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‘Something funny seems to happen’: J.B.S. Haldane and our chaotic, complex but understandable world
E-mail: George.Davey-Smith{at}bristol.ac.uk
Binary oppositions are relatively straightforward to recognize, and it is reassuring to run into them as we read the epidemiological literature. This issue of the IJE doesn't disappoint, in this regard, at least. Epidemiologists study both population and individual-level risk. Perhaps we ignore the former at the expense of the latter, for reasons that run from the methodological through to the political. Nancy Krieger1 suggests that such selective myopia allowed business as usual, while breast cancer rates rose as a response to widespread prescription of hormone replacement therapy for post-menopausal women in rich countries over the past four decades. In an accompanying commentary, Charlotte Paul2 cautions that national incidence rates only provide robust evidence regarding aetiology in strictly limited circumstances, perhaps when changes in rates are occurring contrary to expectation. Epidemiologists—as camp followers of statisticians—are traditionally frequentists or Bayesians, paradigms exercised in the discussions of interpretation of multiple comparisons by Jon Wakefield3 and Sander Greenland.4 Cohort studies can enrol very large numbers of participants, as in the Cohort of Norway (CONOR),5 but usually at the expense of the richness of the data collected. Another cohort profiled in this issue, the GECKO Drenthe Study6 contains <1% of the numbers that are in CONOR, but with unusually rich measures being taken. At a more specific level, we can ask whether low dose radiation increases the risk of non-cancer mortality or not, and come to somewhat different conclusions, as in the important and fascinating contributions from Dave McGeoghegan et al.7 and Paul McGale and Sarah Darby.8
We revisit one of the mothers of all binary oppositions in our ‘Reprints & Reflections’ section, with the extremely enjoyable polemic, ‘In defence of beanbag genetics’,9 written in 1964 by J.B.S. Haldane, in response to an attack on mathematical population genetics from the evolutionary biologist Ernst Mayr. In Mayr's view, to ‘consider genes as independent units is meaningless from the physiological as well as the evolutionary viewpoint’; Haldane strongly disagreed. Our several commentators10–13 discuss the complexity and historical importance of this debate, but in a cartoon form it can be portrayed as delineating the opposition between an essentially reductionist strategy—we can understand the world (or at least the distribution of gene frequencies and their related phenotypes over time and place) through quantitative node-by-node analysis—with a holistic approach, which views the former as overly simplistic. The debate between Mayr and Haldane related to population genetics and how selection at a single locus does (or does not) explain the evolution of population-level phenomena. Despite the different focus to that of epidemiologists interested in how genetic variants relate to risk of disease, interesting parallels can be observed between the beanbag genetics debate and genetic epidemiology. As Newton Morton points out, recent large-scale genetic case–control studies provide support for the beanbag model, with multiple identified loci with little evidence of interaction or non-additivity.10 Similarly, analyses of genetic variation in complex traits suggest only a small role for non-additivity.14 Haldane discusses the generally small fitness advantages that were anticipated in population genetics, and ends his article with power calculations suggesting that samples of 10 000–25 000 would be required to detect the differences in gene frequencies anticipated even for variants that would have evolutionary effects that are very rapid on a geological time scale. Similarly in genetic association studies the generally small effects of common variants on disease risk require very large sample sizes to generate meaningful results, as has been discussed in recent issues of the IJE.15–17 Haldane also briefly suggested that beanbag genetics could contribute to questions of causation, referring to Sewall Wright's classic path analysis work. As James Crow comments, ‘the bean-pool may change, but the essential randomness remains’,11 and Haldane quotes the Roman poet Titus Lucretius Carus in emphasizing the chance element in genetic inheritance. In epidemiology this randomness forms the basis of Mendelian randomization approaches to elucidating environmentally modifiable causes of disease.18–23
Haldane's contributions to studying biology and society were so extensive that it was difficult to pick a particular paper to reprint. Alun Evans provides an entertaining retrospective on Haldane's controversial 1923 pamphlet Daedalus that predicted how biological science would look in 2073.24 In the beanbag genetics paper, Haldane briefly touched on gene by environment interactions, but his extended discussion of this in the first chapter of his 1938 book ‘Hereditary and Politics’25 still makes salutary reading. He wrote a classic paper on the influence of disease on evolution in 1949.26 In this, he postulated that in sickle cell anaemia the ‘corpuscles of the anaemic heterozygotes are smaller than normal, and more resistant to hypotonic solutions. It is at least conceivable that they are also more resistant to attacks by the sporozoa which cause malaria’. This is now seen as a prophetic statement.27 With respect to live epidemiological issues it is interesting to read of Haldane's predictions regarding hormone replacement therapy in his 1927 essay ‘The future of biology’.28
‘We shall also probably be able, if we desire, to stave off the sudden ending of a women's sexual life between the ages of forty and fifty. It is worth pointing out that there is no serious reason to believe that any of the rather expensive products of the sex glands now on the market, and often prescribed by doctors, are of any value except as faith cures’.
