The Haldane-Fisher “opposing pressures” argument

The Haldane-Fisher “opposing pressures” argument is an argument from population genetics that played an important role in establishing the Modern Synthesis orthodoxy, and which continued to guide thinking about causation throughout the 20th century. The flaw in the argument was pointed out by Yampolsky and Stoltzfus (2001) when they showed that a workable theory of variation-biased evolution emerges, not from mutation driving alleles to fixation against the opposing pressure of selection, but from biases in the introduction process. The purpose of this blog is simply to document this influential fallacy.

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.

Note the form of the argument: the theoretical principle in the first clause, combined with an empirical observation (low mutation rates), yields a broad conclusion. The theoretical argument assumes that the way to understand the role of mutation in evolution is to think of it as a force or pressure on allele frequencies. That is, in Modern Synthesis reasoning, evolution is reduced to shifting gene frequencies, and the causes of evolution are declared to be the forces that shift frequencies. One then inquires into the magnitude of the forces, because obviously the stronger forces are more important; strong forces deserve our attention and must be treated fully; very weak forces may be ignored. As indicated by Provine (1978), this kind of argument about the sizes of forces was a key contribution of theoretical population genetics to the Modern Synthesis, anchoring its claim to have undermined all the alternative non-Darwinian theories.

Below I will present the argument in more depth, illustrate how it is invoked in evolutionary writing, and explain why it is important today.

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 that evolutionary tendencies may reflect internal variational tendencies, an idea that conflicts with the neo-Darwinian view that selection is the potter and variation is the clay.

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: 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 (in some way) like selection. For instance, drift and selection can both cause fixations, and so (in the context of population-genetics discussions) they are often contrasted as the two alternative causes of evolutionary change.

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 prominence 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.


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, and it would appear impossible to avoid the conclusion that if any evolutionary phenomenon appears to be inexplicable on this theory, it must be accepted at present merely as one of the facts which in the present state of knowledge seems inexplicable. The investigator who faces this fact, as an unavoidable inference from what is now known of the nature of inheritance, will direct his inquiries confidently towards a study of the selective agencies at work throughout the life history of the group in their native habitats, rather than to speculations on the possible causes which influence their mutations.”

Fisher (1930) The Genetical Theory of Natural Selection

Fisher’s unqualified rejection of internalist theories seems to have been more influential, which is not surprising given that it comes down like a hammer whereas Haldane’s conclusion is subtle by comparison.

“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 (1978) 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. It’s a general application of the forces theory, based on the idea that some forces are strong and others are weak, and the strong forces dominage.

“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

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).

That is, whereas Haldane’s conclusion suggests that important effects of mutation in evolution result from one of two special conditions— high rates of mutation or neutrality—, this is not a safe inference because it ignores the role of biases in origination, whose efficacy does not require high rates of mutation or neutrality.

Although the mutation pressure theory is most relevant today as a historically important fallacy, 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 causation and of evolutionary genetics, exposing the extent to which classic arguments about causation that established the Modern Synthesis do not follow from universal principles, but are grounded in a parochial view designed to support neo-Darwinism.

Objections to declaring the argument a fallacy

When I present this argument, I sometimes hear objections. One is that it is unfair to criticize Fisher and Haldane for not understanding transition bias, because they did not know about it. But we are not trying to be fair to persons: we are trying to be rigorous about theories and arguments. Theories and arguments are supposed to be right. If the opposing-pressures argument is a good pop-gen argument, then it will work in a world with transition bias or GC bias and so on.

For instance, the mutation-selection balance— in the simplest case, f = u / s — is a theory from Haldane and Fisher, and the theory can be right when applied to kinds of mutations that were not known in 1930. In fact, no molecular mechanisms of mutation were known in 1930: this was before the structure of DNA was known, and even before it was known that DNA is the genetic material. Haldane and Fisher knew that not all mutation rates are the same, so when they devised theories, they invoked a mutation rate as a case-specific variable. They derived a mutation-selection balance equation with a form that allows the rate to take on different values, so we are on solid ground in applying it to any deleterious mutation that can be assigned a rate, e.g., a transposon insertion.

Another objection is that the opposing-pressures argument is really just an argument against evolution by mutation pressure— which we still reject generally, for reasons expressed by Haldane and Kimura— and it doesn’t rule out other forms of variation-biased evolution. The problem is that this is not how the argument was understood by generations of evolutionary biologists from Fisher and Huxley to Gould and Maynard Smith. Instead, it was understood to be a very general claim.

Think about it this way. Theoretical arguments like this often have a 3-part structure

  • the set-up: a problem-statement or question that frames the issue and establishes context, possibly with some problematic assumptions
  • the analysis: an analytical core with some modeling or equations
  • the take-away: a conclusion that maps the analysis to the problem, answering the framing question

The analytical core is rarely the problem. If you go back over the examples above and ask how the issue is framed, it is often framed in terms of a very general question like what determines the direction or general trend of evolution (Haldane), or what is the status of internalism (Gould), or could a trend be caused by mutation instead of selection (Huxley), or what is the potential for developmental effects on the production of variation to influence evolution (Maynard Smith, et al). Fisher’s argument quoted above is explicitly general, referring to any theory that attempts to explain evolutionary tendencies by reference to “physiological mechanisms controlling the occurrence of mutations.” He is not just rejecting evolution by mutation pressure or a specific theory labeled “mutationism” or “orthogenesis.” Fisher says that researchers who understand how population genetics works will stay focused on selection and not on how the mutations happen, because that is irrelevant.

For instance, a discussion of how oxidative deamination and repair contribute to CpG bias is clearly a discussion of physiological mechanisms controlling the occurrence of mutations, and therefore is irrelevant to evolution according to Fisher’s argument. To cite a concrete example, the study by Storz, et al. (2019) of the role of CpG bias in altitude adaptation by changes in hemoglobin genes violates Fisher’s guidance because the authors directed their evolutionary inquiry toward the possible causes which influence mutations. Fisher’s argument is explicitly a general argument that applies to any considerations of what determines the occurrence of mutations, that is precisely how generations of evolutionary thinkers understood Fisher’s argument, and that is precisely the basis for concluding firmly that Fisher’s argument is mistaken.


The opposing pressures argument says that, because mutation rates are small, mutation is a weak pressure, and this rules out a possible role for mutational and developmental effects in determining evolutionary tendencies or directions. The argument first appeared in writings of Haldane and Fisher, and was repeated by leading thinkers throughout the 20th century, e.g., emerging in the evo-devo dispute of the 1980s.

The analytical core of the opposing pressures argument is not the problem. The analytical core says that evolution by mutation pressure would require high mutation rates unopposed by selection. The fallacy is to use this analytical core as the basis for a general conclusion about the status of internalism, the sources of direction in evolution, or the potential for variational biases to impose dispositions.

Why would generations of evolutionary thinkers assume that an argument about mutation pressure is an adequate basis for making such broad conclusions, ignoring the introduction process? That’s a story for another day, but the short answer is that, for the people thinking analytically about causation, the introduction process did not exist. For them, the Modern Synthesis had reduced evolution to quasi-deterministic shifts in frequencies of genes in the gene pool. New mutations aren’t involved. The population is a point being pushed around by forces in a space of non-zero allele frequencies. Mass-action pressures are the only effective sources of direction in this kind of system.


Popov I. 2009. The problem of constraints on variation, from Darwin to the present. Ludus Vitalis 17:201-220.

Ulett MA. 2014. Making the case for orthogenesis: The popularization of definitely directed evolution (1890–1926). Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 45:124-132.