Size‐dependent resource allocation and sex allocation in herbaceous perennial plants

Individuals within a population often differ considerably in size or resource status as a result of environmental variation. In these circumstances natural selection would favour organisms not with a single, genetically determined allocation, but with a genetically determined allocation rule specifying allocation in relation to size or environment. Based on a graphical analysis of a simple evolutionarily stable strategy (ESS) model for herbaceous perennial plants, we aim to determine how cosexual plants within a population should simultaneously adjust their reproductive allocation and sex allocation to their size. We find that if female fitness gain is a linear function of resource investment, then a fixed amount of resources should be allocated to male function, and to post‐breeding survival as well, for individuals above a certain size threshold. The ESS resource allocation to male function, female function, and post‐breeding survival positively correlate if both male and female fitness gains are a saturating function of resource investment. Plants smaller than the size threshold are expected to be either nonreproductive or functionally male only.     

Effects of phenological constraints on sex allocation in cosexual monocarpic plants

The effects of two phenological constraints in resource investment to reproduction – resource limitation at the flowering stage and unpredictability of resources gained after flowering – on the resource allocation between male and female functions in monocarpic plants are considered using the ESS (evolutionarily stable strategy) approach. The model predicts that the sex allocation including the seed maturation stage has a female bias, when the quantity of reproductive resources available at flowering is small compared with that which is obtained after flowering, or when the cost of seed maturation relative to ovule production is low. The fluctuation of the quantity of resources available for seed maturation favors overproduction of ovules. As a result, more resources are allocated to female function and less to male function at flowering. The ESS allocation depends on the variability of resources and the cost of seed maturation relative to ovule production. The probability that total resource allocation has a female bias becomes higher than 0.5, and it depends on the cost of seed maturation relative to ovule production rather than resource variability. On the other hand, the probability that resource allocation has a female bias decreases with resource variability if we assume that the floral sex ratio is fixed. Future studies of plant sex allocation would profit by taking account of the phenological process of reproduction such as ovule production or seed maturation.     

Sex allocation in simultaneous hermaphrodites: Trade-offs between sex-specific costs and lifespan

Fitness in self-incompatible simultaneous hermaphrodites incorporates gains and costs from both male and female reproductive function, and evolutionarily stable allocation of gonadal tissue to male or female function depends on these gains and costs. Paradoxically, despite the often equal expected gains but different costs associated with each sex, contributions to expected reproductive success through male and female function must be identical. Whenever allocation costs are unequal and limiting resources are energetically expensive or risky to acquire, these costs must ultimately be paid through reduced survival, resolving the paradox by equally diminishing expected reproductive success as male and as female. Maximizing fitness as lifetime reproductive success – not just reproductive rate alone, as in previous studies – maximizes the product of expected survival time and reproductive rate. The analysis shows how male-biased allocation can thereby arise and generate novel predictions on the relation between intensity of sperm competition and allocation to male function.     

Effect of stochasticity in the availability of pollinators on the resource allocation within a flower

In this article, we develop a simple model to study the effect of stochasticity in pollination on evolutionarily stable (ES) resource allocation within a hermaphrodite flower of animal-pollinating plants. For simplicity, we consider trade-off in resource allocation between attractive structure (petals etc.) and female function (seeds and fruits) with neglecting the amount of resource allocated to male function (pollens and stamens). We show that ES resource allocation does not much depend on the detail of the probability distribution of the number of pollinator visit on a flower, but on the probability that a flower fails to be visited. We also find that: (1) When the flowers are self-incompatible, the ES allocation to the attractive structure monotonically increases as the availability of pollinators in the environment decreases. (2) When there is strong positive correlation among flowers in the number of pollinator visit, the ES allocation is larger than the case without the correlation. (3) When the flowers are self-compatible and engage prior selfing, the ES allocation monotonically increases as the availability of pollinators in the environment decreases to a threshold, under which it suddenly decreases to zero.     

Life‐history trade‐offs promote the evolution of dioecy

Most dioecious plants are perennial and subject to trade‐offs between sexual reproduction and vegetative performance. However, these broader life‐history trade‐offs have not usually been incorporated into theoretical analyses of the evolution of separate sexes. One such analysis has indicated that hermaphroditism is favoured over unisexuality when female and male sex functions involve the allocation of nonoverlapping types of resources to each sex function (e.g. allocations of carbon to female function vs. allocations of nitrogen to male function). However, some dioecious plants appear to conform to this pattern of resource allocation, with different resource types allocated to female vs. male sex functions. Using an evolutionarily stable strategy approach, we show that life‐history trade‐offs between sexual reproduction and vegetative performance enable the evolution of unisexual phenotypes even when there are no direct resource‐based trade‐offs between female and male sex functions. This result might help explain the preponderance of perennial life histories among dioecious plants and why many dioecious plants with annual life histories have indeterminate growth with ongoing trade‐offs between sexual reproduction and vegetative growth.     

