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In more detail, 13 (57%) of 23 colonies sex allocation is also desirable. Split sex- 5 Boomsma, J.J. and Crafen, A. (1990) Eoolution sampled were judged to have a singly ratio theory has clearly given new im- 44,1026-1034 mated queen (allozyme analysis showed petus to the study of sex ratios and 6 Boomsma, J.J. and Grafen, A. (1991) J. Euol. Biol. 3,383-407 that worker-female relatedness equalled social in insects. 7 Grafen, A. (1986) J. Theor. Biol. 122,95-121 0.72). The other 10 colonies (43%) had a 8 Boomsma, J.J. (1991) Trends Ecol. Euol. 6,92-95 doubly or triply mated queen (worker- Acknowledgements 9 Boomsma, J.J. (1993) in Queen Number and female relatedness was 0.43). It is a fair We thank S.D. Albon, A. Balmford and Sociality in lnsecrs (Keller, L., ed.), pp. 86-109, assumption that workers can detect I.P.F. Owens for comments. C.L.C. is Oxford University Press multiple mating in their queen but not supported by a NERC Studentship. 10 Ratnieks, F.L.W.(1991) Evolution 45,281-292 assess her exact mating frequency. This 11 Sundstriim, L. (1994) Nature 367,266-268 A.F.G. Bourke and G-1. Chan 12 Benford, F.A. (1978) J. Theor. Biol. 72, 701-727 allows the colonies with double and triple 13 Nonacs, P. (1986) Q, Rev. Biol. 61, l-21 mating to be treated as one classll. The Institute of Zoology, Zoological Society of 14 Herbers, J.M. (1990)Am. Nat. 136, 178-208 RA of the singly mating class was there- London, Regent’s Park, London, UK NW1 4RY 15 Pamilo, P. (1990)Behau. EcoI. Sociobio/. 27,31-36 fore 0.72/0.25 = 2.9 (worker-male related- 16 Crozier, R.H. and Pamilo, P. (1993) in Evolution ness equals 0.25 independently of mating and Divers@ of Sex Ratio in Insects and Mires frequency). Similarly, the RA of the References (Wrensch, D.L. and Ebbert, M.A., eds), 1 Trivers, R.L. and Hare, H. (1976)Science 191, pp. 369-383, Chapman &Hall multiply-mating class was 0.43/0.25 = 1.7. 249-263 17 Frank, S.A. (1987) Behao. Ecol. Sociobiol. 20, The average per colony sexual pro- 2 Fisher, R.A. (1930) The Genetical Theory of 195-201 ductivity of the two classes was equal. , Clarendon I8 Mueller, U.G. (1991) Science 254,442-444 Consequently, following a method of 3 Hamilton, W.D. (1964)J. Theor. Bio/. 7, l-52 19 Queller, D.C.,Strassmann, J.E., Solfs, CR., Boomsma and Grafene, the expected sex 4 Alexander, R.D.and Sherman, P.W. (1977) Hughes, C.R. and DeLoach, D.M. (1993) Nature ratio (as the proportion of investment in Science 196,494-500 365,639-641 females) of (1) the singly mating class is 1.0 (all females), (2) the multiply mating class is 0.14 (male-biased), and (3) the population is 0.63 (the FXAof the multiply mated class expressed as a fraction). The science of in These predictions follow directly from the theory outlined above. Specifically, the multiply mating class is relatively large ymmetry has long been an important optimal state, perfect bilateral symmetry enough to ‘balance’ the all-female pro- sconcept in and ’!*, (see below), is viewed as a reflection of duction of the singly mating one, produc- but in biology its study was largely lim- disrupted development, that is, develop- ing a male-biased class-specific sex ratio ited to morphology and systematics until mental instability. The assumption of gen- that decreases the population sex ratio 1953 when Mather revealed the value of etic commonality (identical genes striving until equilibrium is reached at a level studying variation in the degree of bi- for an identical purpose) is limited to equalling the RA of the multiply mating lateral symmetry within a population3. FA. It is not a feature of other indices of class6. The difference in sternopleural bristle developmental instability (e.g. morpho- The observed population ratio (0.67) number between the left and the right logical variance5 and antisymmetry6), and the predicted level (0.63) were sat- side of fruit flies, mefuno- which all lack an optimal state as a refer- isfyingly close. Also, as already stated, gaster, was shown to be larger in some ence point. sex ratios were split in the directions inbred lines of flies than in outbred ones. In June last year, more than 50 scien- predicted. However, the singly mating Direction of (for example, tists gathered in Tempe, AZ, USA,to sur- class clearly did not produce females ex- left > right) was not heritable, but the vey what we have learned about asym- clusively (Fig. 1). There are several poss- magnitude of asymmetry was such that it metry and related variables’. FA is now ible explanations for this, one being that could be increased through direct selec- known to be diagnostic for a wide range workers may make occasional mistakes tion under laboratory conditions. More of environmental and genetic stressors in judging colony RA and so rear an strikingly, it was discovered that selec- borne during development. In humans, FA inappropriate sex ratiolo. The mating