Sex ratios

One riddle solved? The primordial soup of the theory of sex allocation


Many species have sex allocation ratios of 1:1. Other species deviate markedly from equality. This must be explained either in terms of natural selection or evolutionary constraint. The sex ratios of heterogonic species in which either one sex is larger or produced in excess numbers, the sex-change time of sex changers, and the allocation to each sexual function in simultaneous hermaphrodites have all been explained on the basis of optimality models that solve for the maximum reproductive fitness.

The objective of the theory of sex allocation is to provide the mathematical tools for answering the following questions, taken from Charnov's (1982, henceforth referred to as "Charnov") book on the subject, The Theory of Sex Allocation:

  1. For a dioecious species, what is the equilibrium sex ration maintained by natural selection?
  2. For a sequential hermaphrodite, what is the equilibrium sex order and time of sex change?
  3. For a simultaneous hermaphrodite, what is the equilibrium allocation of resources to male versus female function in each breeding season?
  4. Under what conditions are the various states of hermaphroditism or dioecy evolutionarily stable? When is a mixture of sexual types stable?
  5. When does selection favour the ability of an individual to alter its allocation to male versus female function, in response to particular environmental or life history situations?

There are many levels to these problems: First of all, there are genomic conflicts of interest between autosomes, sex chromosomes, and maternally inherited, cytoplasmic genetic elements (Lewis 1941, Shaw 1958, Hamilton 1967). Haplodiploid eusocial insects suffer the effects of worker-queen conflicts (Trivers & Hare 1976). Many other elements of the natural history of sexual species influence sex ratios, for instance local mate competition (Hamilton 1967, Werren 1980), whether the parents can estimate the quality of their offspring (Trivers & Hare 1976, Clutton-Brock et al. 1984), whether parasites can gain an advantage by manipulating the sex ratio, and how likely the offspring are to compete for opportunities for reproduction with their parents, especially their mothers - who tend to have greater control over the sex of their offspring (Clark 1978).

Much pioneering work on these issues has been done between the late sixties and early eighties, culminating in the publication of Charnov's book, but the basic questions had been posed much earlier. Charles Darwin recognised the problem, writing on page 399 of his Descent of Man:

In no case, as far as we can see, would an inherited tendency to produce both sexes in equal numbers or to produce one sex in excess, be a direct advantage or disadvantage to certain individuals more than to others; for instance, an individual with a tendency to produce more males than females would not succeed better in the battle for life than an individual with an opposite tendency; and therefore a tendency of this kind could not be gained through natural selection. Nevertheless, there are certain animals (for instance, fishes and cirripedes), in which two or more males appear to be necessary for the fertilisation of the female; and the males accordingly largely preponderate, but it is by no means obvious how this male-producing tendency could have been acquired. I formerly thought that when a tendency to produce the two sexes in equal numbers was advantageous to the species, it would follow from natural selection, but I now see that the whole problem is so intricate that it is safer to leave its solution for the future.

More than half a century after Darwin's struggling and postponing the investigation of the problem, R. A. Fisher (1930) already saw somewhat clearer, putting forward a curt and convoluted argument, starting at the important notion that the genetic contributions of all males to the next generation equal those of all females. He further thought that total resource investment by the parents in all female offspring should equal the total investment in all males, and used essentially an argument which Charnov expresses in terms of evolutionarily stable strategies, namely that in any population which has a bias in production of either sex, parents investing more in the rarer sex will leave more grandchildren relative to the rest of the population, so that the sex ration in the population is driven towards equivalence of investment (Fisher 1930). The next theoretical leap came with Shaw and Mohler, who discounted instances of parental care, and mathematically derived that the equilibrium sex ratio at conception should be unity (Shaw & Mohler 1953). Bodmer and Edwards, however, managed to fully translate Fisher's prose into calculus (Bodmer & Edwards 1960) proving Shaw and Mohler wrong in claiming that "Fisher's treatment is phrased in non-genetical terms and does not lend itself to further development".

However, G. C. Williams points out that Fisher's argument does not really address the question why each individual produces a mixed bag of offspring of both sexes, when it would be sufficient for half the females in the population to produce daughters and the other half sons, or any other ratio that leads to equal overall investment in either sex (Williams 1979, also see Shaw 1958). Individuals producing a mixed brood are likely to be favoured in almost any finite population die to the unpredictability of sex ratio fluctuations about the evolutionary equilibrium (Verner 1965, also see Taylor & Sauer 1980). Another reason suggested by Charnov is that the only imaginable sex chromosome-based sex determination system that would have the effect of some females producing just daughters, others exclusively sons, would be haplodiploidy. The problem awaits further clarification.

The questions of sex allocation theory can be answered theoretically by considering under what conditions various genetic systems would be adaptive, and, inversely, given certain conditions, which genetic system would be chosen. However, this selectionist thinking, as Charnov chooses to call it, forms part of what Gould and Lewontin (1979) have dubbed the adaptationist programme, and which, as they argue, ignores certain other possible explanations for what seem to be adaptations shaped by natural selection. It seems that the consideration of evolutionarily stable strategies provides a narrow view of evolution, for instance with a view to the sex ratios in many diploids (e.g. mammals and bird sex chromosomes) and the thrum to pun ratio in heterostylous plants. Some of these problems could be resolved by determining the phylogeny and evolutionary origins, genetics and molecular mechanisms of sex determination, and also considering the genetics and mechanisms of self-incompatibility in plants, but due to the wealth of different answers nature provides to this problem, this task is far from complete for many taxa.