This seems both archaic (the sudden ending of sexual life at menopause?) and contemporary, with respect to notions of choice and the importance of ensuring the benefits of any such medications.
Haldane's unpublished lectures might also contain many gems, if they were available. His student, the eminent population geneticist John Maynard Smith, recalled that in his 1950s course on population biology at University College, London, Haldane discussed the finite difference form of the logistic equation in relation to population growth.29 As the usual growth rate was varied upwards, small then sustained oscillations in the resultant population were seen, and then, Haldane said, ‘something funny seems to happen’, presumably the chaotic regime reported by later researchers. Maynard Smith pointed out that Haldane did his numerical calculations without mechanical aids, and this could be why he failed to formally anticipate chaos theory—as explicated with respect to Haldane's problem of growth in biological populations by Robert May in his groundbreaking papers of the early 1970s.30 However, in the review of a book by Ernst Mayr for the Journal of Genetics that Haldane mentions he was writing in the article we reprint in this issue9 he suggests that ‘Mayr has failed to grasp the extreme complexity of the results which are possible if one starts out from simple probabilistic axioms’,31 which seems a reasonable gloss on chaos.
For some epidemiologists chaos32 and its sometime companion complexity33 are theories that can help further our disciplinary mission. In reviews and discussion articles chaos and complexity are evoked as tools to help us out of our difficulties.34–41 I am sure my limited ability to comprehend difficult theories explains why I have found many of these discussions unenlightening; to others they promise the dawn of a new golden age for epidemiology. As mentioned earlier, one of the apparent dichotomies can be summed up in the words of the incoming president of the International Epidemiological Association Neil Pearce: ‘the real debate is between population research and research at the individual and micro levels’.42 Chaos theory suggests that small, essentially unmeasurable, perturbations within a system can lead to non-predictable outcomes for that system. Complexity theory, on the other hand, focuses on the large-scale and simple outcomes that can emerge from multiple, highly complex and interacting lower-level phenomena. So things can be complex and simple at the same time. It is of course a personal choice as to whether this paradox is more clearly realized when listening to PJ Harvey singing ‘I can’t believe life is so complex, when I just want to sit here and watch you undress’,43 or reading Neil Pearce's writings on complexity, simplicity and epidemiology.34 (Figure 1). From the epidemiological perspective the emergent simplicity of group-level data can be reassuring. If we aim to understand individual events then we may be attempting to herd (chaotic) cats;44 at a population level we can identify modifiable causes that generate most disease.
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Finally, we would like to thank Mary Shaw for reminding us the importance of the visual, as well as written, domain in the IJE. As Mary explains in her editorial, she is moving to new challenges.45 What is going to be primary school teaching's gain is social epidemiology's loss.
References
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2 Paul C. Commentary: hormone therapy and breast cancer incidence: did epidemiologists miss an effect on national trends? Int J Epidemiol (2008) 37:638–40.
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7 McGeoghegan D, Binks K, Gillies M, Jones S, Whaley S. The non-cancer mortality experience of male workers at British Nuclear Fuels plc, 1946–2005. Int J Epidemiol (2008) 37:506–18.
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