fre- tion for high or low bristle number in- is associated with Down’s syndrome and quency in a few colonies may also have creased the associated asymmetry4. other chromosomal anomalies, inbreed- been misclassified by the observer, since Three kinds of bilateral asymmetry ing, maternal disease, maternal alcohol some queens probably mated with two have been described, based on the form consumption and parental tobacco in- males bearing the same marker allelell. of the distribution of differences between take7-9.Moreover, particular right and left values. Asymmetry that (e.g. in dermal ridge patterns) may be Conclusion shows a normal distribution around a associated with particular disorders (e.g. Sundstrcm’s results provide the best mean of zero is called fluctuating asym- schizophrenia) but not with others (e.g. evidence yet of split sex ratios arising metry (FA), in contrast to directional manic depressive illness)‘O. Thus, asym- from workers’ responses to their vari- asymmetry, in which the mean is biased metry in traits whose ontogenies are able RA. Moreover, they also support to the left or right (e.g. in worker-controlled sex allocationl, the humans). Antisymmetry, in turn, refers to distributions in which symmetrical ‘The symposium was hosted by Therese Markow idea that within-population sex ratio of Arizona State University and funded by the variation may often stem from variable individuals are relatively uncommon (or National Science Foundation, National Insti- RA5,6and Fisherian theory in genera11,2*12. absent) but the asymmetries in a popu- tutes of Health, Kfuwer Academic Publishers and It would now be interesting to check simi- lation show no directional bias (e.g. giant Cenetrix Inc. A special journal issue of Generica lar systems, in other species, for split claws of male fiddler crabs, Uca ktea). and a book entitled Developmental Instability: Its Origins and Evolutionary Implications (Kluwer sex ratios. In addition, testing for worker Assuming that each member of a bilat- Academic Publishers) will present articles con- assessment of RA using methods which eral trait showing FA is the product of the tributed by symposium participants and a syn- are independent of the examination of same genes, departure from the (I priori opsis of round table discussions.

122 0 1994, Elsevier Science Ltd TREE uol. 9, no. 4 April 1994 NEWS & COMMENT well-characterized may allow a means of symmetrical. This confirms the value of mucrochirus) show the same degree of distinguishing periods of heightened sen- FAs in characterizing the adaptive top- FA as the parental stockslg, whereas re- sitivity (‘windows of vulnerability’) to ography of other traits. cent hybrids of two species of sunfishes certain stressors associated with pheno- (Enneucunthus spp.) show elevated FAs’O. deviance later in life (Robert Vrijenhoek, Genetics of symmetry In crosses between Drosophila meluno- Center for Theoretical and Applied Gen- Parasites are a key factor affecting guster and D. simuluns, this elevation in etics, Rutgers University, New Brunswick, in many species, so it is FA occurs only in females*‘. It is absent NJ, USA). In pigtailed macaques (Macaca noteworthy that there are strong, posi- in males, even though there is no history nenesfrina), for example, stressing the tive associations between parasite load of hybridization. mother by repeated capture, between and asymmetry in insects, birds and hu- A breakdown of genie co- 30 and 130 days of pregnancy leads to mans, both because parasites can cause can also occur when otherwise rare alleles increased dermatoglyphic FA in her asymmetry13 and because asymmetri- are fixed into a gene pool via drift in small progenyll. cal individuals are more likely to be- insular populations or by strong direc- come infectedId. Heterozygosity may pro- tional selection. A dramatic example of and vide some protection from parasites, the latter is provided by the Australian phenotypic quality especially, for example, at major histo- blowfly (Luciliu cuprinu) in which an other- The most important advance in our compatibility (MHC) loci, but also more wise rare allele that disrupted develop- understanding of fluctuating asymmetry generally. Since heterozygosity is heri- ment spread during the 1960s because it is the discovery that FA is a good measure table’s, pressure from parasites may give conferred resistance to a pesticide which of phenotypic quality. Indeed, it may be added importance to symmetry in mate was then in use. At first, FA increased the best measure we have. But differences choice to the degree that heterozygosity but it then decreased steadily to its orig- in FA between individuals are often small is positively associated with symmetry. inal value, presumably because modifier and easily overwhelmed by measurement Within populations of rainbow trout genes were selected which integrated the error. Thus, statistical techniques have (Oncorhyncus