A model is constructed to study the effects of local mate competition and multiple mating on the optimum allocation of resources between the male and female reproductive brood in social hymenopteran colonies from the ‘points of view’ of the queen (parental manipulation theory) as well as the workers (kin selection theory). Competition between pairs of alleles specifying different sex investment ratios is investigated in a game theoretic frame work. All other things being equal, local mate competition shifts the sex allocation ratio in favour of females both under queen and worker control. While multiple mating has no effect on the queen’s optimum investment ratio, it leads to a relatively male biased investment ratio under worker control. Under queen control a true Evolutionarily Stable Strategy(ess) does not exist but the ‘best’ strategy is merely immune from extinction. A trueess exists under worker control in colonies with singly mated queens but there is an asymmetry between the dominant and recessive alleles so that for some values of sex ratio a recessive allele goes to fixation but a dominant allele with the same properties fails to do so. Under multiple mating, again, a trueess does not exist but a frequency dependent region emerges. The best strategy here is one that is guaranteed fixation against any competing allele with a lower relative frequency. Our results emphasize the need to determine levels of local mate competition and multiple mating before drawing any conclusions regarding the outcome of queen-worker conflict in social hymenoptera. Multiple mating followed by sperm mixing, both of which are known to occur in social hymenoptera, lower average genetic relatedness between workers and their reproductive sisters. This not only shifts the optimum sex ratio from the workers’ ‘point of view’ in favour of males but also poses problems for the kin selection theory. We show that kin recognition resulting in the ability to invest in full but not in half sisters reverts the sex ratio back to that in the case of single mating and thus completely overcomes the hurdles for the operation of kin selection.

The iterative two-person Prisoners’ Dilemma game has been generalised to theN-person case. The evolution of cooperation is explored by matching the Tit For Tat (TFT) strategy (Axelrod and Hamilton 1981) against the selfish strategy. Extension of TFT toN-person situations yields a graded set of strategies from the softest TFT, which continues cooperation even if only one of the opponents reciprocates it, to the hardest, which would do so only when all the remaining opponents cooperate.

The hardest TFT can go to fixation against the selfish strategy provided it crosses a threshold frequencypc. All the other TFT are invadable by the selfish (D) or the pure defector strategy, while none can invadeD. Yet, provided a thresholdpc is crossed, they can coexist stably withD. AsN, the size of the group increases, the threshold p_c also increases, indicating that the evolution of cooperation is more difficult for larger groups. Under certain conditions, only the soft TFT can coexist stably against the selfish strategyD, while the harder ones cannot. An interesting possibility of a complete takeover of the selfish population by successive invasions by harder and harder TFT strategies is also presented.

When there is a variation in the quality of males in a population, multiple mating can lead to an increase in the genetic fitness of a female by reducing the variance of the progeny number. The extent of selective advantage obtainable by this process is investigated for a population subdivided into structured demes. It is seen that for a wide range of model parameters (deme size, distribution of male quality, local resource level), multiple mating leads to a considerable increase in the fitness. Frequency-dependent selection or a stable coexistence between polyandry and monandry can also result when the possible costs involved in multiple mating are taken into account.

For a population made up of individuals capable of sexual as well as asexual modes of reproduction, conditions for the spread of a transposable element are explored using a one-locus, two-haplotype model. The analysis is then extended to include the possibility that the transposable element can modulate the probability of sexual reproduction, thus casting Hickey’s (1982,Genetics 101: 519–531) suggestion in a population genetics framework. The model explicitly includes the cost of sexual reproduction, fitness disadvantage to the transposable element, probability of transposition, and the predisposition for sexual reproduction in the presence and absence of the transposable element. The model predicts several kinds of outcome, including initial frequency dependence and stable polymorphism. More importantly, it is seen that for a wide range of parameter values, the transposable element can go to fixation. Therefore it is able to convert the population from a predominantly asexual to a predominantly sexual mode of reproduction. Viewed in conjunction with recent results implicating short stretches of apparently non-coding DNA in sex determination (McCoubreyet al. 1988,Science 242: 1146–1151), the model hints at the important role this mechanism could have played in the evolution of sexuality.

Polyembryony, referring here to situations where a nucellar embryo is formed along with the zygotic embryo, has different consequences for the fitness of the maternal parent and offspring. We have developed genetic and inclusive fitness models to derive the conditions that permit the evolution of polyembryony under maternal and offspring control. We have also derived expressions for the optimal allocation (evolutionarily stable strategy, ESS) of resources between zygotic and nucellar embryos.