Resource Allocation and the Evolution of Self-Fertilization in Plants

This article develops a simple evolutionarily stable strategy (ESS) model of resource allocation in partially selfing plants, which incorporates reproductive and sex allocation into a single framework. The analysis shows that, if female fitness gain increases linearly with resource investment, total reproductive allocation is not affected by sex allocation, defined as the fraction of reproductive resources allocated to male function. All else being equal, the ESS total reproductive allocation increases with increasing selfing rate if the fitness of selfed progeny is more than half that of outcrossed progeny, while the ESS sex allocation is always a decreasing function of the selfing rate. Self-fertilization is much more common in annual than in perennial plants, and this association has been commonly interpreted in terms of an effect of life history on mating system. The model in this article shows that self-fertilization can itself cause the evolution of the annual habit. Incorporating the effects of pollen discounting may not have any influence on total reproductive allocation if female fitness gain is a linear function of resource investment, although the evolutionarily stable sex allocation is altered. Evolution of the selfing rate is found to be independent of reproductive and sex allocation under the mass-action assumption that self- and outcross pollen are deposited simultaneously on receptive stigmas and compete for access to ovules.     

Flow cytometric sexing of spider sperm reveals an equal sperm production ratio in a female-biased species

Producing equal amounts of male and female offspring has long been considered an evolutionarily stable strategy. Nevertheless, exceptions to this general rule (i.e. male and female biases) are documented in many taxa, making sex allocation an important domain in current evolutionary biology research. Pinpointing the underlying mechanism of sex ratio bias is challenging owing to the multitude of potential sex ratio-biasing factors. In the dwarf spider, Oedothorax gibbosus, infection with the bacterial endosymbiont Wolbachia results in a female bias. However, pedigree analysis reveals that other factors influence sex ratio variation. In this paper, we investigate whether this additional variation can be explained by the unequal production of male- and female-determining sperm cells during sperm production. Using flow cytometry, we show that males produce equal amounts of male- and female-determining sperm cells; thus bias in sperm production does not contribute to the sex ratio bias observed in this species. This demonstrates that other factors such as parental genes suppressing endosymbiont effects and cryptic female choice might play a role in sex allocation in this species.     

Cryptic male choice: sperm allocation strategies when female quality varies

We examined evolutionary stable sperm allocation and included stochastic variation in male mating frequency, not included in previous models examining sperm allocation strategies. We assumed sperm mixing and variation in female quality and used a genetic algorithm to analyse the evolution of male sperm allocation. Our results show that males should invest more sperm in initial copulations than in subsequent copulations as a male might fail to mate again. The inclusion of variation in female fecundity had no influence on the evolutionary stable sperm allocation strategy if males were unable to recognize female quality. If males were assumed to allocate sperm in response to female quality, the proportion of sperm allocated was positively correlated with female quality. Moreover, with increasing variance in female quality, males conserved more sperm for later copulations. Literature data on sperm allocation from diverse taxa show a good fit with the predictions given by our model.     

Evolutionary modeling predicts a decrease in postcopulatory sperm viability as a response to increasing levels of sperm competition

Sperm competition has been found to have a strong influence on the evolution of many male and female reproductive traits. Theoretical models have shown that, with increasing levels of sperm competition, males are predicted to increase ejaculate investment, and there is ample empirical evidence supporting this prediction. However, most theoretical models concern sperm number, and although the predictions are likely to apply to other sperm traits that will affect the sperm competitive ability of males, substantiated predictions are difficult unless the evolution of specific traits is explicitly modeled. Here I present a novel theoretical model aiming at predicting evolutionarily stable sperm viability in relation to female mating frequency in a mating system with internal fertilization. At odds with verbal arguments, this model demonstrates that sperm viability is expected to decrease with increasing female remating rates and thus to decrease with increasing levels of sperm competition. The major reason for this is that, with increasing female remating rates, the prospects of future fertilization success will decrease, which acts to reduce the benefit of long-lived viable sperm. An additional interesting result is that, as the cost of sperm viability increases, the overall energy investment in ejaculates will decrease. These novel results should have a strong impact on future sperm competition studies and will also have implications for our understanding of the evolution of female polyandry.     