mykiss) and cutthroat trout new allele into the genomee. Selection for been developed for assessing measure- (Oncorhyncus clarki), there exist signifi- new or rare alleles conferring resistance ment error and removing it from measures cant negative correlations between indi- against parasites may disrupt host de- of FA (Richard Palmer, University of vidual heterozygosity (measured across velopment in a similar manner. But con- Alberta, Edmonton, Canada). Phenotypic > 10 loci) and FA16,17. In rainbow trout, trary to the blowfly example, FA among quality is a key evolutionary variable, de individuals heterozygous at just two of resistant hosts could remain high across fined as the expected ability of an indi- these loci are more symmetrical than generations because novel resistance- vidual to succeed in life, that is, to express the respective homozygotes16. But in rain- conferring alleles continually cycle be- high inclusive fitness. bow trout, individuals who carry one null tween high and low frequency via fre- For bilaterally symmetrical traits and one active allele at a lactate dehydro quency-dependent interactions between showing FA, we are permitted to assume genase locus (LDH-Bl) locus express host and parasite . This raises that the is trying to be sym- higher FA than active allele homozygotes, the intriguing possibility, that high FA metrical (for optimization reasons men- even though they are heterozygous (Robb may, under some conditions, reveal resist- tioned below). Therefore, inability to Leary, University of Montana, Missoula, ance against disease. It is interesting that achieve symmetry is a measure of in- MT, USA). Beyond these, data are sparse whisker FA in lions is negatively corre- ability to achieve a desired state. For and show no association (e.g. house mice, lated with longevity in males, but posi- other measures of quality, by contrast, we Mus musculus18). Comparisons of popu- tively correlated in femalesz*. The reasons usually only know an optimal range (e.g. lations within a species show negative for this are unknown. large size) and not an optimal value associations between heterozygosity and (symmetry itself). If symmetry provides a mean FA (e.g. lizards, Uta stunsburiunu) Symmetrical transformations handy way of ranking individuals accord- as well as no association (e.g. pocket Mathematicians define symmetry as ing to phenotypic quality (and therefore gophers, Thomomys bottue) (Geoffrey any transformation of one set of data often genotypic quality), then Clarke, CSIRO Division of Entomology, rendering it identical, or isomorphic, to are expected to use symmetry as a cue Canberra, Australia). Inbred species, a second set’. The two sets are then said in mate choice, and sexual selection may such as cheetahs (Acinonyxjubutus), may to be symmetrical with reference to the favour the evolution of display traits in show elevated FAs compared to outbred transformation. Bilateral symmetry in- males that easily reveal asymmetry. In ones, such as leopards, Puntheru purdus, volves a mirror-image transformation, fact, in swallows, and ourselves, individ- but even this has been questioned and is whereas radial symmetry involves rotat- uals respond directly to symmetry and not a general trend. ing a set of data a fixed number of degrees prefer the most symmetrical members A comparison between hybrids and around a central point. Different kinds of of the opposite sex (for a detailed treat- parental populations may help to explain radial symmetry may be generated by ment of these points with supporting some of these differences. Two different differences in the number of symmetri- references see Watson and Thornhill’s forces are imagined to effect FA in hybrids. cal transformations possible in 360” (e.g. recent TREE reviewn). Sexually-selected Hybrids are likely to show greater hetero- four rotations of 90” or six of 60”). Analogs traits, whether they be exaggerated bird zygosity than parental stocks because of to FA can be constructed (Karl Freeman, plumage used in courtship, or spurs used divergent selection in the two stocks. Wayne State University, Detroit, MI, USA), in combat, typically show between five But this same selection will have pro- and Moller (unpublished) has demon- and ten times as much FA as compar- duced divergent genotypes which, when strated that altered to become able non-sexually selected traits (Anders combined, may be less co-adapted than radially asymmetrical attract fewer polli- Moller, Uppsala University, Sweden). In parental stocks. This will be especially nators. Mathematicians have shown that some species, individuals with the largest true of recent hybrids which have had in the calculus of variations, the solution secondary sexual structures also have the little time to re-evolve co-adaptation. to optimization problems will often pos- most symmetrical ones, while in others, In turn, long-standing hybrids between sess . For example, the most average-sized structures are the most subspecies of bluegill sunfish (Lepomis symmetrical three-dimensional object (the

