Science advances by deeper mathematical and conceptual understandingby Nicholas Beale / August 23, 2012 / Leave a comment
Published in September 2012 issue of Prospect Magazine
We’d like to suggest an idea, which we might call the “Complexity Principle”: Biological systems are almost always more complex than you think – even when you allow for the fact that they are more complex than you think. They operate at many levels: molecule, gene, cell, organism, population, ecosystem and often others. And in most cases the flows of information are at least as important as the flows of matter and energy. Nowhere is this more true than in the realm of human behaviour. Neither electrons nor genes can be selfish, altruistic, rational or emotional: humans certainly can even when discussing science, and some of this was evident in the recent strongly critical review by Richard Dawkins of EO Wilson’s The Social Conquest of Earth, which includes phrases such as ‘erroneous and downright perverse misunderstandings of evolutionary theory’.
Wilson indeed goes against some of the certainties of the evolutionary theory that was current when Dawkins was a working scientist. But real scientists understand that theory advances with new discoveries, and great scientists sometimes find results that are wholly against current scientific consensus. Even in physics our basic understanding of the composition of the universe has been transformed in the last 40 years.
In his books, Dawkins places heavy emphasis on the gene being the primary element upon which natural selection operates. The gene tends to act in a way that promotes its survival, whence the idea of the selfish gene. The fact that organisms often act unselfishly is explained by the fact that helping relatives at the expense of oneself may promote the survival of one’s genes, because there is a tendency to share genes with one’s relatives. This was informally characterised as “I will risk my life to save two of my brothers or four cousins” and in the 1960s WD Hamilton expressed this idea more formally in terms of the “inclusive fitness” defined by rB – C, where B is the benefit, C the cost, and r is the Relatedness between the individuals involved. This quantity is called “Inclusive Fitness” because it includes the fitness of other related individuals, and the process is referred to as “kin selection” because it does not just depend on the evolutionary fitness of one individual but on the “fitness” of others who are likely to carry the gene. Readers will appreciate that here and elsewhere we are neglecting some technicalities which, whilst fascinating, will confuse most readers and don’t make any difference to our fundamental points. The “Further Reading” section gives additional information on various points.
Hamilton was clear that his account was an approximation. But people were ready for the idea of genes as the hidden and all-powerful agents behind all life, and there were tremendous advances in molecular biology from Crick and Watson onwards. So Hamilton’s Rule provided much of the theoretical underpinning for a massively successful popularisation in The Selfish Gene.
Much has happened in biology in the last 50 years. As usual, scientific advances have raised many new questions and reminded us of the Complexity Principle. Completion of the Human Genome Project made it clear that the relationship between genes and characteristics was much more complex than had previously been supposed: in almost all cases many, many genes are involved in any characteristic and one gene may be involved in many different functional circuits. Genes are not, as was previously imagined, discrete units of instruction threaded in the DNA rather like codes punched into a paper tape but patterns of information that may be dispersed quite widely over the DNA, and indeed the same parts of the DNA may be read differently as different genes depending on the circumstances. At a basic physical level, what matters is the behaviour of the actual molecules in the cells, one aspect of which is genes being switched on and off by epigenetic markers and other factors. Jablonka & Lamb write of “Evolution In Four Dimensions: Genetic, Epigenetic, Behavioral, And Symbolic”. The latter dimensions are by no means confined to humans. Bird song, for example, which is learned and not merely genetic, plays an important role in the survival of groups of birds and in sexual selection: an enormously powerful evolutionary force that is inherently cultural. It is also a sobering fact that 90% of the cells in “our” bodies are in fact microbes, and that our so-called microbiomes play an essential role in our health and survival. It seems that our microbiomes tend to evolve over our lifetimes towards those of the groups in which we live, and have very little to do with our genetic inheritance.
There have also been major advances in the mathematics of evolution, and a discipline has emerged of Evolutionary Dynamics. This goes beyond simple rules like Hamilton’s Rule to being able to make precise calculations about the dynamics of systems behaviour, using evolutionary game theory and population genetics. Early successes included insights into why HIV takes so long to develop into AIDS, and how “tit for tat” can be supplanted by forgiveness, and more recently this approach has given important insights into the evolution of language and the genetics of cancer. Much of this work has focused on the evolution of cooperation of various types and under various circumstances, and it was only a matter of time before this 21st century approach collided with Hamilton’s Rule.
EO Wilson, probably the world’s greatest expert on eusocial insects, had become increasingly dissatisfied with kin selection as the sole and dominant explanation of pretty much everything in evolution. This dissatisfaction was shared by his Harvard colleague Martin Nowak, a pioneer of Evolutionary Dynamics. Nowak’s PhD student Corina Tarnita realised that they could formulate a precise mathematical model that would validate many of their concerns, and a paper was submitted to Nature. After rigorous peer review the paper (Nowak, Tarnita and Wilson or NTW), with a 48 page online mathematical appendix, was published in 2010 and featured on the front cover.