THE QUICK AND THE DEAD? SPERM COMPETITION AND SEXUAL CONFLICT IN SEA

Our view of sperm competition is largely shaped by game-theoretic models based on external fertilizers. External fertilization is of particular interest as it is the ancestral mode of reproduction and as such, relevant to the evolution and maintenance of anisogamy (i.e., large eggs and tiny, numerous sperm). Current game-theoretic models have been invaluable in generating predictions of male responses to sperm competition in a range of internal fertilizers but these models are less relevant to marine broadcast spawners, the most common and archetypal external fertilizers. Broadcast spawners typically have incomplete fertilization due to sperm limitation and/or polyspermy (too many sperm), but the effects of incomplete (<100% fertilization rates) fertilization on game-theoretic predictions are unclear particular with regards to polyspermy. We show that incorporating the effects of sperm concentration on fertilization success changes the predictions of a classic game-theoretic model, dramatically reversing the relationship between sperm competition and the evolutionarily stable sperm release strategy. Furthermore, our results suggest that male and female broadcast spawners are likely to be in conflict at both ends of the sperm environment continuum rather than only in conditions of excess sperm as previously thought. Across the majority of the parameter space we explored, males release either too little to too much sperm for females to achieve complete fertilization. This conflict could result in a coevolutionary race that may have led to the evolution of internal fertilization in marine organisms.     

Size-dependent sex allocation in hermaphroditic plants: the effects of resource pool and self-incompatibility

The effects of the resource pool and resource obtained during a season for seed maturation and self-incompatibility on the size-dependency of evolutionarily stable sex allocation were analysed theoretically. In hermaphroditic plants, reproductive resources allocated between male and female function may not be paid from a single resource pool, because plants can mature seeds using not only reserved resources but also newly gained resources after flowering. But the resource investment to male function is limited to the flowering stage. Under the assumption of constant reserve efficiency and diminishing resource return per investment to leaves, large plants should use both reserved and newly gained resources for seed maturation, while small plants should use only new resources. When both reserved and new resources are used, the optimal allocation for self-compatible species is to invest a constant amount of resources into male function irrespective of resource size, because the female fitness curve increases linearly and the male curve decelerates due to local mate competition. In self-incompatible species, on the other hand, fitness gain per investment through male function and the optimal amount of resources invested in male function decrease with size. Thus a decrease in maleness with size should be emphasized more in self-incompatible species than in self-compatible one. When only new resources are used for seed growth, the female fitness curve as well as male one decelerates with investment. Consequently, the investment in both male and female functions should increase with size, in both self-compatible and self-incompatible species. The magnitude of reserve efficiency relative to efficiency of resource gain after flowering affects size-dependent pattern of sex allocation, while the cost of seed maturation relative to ovule production has little effect on it. The plant size variation in a population emphasizes size-dependency of sex allocation. When size variation is large enough, it is possible that large plants become complete female in self-incompatible species, but it is not in self-compatible species.     

FLORAL SEX ALLOCATION IN SEQUENTIALLY BLOOMING PLANTS

In plants whose flowers develop in a sequence, different flowers may exhibit temporal variation in pollen donation and receipt such that the fitness contributions through male and female functions can vary among flowers. Dichogamy, or directional pollinator movements within inflorescences, can create situations where flowers in different stages in the sequence may differ in the numbers of flowers in the female stage available as potential mates. We present an evolutionarily stable strategy (ESS) analysis of the resource allocations expected in different flowers in hermaphroditic plants when the mating environments vary among flowers. This introduces a modular element into sex-allocation models. Our analysis shows that such variation in the mating environments of flowers can select for differences in sex allocation between flowers. When male and female fertilities are nonlinear functions of the allocations, variation in resource availability can also select for variation in sex allocation among flowers. The influence of dichogamy and pollinator directionality on floral sex allocation is discussed, and the empirical evidence supporting the predictions derived from the model is briefly reviewed. The implications of our results for the evolution of andromonoecy and monoecy are discussed.     