123 NEWS & COMMENT sphere) maximizes volume per unit sur- is positively associated with the degree of 3 Mather, K. (1953) Heredity 7,297-336 face area. Likewise, a locomotor ap- cooperation between them26. Fair compro- 4 Thoday, J.M. (1958)Heredify 12,401-415 paratus, such as wings, must usually be mises of competing interests (such as 5 Mitton, J.B. (1978) Nature 273,661-662 selected for symmetry in order to mini- between mates, or parents and off- 6 McKenzie, J.A. and O’Farrell, K. Generica (in press) mize costs associated with asymmetry, spring) will themselves be symmetrical 7 Markow, T.A. and Martin, J.F. (1993)Ann. Hum. such as energy expenditure in flight. This and may reduce the costs of conflict. Eiol. 20,389-394 suggests, of course, that some species The deeper study of symmetry in biology 8 Livshits, G. and Kobylianski, E. (1991) Hum. will be more strongly selected for par- promises many more exciting discoveries. Biol. 63,441-466 ticular symmetries than will others (e.g. 9 Kieser, J.A. (1992)Ann. Hum. Bio/. 19,513-520 wing symmetry in migratory versus non- Acknowledgements 10 Markow, T.A. (1992) Psycho/. Med. 22,295-305 migratory birds). We thank Garth Baker for help with the 11 Newell-Morris, L.L., Fahrenbruch, C.E. and mathematics of symmetry and Sackett, G.P. (1989) Biol. Neonate 56,61-75 Symmetry and social relations Gordon Getty, Russell Lande, 12 Watson, P.J. and Thornhill, R. (1994) Trends Ecol. Eool. 9,21-25 It seems likely that evaluating the Therese Markow and Giles Mead for 13 Mgller, A.P. (1992)J. &of. Biol. 5,691-699 phenotypic quality (and, therefore, FA) of comments on the manuscript. We thank the Ann and Gordon Getty Foundation, 14 Schall, J.J. and Calos, J.B. Evolution (in press) others is useful in a variety of contexts the Biosocial Research Foundation and 15 Mitton, J.B., Schuster, W.S.F., Cothran, E.G. beyond mate choice; for example, in all@ the DuPont Company (fellowship to and De Fries, J.C. (1993) Heredity 71,59-63 eating resources to offspring and other M.P.) for support. 16 Leary, R.F., Allendorf, F.W. and Knudsen, K.L. kin23.Likewise, organisms are expected to (1983) Nature 301,71-72 value phenotypic quality in their recipro- Michal Polak 17 Leary, R.F., Allendorf, F.W. and Knudsen, K.L. cal partners. This may help explain why (1984)Am. Nat. 124,540-551 we attend to physical attractiveness so Dept of Zoology, Arizona State University, 18 Wooten, M.C. and Smith, M.H. (1986) J. Mamm. 67,725-732 early in life (e.g. at six months of age24) Tempe, AZ 85287-1501 and Center for Insect 19 Felley, J. (1980) Cope@ 18-29 Science, Tucson, AZ 85721, USA. and continually thereafter. 20 Graham, J.H. and Felley, J.D. (1985) Euolulion Symmetry between individuals may 39, 104-114 Robert Trivers be important in social relations. By defi- 21 Markow, T.A. and Ricker, J.P. (1991) Cenetica nition, reciprocal altruism requires a 84,115-121 Institute of Marine Sciences, Universityof 22 Packer, C. and Pusey, A.E. (1993)Nature 362,595 degree of symmetry (regular reversal of California, Santa Craz, CA 95064, USA. donor-recipient roles). In species of sea- 23 Thornhill, R. and Gangestad, S.W. (1993) bass (Serranidae), more-symmetrical egg Human Nature 4-237-269 References 24 trading is associated with greater econ- Langlois, J.H., Ritter, J., Roggman, L.A. and 1 Weyl, H. (1952) Symmefry, Princeton Vaughn, L.S. (1991) Deu. fsychol. 27, 79-84 omy of design (reduction in testes size) University Press 25 Fischer, E.A. and Petersen, C.W. (1987) (Ref. 25). Likewise, in baboons, Papio 2 Lee, T.D. (1988) Symmetiies, Asymmetnes and BioScience 37,482-489 spp., the degree of symmetry in greet- the Worldbf Particles. Universiti of 26 Smuts, B.B. and Watanabe, J.M. (1990) Inl. J. i$.s exchanied between a pair of males Washington Press Prima~ol. 11,147-172

Trends in Ecolqp & Em&ion CflpEE) is a journal ??Palaeontologkal data, and identifying of news, reviews and comment on current mass extinctions, M.J. Benton developments in and evolutionary

biology. It is not a vehicle for the publication ??Genetic exchange and evoljutionary of original results, hypotheses, syntheses or divergence in prokaryotes, FIM Coizan metaanalyses. News & articles report on specific ??The genetic, mufecular and phenotypic new developments published in the primary consequences of selection for insecticide literature; they also cover conferences. The resistance, J.A. McKenzie and l? Batt&zam

??Centromarm: moving chromosomes throt@~ space huedtime, D. Shaw err essays are always peer reviewed. Articles in TREE are commissioned by the ??Interpetfng phenotypic variation in Ectitor. Manuscripts may nevertheless be plaints, J,S. C&man ettal. rejected by the peer and ed&~kal r@vkw pFOCe?BS: CO ~~~~ do@s sot ~~~~ publication.

124 TREE vol. 9, no. 4 April 1994