Part of the recent struggle for progress in this field may be due to the fact that the half male, half female ratio that Fisher considered and which is so well known of our own species - indubitably the reason why it has been attractive to tackle the problem - could be little more than a result of the mechanism of sex determination, which is by sex chromosomes in mammals and birds, amongst others, and of normal chromosome segregation (Williams 1979, also see Shaw 1958). However, Charnov quips that this poses simply another, similar question, namely that of the evolution and adaptive significance of sex chromosomes (Charnov 1982). However, this question may only have to be answered for a distant ancestor of each affected taxon which first evolved the mechanism (assuming great difficulty in evolving a sex chromosome-independent sex determination mechanism, e.g. reverting to earlier sex determining systems), and even so, the reason for this evolutionary step may be independent of its implications on sex ratio.

The continued relative scarcity of literature on this subject, and the fact that no further books have been published since Charnov's 1982 effort could give the impression that the major problems in this field have been addressed. However, the mathematical models in Charnov's book are in a way pleasingly simple - "those of a biologist rather than a mathematician, as Parker (1983) remarks. But on the other hand, a more complex model fully describing the phenomena should be available, considering the nontrivial complexities of the genetic systems involved, and the ultimate aim ought to be a unified theory which can be expressed in one mathematical argument. His approach is also geometrically biased, and can be criticised for incompleteness of some algebraic derivations. Field observation and experiment in this area are strongly taxonomically biased, and much of the evidence cited by Charnov is anecdotal.

Another factor that may have hampered advance in the subject area is that Charnov's book has certain shortcomings, mostly of style. Occasionally, he will give losts of questions at the start of a chapter but will not attempt to answer them in the same chapter. He further discourages the reader by not clearly distinguishing between evolutionarily stable strategies and the more general concept of genetic equilibria in his introductory chapter on sex ratio. One may also become disenchanted with his frequent use of abbreviations, such as ESS (evolutionarily stable strategies), LMC (local mate competition), LRC (local resource competition) and RS (reproductive success).

I shall go on to review the evidence for various hypotheses given by Charnov, in the order in which he put them, point out the weaknesses of the evidence in 1982, and discuss whether progress has been made. Of course, Charnov's compilation must inevitably have been incomplete at the time, and we must also guard against his making rhetorical choices between studies he cites.

Hypotheses on sex allocation in dioecious species have only been reasonably tested in parasitoid wasps and mites so far. The chapter on spatially structured populations, for instance, discusses mostly haplodiploid organisms. Some hypotheses remain unconfirmed: Do female parasitic wasps benefit more from being large? Other groups need yet to be satisfactorily studied, such as vertebrates, nematodes and some higher plants. Among the studies of diploids with genetic sex determination, some of the most extensive studies show no variance of sex ratio. Variance being one of the pillars of natural selection, we should not expect to see any adaptation of the primary sex ratio in such cases. In particular, there has been little evidence of short-term adaptation of sex ratio in higher vertebrates, although some deviations have been observed, most of them maladaptive.

The discussion of sequential hermaphrodites features strong quantitative data on pandalid shrimps and coral reef fishes, but few data available for other sex changers, such as marine molluscs (Patella, Crepidula) and an annelid worm, the polychaete Ophryothrocha.

Simultaneous hermaphroditism is the least understood among the sexual genetic systems. Barnacles will probably turn out to be a rewarding aim for further stidues of simultaneous hermaphroditism.

In general, Charnov's citation of empirical studies is zoologically biased, encouraging further work on plants. Furthermore, the discussion focuses too strongly on higher eukaryotes.

In his 1983 review of Charnov's book, Parker suggests some major areas that the theoretical enquiry should be extended to , namely the allocation of alternative reproductive functions, such as relative dedication of energy to sperm production, mate guarding and mate searching; the asymmetric effect of some expenditures (e.g. increased mobility) in simultaneous hermahprodites on the two sex functions; and the trade-offs associated with internal and external fertilisation and their relation to sex allocation.

Since 1982, the zoological bias of data has been somehwat remedied (e.g. Schoen 1992, McKone 1987, Pannell 1997, Barrett et al. 1999, Pannell & Ojeda 2000). It seems that plant scientists are generally becoming more interested in testing evolutionary hypotheses alongside ecological ones. Greater interest is also being taken in barnacles as simultaneous hermaphrodites (e.g. Raimondi & Martin 1991), and G. Sella, among others, is investigating simultaneous hermaphroditism in Ophryotrocha, and drawing comparisons with the closely related gonochoric genus Dinophilus. On the other hand, only two papers on sex ratio and change in Patella have emerged, while Crepidula has been somewhat more studied (10 papers since) particularly recently, by people such as R. Collin. Simultaneous hermaphrodites have also been given considerable attention (93 papers since). Theory has been further developed, also considering the peculiarities of plants (e.g. Lloyd 1987), even if there is a general recession of interest. We are left to conclude that many of Charnov's suggestions for further investigation are still valid, and that a further development of theory, especially a union of the various equations we have, should be encouraged.

While we have a rich, though controversial body of theory on sex allocation, the emphasis must be placed on verifying them with empirical studies. Thus the study of sex ratios may become a fruitful testing ground for the more general predictions of evolutionary theory.


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