How geitonogamous selfing affects sex allocation in hermaphrodite plants

Does the mode of self-pollination affect the evolutionarily stable allocation to male vs. female function? We distinguish the following scenarios. (1) An ‘autogamous’ species, in which selfing occurs within the flower prior to opening. The pollen used in selfing is a constant fraction of all pollen grains produced. (2) A species with ‘abiotic pollination’, in which selfing occurs when pollen dispersed in one flower lands on the stigma of a nearby flower on the same plant (geitonogamy). The selfing rate increases with male allocation but a higher selfing rate does not mean a reduced export of pollen. (3) An ‘animal-pollinated’ species with geitonogamous selfing. Here the selfing rate also increases with male allocation, but pollen export to other plants in the population is a decelerating function of the number of simultaneously open flowers. In all three models selfing selects for increased female allocation. For model 3 this contradicts the general opinion that geitonogamous selfing does not affect evolutionarily stable allocations. In all models, the parent benefits more from a female-biased allocation than any other individual in the population. In addition, in models 2 and 3, greater male allocation results in more local mate competition. In model 3 and in model 2 with low levels of inbreeding depression, hermaphroditism is evolutionarily stable. In model 2 with high inbreeding depression, the population converges to a fitness minimum for the relative allocation to male function. In this case the fitness set is bowed inwards, corresponding with accelerating fitness gain curves. If the selfing rate increases with plant size, this is a sufficient condition for size-dependent sex allocation (more allocation towards seeds in large plants) to evolve. We discuss our results in relation to size-dependent sex allocation in plants and in relation to the evolution of dioecy.     

Variation in lifetime male fitness in Ipomopsis aggregata: tests of sex allocation theory

Sex allocation theory assumes that a shift in allocation of resources to male function both increases male fitness and decreases female fitness. Moreover, the shapes of these fitness gain functions determine whether hermaphroditism or another breeding system is evolutionarily stable. In this article, I first outline information needed to measure these functions in flowering plants. I then use paternity analysis to describe the shapes of the fitness gain functions in natural populations of the hermaphroditic herb Ipomopsis aggregata. I also explore the relationships of male fitness (number of seeds sired) and female fitness (number of seeds produced) to the number of flowers produced by a plant. Plants with greater investment of biomass in the androecium, compared to the gynoecium and seeds, showed increased success at siring seeds, assumed by the models. That sex allocation trait, however, explained only 9% of the variance in estimates of male fitness. The shapes of the fitness gain functions were consistent with theoretical expectations for a hermaphroditic plant, but the model predicted a more female-biased evolutionarily stable strategy (ESS) allocation than was observed. These results lend only partial support the classical sex allocation model.     

Sex ratio conflict and worker production in eusocial hymenoptera

The best known of the conflicts occurring in eusocial Hymenoptera is queen-worker conflict over sex ratio. So far, sex ratio theory has mostly focused on optimal investment in the production of male versus female sexuals, neglecting the investment in workers. Increased investment in workers decreases immediate sexual productivity but increases expected future colony productivity. Thus, an important issue is to determine the queen's and workers' optimal investment in each of the three castes (workers, female sexuals, and male sexuals), taking into account a possible trade-off between production of female sexuals and workers (both castes developing from diploid female eggs). Here, we construct a simple and general kin selection model that allows us to calculate the evolutionarily stable investments in the three castes, while varying the identity of the party controlling resource allocation (relative investment in workers, female sexuals, and male sexuals). Our model shows that queens and workers favor the investment in workers that maximizes lifetime colony productivity of sexual males and females, whatever the colony kin structure. However, worker production is predicted to be at this optimum only if one of the two parties has complete control over resource allocation, a situation that is evolutionarily unstable because it strongly selects the other party to manipulate sex allocation in its favor. Queens are selected to force workers to raise all the males by limiting the number of eggs they lay, whereas workers should respond to egg limitation by raising a greater proportion of the female eggs into sexual females rather than workers as a means to attain a more female-biased sex allocation. This tug-of-war between queens and workers leads to a stable equilibrium where sex allocation is between the queen and worker optima and the investment in workers is below both parties' optimum. Our model further shows that, under most conditions, female larvae are in strong conflict with queens and workers over their developmental fate because they value their own reproduction more than that of siblings. With the help of our model, we also investigate how variation in queen number and number of matings per queen affect the level of conflict between queens, workers, and larvae and ultimately the allocation of resource in the three castes. Finally, we make predictions that allow us to test which party is in control of sex allocation and caste determination.     

DOES THE TRADE-OFF BETWEEN GROWTH AND REPRODUCTION SELECT FOR FEMALE-BIASED SEXUAL ALLOCATION IN COSEXUAL PLANTS?

We analyzed sexual allocation in cosexual plants while taking the trade-off between growth and reproduction into consideration and showed that this trade-off does not select for female-biased sexual allocation. There are two problems in sexual allocation: optimizing the amount of resources allocated to reproduction in a growing season and equalizing the resources allocated to the male and the female functions. If these two are possible at the same time, equal resource allocation to the male and the female functions is the evolutionarily stable strategy (ESS; given that the fitness gains through the male and the female functions are proportional to the amount of the resources allocated to these functions). Biased sexual allocation only occurs when constraints make it impossible to simultaneously optimize allocation to reproduction and allocation to male and female functions. However, even if female-biased sexual allocation occurs due to the addition of other constraints, the trade-off between growth and reproduction itself is not an important factor that selects for female-biased sexual allocation.     

