Experientia 41 (1985), Birkh/iuser Verlag, CH-4010 Basel/Switzerland Sex allocation in animals 1265 by E. G. Leigh, Jr, E.A. Herre and E. A. Fischer Smithsonian Tropical Research Institute, Apartado 2072, Balbao (Panama), Department of Zoology, University of Iowa, Iowa City (Iowa 52242, USA), and Department of Psychology NI-25, University of Washington, Seattle (Washington 98195, USA) Key words. Sex allocation; sex ratio; sex change; hermaphrodites; gonochores; natural selection; trait-group selection; individual selection; selection within populations; selection between species; outlaw genes; fig wasps; bluehead wrasses; Thalassoma bifasciatum. Introduction Sex allocation refers to the apportionment of effort be- tween 'male' and 'female' functions, whether it takes the form of deciding the ratio of male to female offspring, the age at which to change from one sex to the other, or the balance between male and female functions in a her- maphrodite. This subject represents one of the most fruit- ful blends of theory and observation in all of evolutio- nary biology 9. The theory of sex allocation provides pre- cise, distinctive, seemingly accurate predictions concern- ing a wide variety of measurable phenomena. Moreover, sex allocation has assumed particular importance as the source of the best evidence for the efficacy of selection within populations 29. This paper is not a review of the literature on sex alloca- tion in animals: Charnov 9 has done that, and he needed a whole book for the job. Instead, we will treat the theory of sex allocation as an example of the study of adapta- tion. We will analyze the assumptions and display the structure of the theory of sex ratio, and consider some generalizations of this theory. We then ask when sexes should be separate and permanent, when animals should be one sex when young and the other when old, and when they should be simultaneous hermaphrodites. Finally, we consider the nature of the evidence for this body of theory, and the wider implications of this theory for evolutionary biology. Prolegomena to the study of adaptation One shows that a structure or behavior is adaptive by demonstrating its appropriateness for a function impor- tant to the life or wellbeing of the organism s~. This in- volves two steps: enumerating the 'fitness set' of possible structures or behaviors that could conceivably serve that function, that is to say, the set of possible phenotypes; and providing a criterion for comparing their appro- priateness. Levins 32'33 schematized the analysis by gen- erating contours of equal value on the fitness set. Finding the fitness set is often a rather ad hoc affair, at best an art, at worst a tissue of circular argument. The art lies in choosing a problem where the relevant aspects of the possible phenotypes can be specified by one or two coordinates, and where the optimum lies inside the fitness set, leaving no question that the 'best' phenotype is at- tainable. To find the adaptive function, we must first discover how natural selection acts on the trait concerned: is the deci- sive process selection between genes, between individu- als, or between whole populations? Thus we must know how to distinguish the various levels of selection. Selection presupposes units which replicate, with some degree of heritable variation affecting the rates of sur- vival and replication of these units 34. Genes are units of selection TM, but so can species be 47,48. Populations within a species are sometimes so distinct, exchanging almost no migrants, and so obviously replicate by 'fission', that one can then speak of selection between populations 34. Genes, however, replicate primarily according to their contribution to the viability and fecundity of the individ- uals carrying them: to this extent, we may say that the fates of these genes are governed by selection between individuals. Genes occasionally spread by means harmful to their bearer organisms, but such genes violate the common interest of the genome as a whole: at other loci, individual selection favors modifiers which suppress these 'outlaw genes '~'28,29. Genes may also be selected according to their effects on interactions between rela- tives, leading to kin selection 2~. One also hears of 'group selection'. Unfortunately, this term has a double meaning. Group selection can mean selection between populations, a term that only applies if populations are units of selection. Group selection can also mean the influence on genic fitness of interactions between members of the same 'traitgroup '65, an influence which reflects how an individual's fate is linked with that of its neighbors. This influence does not even depend on the subdivision of a species into discrete groups 6. The latter definition is so much more inclusive - contrast, for example, the conclusions of Uyenoyama and Feldman 56 with those of Leigh 3~ - that group selection is no longer a useful word. When populations are units of selection we will speak of selection between populations, and we will refer to all other processes where genic selection is in- fluenced by interactions between groups as traitgroup or neighbor selection. Analytical review of sex allocation theory I) Introit Sex allocation theory seems to be a textbook analysis of adaptation28.39. We begin by outlining the theory as it first developed, and then analyze its mathematical founda- tions and consider some of the relevant evidence. The theory originally asked how offspring of gonochores - organisms where sexes are separate - should be appor- tioned between the two sexes. The theory assumed that 1) alleles affecting sex ratio affect nothing else, neither the survival prospects of their bearers, nor their bearers' abil- ity to find mates, nor other features of their reproductive capacity; 2) each allele affecting sex ratio prescribes a fixed sex