J. Genet. Vol. 69, No. 1, April 1990, pp. 17-32. 9 Printed in India. Memes of Haldane and Jayakar in a theory of sex W. D. HAMILTON Department of Zoology, South Parks Road, Oxford OX1 3PS, U.K. Abstract, The history of mathematical modelling of communities and polymorphisms under intrinsic fluctuating selection is outlined. Authors have usually encountered difficulty in obtaining stability in cases involving host-parasite relations. Stability may in fact be uncommon. On the other hand protection of diversity (non-extinction of rare species or variants) may instead be common and important. Within multilocus systems, mild truncation selection on a host-parasite system both protects variation and is supportative of sexuality against parthenogenesis even when sex pays a full cost-that is, even if sex has halved the efficiency of reproduction due to production of males. Truncation based on heritable health, which is itself based on polygenic resistance to parasites, provides the most robust and universal model supporting sex yet presented. The separate and joint roles of J. B. S. Haldane and S. D. Jayakar in originating ideas now incorporated in the model are discussed. Keywords. Cycles; protected polymorphism; parasites; multilocus genetics; truncation; sex. Introduction For the past ten years I have developed an idea that the ultimate evolutionary cause of sex is disease. The idea is increasingly credible. This is not so much because favourable evidence is accumulating, although the scraps that come to light from time to time, usually having been published incidental to some other objective, are mostly favourable. It is rather the model itself, its engineering and appropriateness for its task, that has improved. A version now evolved with R. Axelrod and R. Tanese (Hamilton et al. 1990) requires only as a workable and realistic minimum to make sex secure, even when carrying the full twofold cost, the following three assumptions: firstly that diseases are many; secondly that resistances are polymorphic; and thirdly that selection has 'softness' or ideally a pattern of truncation in its operation. The last assumption indicates that if the theory is right sex ought to be most universal in species whose members compete for places in hierarchies and live in saturated habitats; parthenogenesis, in contrast, shOuld be most common in colonising species living in unstable, physically severe habitats. This is exactly what is found, a point that seems to favour our theory over others which for the most part leave the ecological correlates of asexuality unexplained (see reviews in Bell 1982, Stearns 1987, Michod and Levin 1988). Feeling at last in sight of a theory which can respect if not yet quite reverence Mother Nature's bizarre invention of maleness, wherever it occurs, and thus also slightly more at ease about the future continuation of my own kind within the human species (I can now tell people that we males are necessary for health) I find myself more interested in the history of the ideas that have become the ingredients Of what I see as the successful theory. Ingredient is the word. Evolving tlie theory has been like working out a recipe for a cake, or rather, as I would hope, trying to reproduce someone else's unknown recipe-Mother Nature's. It has been a matter 17 18 W. D. Hamilton of experimenting with materials, putting jars back on the shelf, taking others-in fact trying to use various insights of population genetics and ecological theory that have been evolved over the past 35 years (and some from even farther back as will be seen). It is insights accepted out of all this and their origins that this paper will attempt to describe. Its central theme will be those insights which foreshadow the demise of the ecological and genetical expectation of stasis, or in other words which tend to reject a supposed abundance of stable equilibria in the genetical living world (Hamilton 1982. 1986l. Evolution and disease In writing this historical sketch I have not had time to search the literature as thoroughly as I should, and even out of work known to me only a skeleton is cited. A good fairly recent review of much of the rest is in Levin (1983). I ask myself how thorough it is worth trying to be when one is writing history of the future and of an unlikely future at that, as most see it In the eyes of many, irrespective of coherence of theory, I will seem way ahead of my facts already and to be as if writing the history of how world population growth was halted long before any such event has happened. Why write history of what may prove to be false? Hardly anyone seems to agree with me that disease is particularly important for sex, leave alone endorses my particular model. My excuses for an admittedly presumptuous approach are two. Firstly, I was asked to write a paper relevant to work of Suresh Jayakar and for sure Suresh is deep in the story I want to tell. Secondly, irrespective of what others may feel l personally am much happier with my model than I have been with any since the 1960's 'reformation' did away with an old faith (Hamilton 1975a). The latest version using many loci and truncation selection has made an order of magnitude improvement in both robustness and realism giving us an idea that at last makes sense on all fronts of the evidence. It has been said that any new and true theory has to go through three stages as it becomes accepted. In the first it is described as obviously wrong; in the second as contrary to religion; in the third as obviously right as was known long ago. Perhaps here is a justification for pushing my idea directly towards the third stage because, as my history is about to show now, part by part, all of the idea of sex and parasites was already known long ago. If the Mendelian system is for the "purpose' that the theory of sex from parasitism suggests, then it is no surprise to find that suitable theoretical properties exist in the sexual process. Nor is it surprising that. in making a striking product, the properties have often been striking themselves and therefore noticed. What is surprising is that the whole compound of diploid recombining Mendelian genetics, source of all such properties, should be accepted for so long accompanied by only very weak theorms of why it should exist. Usually when one looks for the earliest hint of any new idea in evolutionary biology it turns out that a careful search of the writings of Darwin reveals that he wrote and understood more about it than anyone has yet noticed. Wallace too is worth searching for he too ranged deep although on a narrower front. If nothing is found in Darwin or Wallace the next likelihood is to try the contributions of Weissman, another thinker as opposed to mere documenter of evolution; then failing Weissman one turns with high expectations to the writings of what may be Memes of Haldane and Jayakar in a theory of sex 19 called the Founding Peers of tile genetical unification-Wright, Fisher, Haldane. Born over the three years 1889 to 1892, these three made surprisingly equal and independent contributions. At their hands Darwinian theory was revised into line with Mendelism and many further consequences were described. Following the above protocol with respect to a possible understanding of sex as a response to parasitism, it turns out that Darwin's contribution was, firstly, not to fail to point out disease as an important agent of natural selection, and, secondly, and quite separately, to investigate a related and ultimately convergent theme that arose on the side of sex. He gave plentiful discussion to the adaptations by which sexual organisms secure outbreeding while admitting to remain puzzled why they were there. For a long time he saw outbreeding as somehow vaguely helping to cause variation. Later, however, he was led by the 'blending' arguments of Fleeming Jenkin to a quite opposite view, that sexuality might be hindering variability. Forced to look for new abundant sources to replenish what 'blending' seeined to be draining away, he fell back in later editions of The Origin on 'use and disuse' and Lamarckian concessions. As became cleat" with the advent of particulate Mendelism blending is not really a problem, but the continued existence of so much vltriability and how outbreeding affects it in the long run are still unsolved issues. Possibly it is only with understanding of the role of parasites on lines that I outline below that Darwin's intuition that outcrossing would help macroevolution by creating variability begins to be justified. This help may be coming, however, by more devious pathways than anyone from Darwin to Lysenko, even including the intervening founders of Neodarwinism, ever suggested (Hamilton 1990; Hillis 1990). Even while such new themes arise, however, proponents of sex theories that do not attempt to account for outbreeding (e.g. Walker 1978, Bernstein et al. 1988) continue unwisely to neglect Darwin's early concern and findings. On the fi'ont of disease, after Darwin there followed a gap during which information accumulated on the heterogeneity and detailed genetics of disease resistance in both natural and domestic populations but little was said about any general implication, even though, as it seems to us now, the high heritability, so contrary to expectations for a fitness enhancing trait, might have warned of an odd and interesting situation. Tile failure to relate such findings to sex, however, is not surprising in view of the fact that nearly every one was satisfied that they already understood what sex was for.