It caused a sensation. Part of this was the mathematics, which shows that Hamilton’s Rule, as generally understood, simply doesn’t work in certain cases, and that it is possible to account for the evolution of eusociality without relying on inclusive fitness at all. And part was the somewhat incendiary language: “the production of inclusive fitness theory must be considered meagre”, its use “requires stringent assumptions, which are unlikely to be fulfilled by any given empirical system”, “even in the limited domain of inclusive fitness theory, Hamilton’s rule does not hold in general” and “Hamilton’s Rule is either unnecessary or wrong”. Four separate groups of scientists wrote to Nature objecting to aspects of the paper, and one of these letters has 137 signatures. Two have subsequently published papers that amplify and extend these rebuttals. There are two main strands to these complaints.
Firstly, the 137 offer several instances where Kin Selection and Hamilton’s Rule have made predictions that have been confirmed by experiment. It’s fair to say that these predictions seem to be fairly rough correlations, that would not impress physicists: but biological systems are complex and perhaps not much more can be expected. NTW remark that “It is not enough to obtain data on genetic relatedness and then look for correlations with social behaviour. Instead one has to perform an inclusive fitness type calculation for the scenario that is being considered and then measure each quantity that appears in the inclusive fitness formula. Such a test has never been performed.” By contrast some of the Evolutionary Dynamics papers make very precise quantitative predictions that fit the data well. It looks to us as though Hamilton’s Rule, in these contexts, is a useful rule of thumb rather than a fundamental principle.
Secondly, they complain that the version of Hamilton’s Rule used by Nowak, Tarnita and Wilson is too simplistic. Instead of using the standard textbook Benefits, Costs and Relatedness, it is possible to redefine B, C and r in sophisticated ways which depend on the detailed evolutionary dynamics of the system in question. With these adjustments, Hamilton’s Rule will indeed hold. These points were known to some kin selection experts, although they were “often implicit” in the discussions. NTW discuss these sophisticated versions but point out that you can only understand the behaviour of an evolutionary system by following through the evolutionary dynamics. Once you have done so Hamilton’s Rule adds nothing new: it’s just a mathematical identity which can be seen as an “accounting method”. In particular, with these redefinitions, Hamilton’s Rule tells you nothing about whether kin selection (as generally understood) is the dominant force in an evolutionary system. The Complexity Principle holds: relatedness is of course usually very important in evolution, but it is almost never all-important.
Dawkins also offers an argument in favour of kin selection (against group selection) that only genes are “replicators” and therefore the only entities whose survival makes a long term difference. This depends on a hopelessly over-simplistic view in which organisms are simply a collection of their genes. This is about as misleading as considering a Shakespeare play to be simply a collection of words. The sequence and (3-Dimensional) layout of the genetic material matters a great deal. In addition, a genome is only meaningful in the context of a cell within an organism, rather as Shakespeare’s plays only reveal their meaning within a culture. Denis Noble’s book The Music of Life gives an excellent exposition of this theme, though many of the scientific advances that undermine kin selection fundamentalism have occurred after that book was written. The fact is that you can apply evolutionary dynamics at any level where there is selection, mutation and replication.
David Sloan Wilson suggests that this debate is largely over amongst biologists because everyone accepts that selection operates on multiple levels. It is not clear to us that this is yet the case. Stephen Pinker, for example, argues against group selection because it is poorly defined and also because the mutations are not random as in a truly pure Darwinian theory. Adapting the mathematics to the reality of multi-level selection and causality is certainly complex, but there seems to us no point in denying the importance of these higher order effects. We also note that the concept of a “random” mutation is a bit more elusive than some biologists seem to suppose, and that anyway sexual selection, as we have noted above, certainly isn’t “random” in the kind of way that genetic mutations are.
Readers may ask, if this is all true, why doesn’t Professor Dawkins understand this? It is relevant to remember that Professor Dawkins is the most talented populariser of evolutionary ideas of his generation, but has made little contribution to the primary scientific literature. A rich admirer endowed a chair for him at Oxford as professor for public understanding of science. When he was elected a Fellow of the Royal Society, it was as a “general candidate” rather than for specific contributions to research. In common with most biologists of his generation, he doesn’t have a strong mathematical background. He has outstanding literary talents, but it is understandable that a popular author might find it difficult to accept the extent to which his ideas are over-simplistic, or to follow rigorous mathematical arguments when they transcend the ideas on which he has built his reputation.
What then of the objectors, many of whom are eminent in their fields? It’s true that most of these eminent biologists don’t have a rigorous mathematical background, but it’s also true that the language of NTW, whilst accurate from a mathematical point of view, was a trifle over-inflammatory. Recall the Complexity Principle. Even if it is true, logically, that you need a proper calculation of the evolutionary dynamics to understand what is happening in an evolutionary system, any model in real-life situations will inevitably be a vast simplification, and in these situations rules of thumb that have stood the test of time are useful. Simplified ideas of kin selection will often give a pretty good “first order” understanding of what is going on, and indeed deviations from (the simple version of) Hamilton’s Rule will indicate as to when some these more complex effects are important. It would have been more tactful to mention this, but Nature papers are not intended for tact but for rigour. Equally, although NTW have clearly shown that kin selection is neither necessary nor sufficient for the evolution of eusociality, it remains an open question to what extent their alternative mechanisms have in fact been important in non-human evolution. It would certainly have been tactful for EO Wilson to have mentioned the dissenting views in his book, but book texts are in practice pretty well frozen long before they are published and perhaps he will be able to address this point in a subsequent edition.
