Haldane's dilemma

 
Today is JBS Haldane's 119th birthday. Together with Fisher and Wright, Haldane is considered the founder of the mathematical theory of population genetics. Population genetics studies how allele frequencies (the prevalence of different copies of genes) change in populations due to processes like natural selection and genetic drift. In other words, how mutations arise and how they undergo a turnover in the population.

To celebrate Haldane's birthday, I thought I'd discuss his 1957 paper, "The Cost of Natural Selection" [1], which, unfortunately, has gained popularity after some people started using it as an argument against evolution. In this paper, Haldane states that multiple favorable traits cannot be selected at once:

"In this paper I shall try to make quantitative the fairly obvious statement that natural selection cannot occur with great intensity for a number of characters at once unless they happen to be controlled by the same genes."

Haldane poses the following question: supposing you have constant selective pressure towards one trait in particular, how many individuals without the trait need to die before the new trait takes over? Too many deaths will cause the population to go extinct, but too little will never allow the turnover of the new trait. This is what he defines the "substitution cost," or, in other words, the cost for a trait to become advantageous.

He calculates the substitution cost under a very particular scenario: suppose that a sudden change happens in the environment (like a shift in climate, or the introduction of a new predator), and this causes a certain species to be less adapted to the environment, and therefore, to have lower reproduction rate. The less fit individuals will die first, thus allowing natural selection to push forward the fitter ones. Suppose that a particular mutated gene, until then rare in the population, favors adaptation to the new environment. Gradually, the population will see a shift in prevalence of the new trait. Individuals without the trait will progressively go extinct and in this process other traits may get lost. As a result, under this scenario, no more than one gene can be selected at once.

The concepts in this paper were later referred as "Haldane's dilemma" by paleontologist Van Valen, who formulated the dilemma as "for most organisms, rapid turnover in a few genes precludes rapid turnover in the others. A corollary of this is that, if an environmental change occurs that necessitates the rather rapid replacement of several genes if a population is to survive, the population becomes extinct."

In his 1957 paper Haldane concludes:

"Unless selection is very intense, the number of deaths needed to secure the substitution, by natural selection, of one gene for another at a locus, is independent of the intensity of selection. It is often about 30 times the number of organisms in a generation. It is suggested that, in evolution, the mean time taken for each gene substitution is about 300 generations. This accords with the observed slowness of evolution."

This may indeed sound surprising. If it takes 300 generations for one trait to replace the old one, how can we possibly have achieved the kind of diversity we observe today? Two of Haldane's assumptions are problematic: (1) he assumed an infinite size population; (2) he assumed the selective pressure on the new trait to be constant over the years.

Haldane's claim have been revised and re-elaborated by many scientists, and probably the most famous one is evolutionary biologist Motoo Kimura, who, in the early '60s, used a diffusion equation to recalculate the substitution cost. Kimura noticed that under Haldane's model, it would take an enormous number of offsprings to keep the current rate of natural selection. This became the basis of Kimura's neutral selection theory, in which he claimed that the vast majority of genetic changes are not "selected." Instead, according to Kimura, genetic changes are mostly random changes with no effect (neutral), which get fixated in the population simply because of the resampling from one generation to the next (a process called "genetic drift"). In other words, according to Kimura, the fact that some individuals reproduce and others don't causes certain traits to gradually disappear from the population.

So, which is it? Completely neutral mutations that get fixed because of random mating, or complete selection on every single trait? Most likely, it's a combination of both. Very few traits are truly selected for. Mutations arise constantly and, in a small population, they can pick up just because of genetic drift. Historically, people migrated and the geography of the landscape changed, causing populations to split. In a small population a minor mutation is more likely to pick up and then get fixated because of genetic drift, whether the mutation is advantageous or not. However, if the mutation is indeed advantageous, a sudden selective sweep would pick it up. But this -- most likely -- didn't happen under constant pressure over years, like Haldane originally formulated. It was more likely occasional sweeps (think of a particularly virulent flu season, for example) that switched the minor allele from minor to wild-type, and then genetic drift did the rest.

As for Haldane's numbers, they're not as far off as one may think. I did, however, find a paper published in 1977 [2] in which the author showed that Haldane had overestimated the cost of natural selection by allele substitution. Darlington states: "The cost is reduced if recessive alleles are advantageous, if substitutions are large and few, if selection is strong and substitutions are rapid, if substitutions are serial, and if substitutions in small demes are followed by deme-group substitutions. But costs are still so heavy that the adaptations of complex organisms in complex and changing environments are never completed. The rule probably is that most species most of the time are not fully adapted to their environments, but are just a little better than their competitors for the time being."

In other words, evolution is a work in progress.

Dilemma aside, I love Haldane for this famous quote:

"Theories have four stages of acceptance. i) this is worthless nonsense; ii) this is an interesting, but perverse, point of view, iii) this is true, but quite unimportant; iv) I always said so."

And if you've ever tried to publish a scientific paper, or to publish anything at all as a matter of fact, you know exactly what Haldane was talking about.

[1] Haldane, J. (1957). The cost of natural selection Journal of Genetics, 55 (3), 511-524 DOI: 10.1007/BF02984069

[2] Darlington PJ Jr (1977). The cost of evolution and the imprecision of adaptation. Proceedings of the National Academy of Sciences of the United States of America, 74 (4), 1647-51 PMID: 266204

Photo: blue hour is the time of the day when longer exposure time grants you a blue sky and soft, yellow lights. It's particularly beautiful in an urban setting when all the city lights lit up.