

Ford (1971), Ecological Genetics

Provine begins by stating the issue very modestly, but then concludes that the argument “discredited” alternative theories. However, note that the pressure theory was invented by Haldane and Fisher: the position of the mutationists was not a monistic theory of mutation pressure, but a dualistic theory of “mutation proposes, selection disposes (decides).”

“the mathematical evolutionists demonstrated that some paths taken by evolutionary biologists were unlikely to be fruitful. Many of the followers of Hugo de Vries, including some Mendelians like Raymond Pearl, believed that mutation pressure was the most important factor in evolutionary change. The mathematical models clearly delineated the relationships between mutation rates, selection pressure, and changes of gene frequencies in Mendelian populations. Most evolutionists believed that selection coefficients in nature were several orders of magnitude larger than mutation rates; upon this assumption, the mathematical models indicated that under most conditions likely to be found in natural populations, selection was a vastly more powerful agent of evolutionary change than mutation … These mathematical considerations … discredited macromutational theories of evolution and theories emphasizing mutation pressure as the major factor in evolution.”

Provine (1978) The role of mathematical population geneticists in the evolutionary synthesis of the 1930s and 1940s.

In the seminal paper on developmental constraints, Maynard Smith et al (1985) identify the Haldane-Fisher argument as an impediment to recognizing developmental biases as genuinely causal

“Two separate issues are raised by these examples.  The first 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.” (p. 282)

Maynard Smith, et al. (1985) Developmental Constraints

Below is one of several contemporary statements that seem to gesture toward the Haldane-Fisher argument, without betraying any clear link. I would tag this as “Haldane-Fisher argument + game of telephone + qualifications” rather than just “Haldane-Fisher argument”.

“For instance, it is possible to say confidently that natural selection exerts so much stronger a force than mutation on many phenotypic characters that the direction and rate of evolution is ordinarily driven by selection even though mutation is ultimately necessary for any evolution to occur.”

Futuyma and others, 2001, in a white paper written by representatives of various professional societies

Gould was obviously sympathetic to internalist thinking but he got his ideas on this issue straight from Fisher (1930). Note that Gould is writing 75 years after Haldane.

“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.” (p. 510)

Gould (2002) The Structure of Evolutionary Theory

Further examples

This section is reserved for further examples supplied by readers.

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