Female sperm use and storage between fertilization events drive sperm competition and male ejaculate allocation

Sperm competition theory has traditionally focused on how male allocation responds to female promiscuity, when males compete to fertilize a single clutch of eggs. Here, we develop a model to ask how female sperm use and storage across consecutive reproductive events affect male ejaculate allocation and patterns of mating and paternity. In our model, sperm use (a single parameter under female control) is the main determinant of sperm competition, which alters the effect of female promiscuity on male success and, ultimately, male reproductive allocation. Our theory reproduces the general pattern predicted by existing theory that increased sperm competition favors increased allocation to ejaculates. However, our model predicts a negative correlation between male ejaculate allocation and female promiscuity, challenging the generality of a prevailing expectation of sperm competition theory. Early models assumed that the energetic costs of precopulatory competition and the level of sperm competition are both determined by female promiscuity, which leads to an assumed covariation between these two processes. By modeling precopulatory costs and sperm competition independently, our theoretical framework allows us to examine how male allocation should respond independently to variation in sperm competition and energetic trade‐offs in mating systems that have been overlooked in the past.     

Mating frequency and resource allocation to male and female function in the simultaneous hermaphrodite land snail Arianta arbustorum

Sex allocation theory predicts that mating frequency and long‐term sperm storage affect the relative allocation to male and female function in simultaneous hermaphrodites. We examined the effect of mating frequency on male and female reproductive output (number of sperm delivered and eggs deposited) and on the resources allocated to the male and female function (dry mass, nitrogen and carbon contents of spermatophores and eggs) in individuals of the simultaneous hermaphrodite land snail Arianta arbustorum. Similar numbers of sperm were delivered in successive copulations. Consequently, the total number of sperm transferred increased with increasing number of copulations. In contrast, the total number of eggs produced was not influenced by the number of copulations. Energy allocation to gamete production expressed as dry mass, nitrogen or carbon content was highly female‐biased (>95% in all estimates). With increasing number of copulations the relative nitrogen allocation to the male function increased from 1.7% (one copulation) to 4.7% (three copulations), but the overall reproductive allocation remained highly female‐biased. At the individual level, we did not find any trade‐off between male and female reproductive function. In contrast, there was a significant positive correlation between the resources allocated to the male and female function. Snails that delivered many sperm also produced a large number of eggs. This finding contradicts current theory of sex allocation in simultaneous hermaphrodites.     

Resource-dependent sex-allocation in a simultaneous hermaphrodite

Most sex allocation theory is based on the relationship between the resource investment into male and female reproduction and the consequent fitness returns (often called fitness-gain curves). Here we investigate the effects of resource availability on the sex allocation of a simultaneously hermaphroditic animal, the free-living flatworm Macrostomum lignano. We kept the worms under different resource levels and determined the size of their testes and ovaries over a period of time. At higher resource levels, worms allocated relatively more into the female function, suggesting a saturating male fitness-gain curve for this species. A large part of the observed effect was due to a correlated increase in body size, showing size-dependent sex allocation in M. lignano. However, a significant part of the overall effect was independent of body size, and therefore likely due to the differences in resource availability. Moreover, in accordance with a saturating male fitness-gain curve, the worms developed the male gonads first. As the group size was kept constant, our results contrast with expectations from sex allocation models that deal with local mate competition alone, and with previous experiments that test these models.     

Sperm allocation strategies and female resistance: a unifying perspective

The classical viewpoint in sperm competition theory, which holds that males evolve sperm allocation strategies in response to a given degree of sperm competition, has recently been challenged by an alternative viewpoint, which holds that the degree of sperm competition is itself a consequence of these same strategies. Here, we present a game theory model that unites these alternative views as the endpoints of a continuum. Based on the recognition that female control over mating may limit the extent to which male strategies affect the degree of sperm competition, we investigate sperm allocation strategies in a setting where females can resist excessive matings more or less successfully. We discuss how conflicting predictions made by previous theory relate to implicit assumptions about female resistance behavior. Moreover, we show that female resistance, while being highly relevant to the predicted relationship between ejaculate size and the degree of sperm competition, has little effect on the predicted positive correlation between relative testis size and the degree of sperm competition. This result strengthens one of the central predictions of sperm competition theory and is in accordance with empirical findings from a wide range of taxa.