What might the educated general reader take away from this? Metaphors and rules of thumb can be useful in science, but must not be mistaken for fundamentals. Anyone who tries to tell you that “only X is going on” in a biological system is either ignorant or attempting to mislead. Science advances by deeper mathematical and conceptual understanding, which can sometimes over-turn or supplant previous orthodoxies. Science is full of open questions: even in physics no-one is sure how many spatial dimensions or universes there are, or what 95% of the mass of this universe consists of. Finally, consider the Complexity Principle: Biological systems are almost always more complex than you think – even when you allow for the fact that they are more complex than you think.
The Editors of Prospect have kindly allowed us to put here the kind of information here that we would normally have in footnotes. These comments are made in the order in which the “footnotes” would have appeared in the text:
Hamilton’s original paper is “the Genetical Evoluton of Social Behaviour” J Theoret. Biol (1964) 7 1-16. In it he states “the following account based on use of the above coefficients must give a good approximation to the truth when selection is slow and may be hoped to give some guidance even when it is not.”
For some of the complexities about genes see Allen et al, “Hundreds of variants clustered in genomic loci and biological pathways affect human height” Nature 467 832-838(2010) This identified at least 180 genes involved in stature (height) , which is known to be 80% hereditable, and yet even taken together these genes only accounted for10-20% of the hereditable variation. There is a fascinating discussion of the microbiome in David A Relman “Learning about who we are” Nature 486, 194-195 (2012) and the papers it discusses.
The modern mathematics of evolution are explained in Martin A Nowak’s book Evolutionary Dynamics: Exploring the Equations of Life (Harvard, 2009) based on the course he gives at Harvard. For the relevant scientific papers see ped.fas.harvard.edu.
The NTW paper is on the PED website (Nature 26 Aug 2010). The objecting letters are on the Nature website. As far as we know the last time something like this bulk letter of objection happened was when 100+ Physicists signed a pamphlet objecting to Relativity. Interestingly the two most distinguished biologists cited by Dawkins as objecting did not sign any of the letters: Robert Trivers in fact withdrew his signature after he had looked into the details of the argument. The discussion of the modified versions of Hamilton’s Rule is on pp 17-18 of the Supplementary Online Material of NTW. For examples of precise Evolutionary Dynamics predictions see eg Lieberman et al. “Quantifying the evolutionary dynamics of language” (Nature 2007) and Diaz et al “The molecular evolution of acquired resistance to targeted EGFR blockade in colorectal cancers. (Nature 2012) both of which are on the PED website.
On Dawkins’ argument that “only genes are replicators” See Denis Noble “Neo-Darwinism, the Modern Synthesis and selfish genes: are they of use in physiology?” J. Physiol 589.5 (2011) pp 1007–1015 which deals with some of the confusions behind this. A good summary of the latest state of play in this area is the debate between Denis Noble and Sydney Brenner at http://www.virtual-liver.de/wordpress/en/2012/07/16/the-virtual-liver-network-keynote-debate/ One of the many striking phenomena Noble cites in this is genetic buffering. In many biological systems, knocking out a single gene has no discernable effect on the phenotype. Studies suggest that about 80% of single knockouts are normally “silent” in that respect. For the importance of 3D configuration of genetic material see Liebermann-Aiden et al “Comprehensive mapping of long-range interactions reveals folding principles of the human genome” Science 326 289-292 (2010)
Stephen Pinker’s comments are in his article “The false allure of Group Selection” 18 June 2012 http://edge.org/conversation/the-false-allure-of-group-selection. But in addition it is now becoming clear that genetic mutations are not really random in a conventional sense. See eg Eugene V. Koonin “A half-century after the molecular clock: new dimensions of molecular evolution” EMBO reports VOL 13, NO 8 (2012) and James Shapiro Evolution, a view from the 21st century (FT Press Science, 2011) Shapiro’s website (http://shapiro.bsd.uchicago.edu/) gives a wide set of references including a preprint of his paper “Rethinking the (Im)Possible in Evolution” Progress in Biophysics and Molecular Biology (2013)
Our “What then of the objectors” paragraph is not at all intended to be disrespectful of the many eminent scientists who have co-signed these letters, all of whom are much more knowledgeable about biology than we are. Perhaps, with our mathematical backgrounds, we are more used to the idea of following where the maths leads us and to a level of rigour which isn’t usual in biology. On our “Open question” point we note that Hughes et al “Ancestral Monogamy Shows Kin Selection Is Key to the Evolution of Eusociality” Science 320, 1213 (2008) doesn’t settle the question, since the mating behaviour of ancestral species are inferred from that of their present descendants. Interestingly Dawkins was not invited to co-sign the letter from 137 scientists (according to http://richarddawkins.net/articles/606562-dawkins-on-nowak-et-al-and-kin-selection)