It is seen that (i) Polyembryony can evolve more easily under maternal control than under that of either the offspring or the ‘selfish’ endosperm. Under maternal regulation, evolution of polyembryony can occur for any clutch size. Under offspring control polyembryony is more likely to evolve for high clutch sizes, and is unlikely for low clutch sizes (<3). This conflict between mother and offspring decreases with increase in clutch size and favours the evolution of polyembryony at high clutch sizes, (ii) Polyembryony can evolve for values of “x” (the power of the function relating fitness to seed resource) greater than 0.5758; the possibility of its occurrence increases with “x”, indicating that a more efficient conversion of resource into fitness favours polyembryony. (iii) Under both maternal parent and offspring control, the evolution of polyembryony becomes increasingly unlikely as the level of inbreeding increases, (iv) The proportion of resources allocated to the nucellar embryo at ESS is always higher than that which maximizes the rate of spread of the allele against a non-polyembryonic allele.

Finally we argue that polyembryony is a maternal counter strategy to compensate for the loss in her fitness due to brood reduction caused by sibling rivalry. We support this assertion by two empirical evidences: (a) the extent of polyembryony is positively correlated with brood reduction inCitrus, and (b) species exhibiting polyembryony are more often those that frequently exhibit brood reduction.

Competition between seeds within a fruit for parental resources is described using one-locus-two-allele models. While a “normal” allele leads to an equitable distribution of resources between seeds (a situation which also corresponds to the parental optimum), the “selfish” allele is assumed to cause the seed carrying it to usurp a higher proportion of the resources. The outcome of competition between “selfish” alleles is also assumed to lead to an asymmetric distribution of resources, the “winner” being chosen randomly. Conditions for the spread of an initially rare selfish allele and the optimal resource allocation corresponding to the evolutionarily stable strategy, derived for species with n-seeded fruits, are in accordance with expectations based on Hamilton’s inclusive fitness criteria. Competition between seeds is seen to be most intense when there are only two seeds, and decreases with increasing number of seeds, suggesting that two-seeded fruits would be rarer than one-seeded or many-seeded ones. Available data from a large number of plant species are consistent with this prediction of the model.

Any statement on the optimality of the existing code ought to imply that this code is ideal for conserving a certain hierarchy of properties while implying that other codes may have been better suited for conservation of other hierarchies of properties. We have evaluated the capability of mutations in the genetic code to convert one amino acid into another in relation to the consequent changes in physical properties of those amino acids. A rather surprising result emerging from this analysis is that the genetic code conserves long-range interactions among amino acids and not their short-range stereochemical attributes. This observation, based directly on the genetic code itself and the physical properties of the 20 amino acids, lends credibility to the idea that the genetic code has not originated by a frozen accident (the null hypothesis rejected by these studies) nor are stereochemical attributes particularly useful in our understanding of what makes the genetic code ‘tick’. While the argument that replacement of, say, an aspartate by a glutamate is less damaging than replacement by arginine makes sense, in order to subject such statements to rigorous statistical tests it is essential to define what constitutes a random sample for the genetic code. The present investigation describes one possible specification. In addition to obvious statistical considerations of testing hypotheses, this procedure points to the more exciting notion that alternative codes may have existed.

The very insightful Trivers-Willard hypothesis, proposed in the early 1970s, states that females in good physiological condition are more likely to produce male offspring when the variance of reproductive success among males is high. The hypothesis has inspired a number of studies over the last three decades aimed at its experimental verification, and many of them have found adequate supportive evidence in its favour. Theoretical investigations, on the other hand, have been few, perhaps because formulating a population-genetic model for describing the Trivers-Willard hypothesis turns out to be surprisingly complex. The present study is aimed at using a minimal population-genetic model to explore one specific scenario, namely how is the preference for a male offspring by females in good condition altered wheng, the proportion of such females in the population, changes from a low to a high value. As expected, when the proportion of such females in good condition is low in the population, i.e. for low values ofg, the Trivers-Willard (TW) strategy goes to fixation against the equal investment strategy. This holds true up to g_max, a critical value ofg, above which the two strategies coexist, but the proportion of the TW strategy steadily decreases asg increases to unity. Similarly, when the effect of well-endowed males attaining disproportionately high number of matings is more pronounced, the TW strategy is more likely to go to fixation. Interestingly, the success of the TW strategy has a complex dependence on the variance of the physiological condition of females. If the difference in the two types of conditions is not large, TW strategy is favoured, and its success is more likely as the difference increases. However, beyond a critical value of the difference, the TW strategy is found to be less and less likely to succeed as the difference becomes larger. Possible reasons for these effects are discussed.