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.     

THE EFFECT OF INVESTMENT IN ATTRACTIVE STRUCTURES ON ALLOCATION TO MALE AND FEMALE FUNCTIONS IN PLANTS

Expressions for male and female fitnesses of partially self-fertilizing cosexual plants are derived, assuming that allocation to pollinator attraction at the time of flowering may decrease resources available for male and female primary structures. The total female fertility is assumed to be controlled by factors at two stages, flowering-time and fruiting-time, with resources for fruit maturation being limited so that maximum seed production may be limited by the availability of these resources. The fitness formulas are used to calculate ESS (evolutionarily stable strategy) allocations at flowering time to primary male and female sex functions and to attractive structures. These are compared with some data that are available for dry weights of different flower parts. The fitnesses of unisexual mutant forms are calculated, assuming that they are introduced into a population consisting mostly of the initial cosexual form and that they obey the same gain curves as that form. When compared with the fitness of the ESS cosexual form, this enables one to ask whether unisexual forms will be favored. We show that the spread of females is unlikely, unless there is high inbreeding depression and a rather high selfing rate, and that in some circumstances a linear relation between number of fertilized ovules and number of seeds matured can be less favorable for the invasion of females than is a highly concave relation. With a nearly linear relation between numbers of fertilized ovules and mature seeds, invasion by females is more likely when investment in attraction is low than when it is high. These effects are discussed in relation to the distribution of dioecy. The spread of male mutants is never likely in these models.     

Sex allocation in a patchy environment: a marginal value theorem

The ESS sex allocation when male/female fitnesses vary with patch type is a set of values which either equalizes the marginal values of the male/female fitness tradeoffs, or are pure sexes. This is shown for a hermaphrodite; the result is then generalized to other sex allocation cases.     

Androdioecy and the evolution of dioecy

The likelihood that dioecy could evolve via androdioecy is examined. It is concluded that female-sterility mutations are unlikely to be able to invade populations of self-compatible hermaphrodite species, even if the resources that an hermaphrodite devotes to seed production can be diverted to yield increased survival and also to increase male fertility. These findings are in agreement with the great rarity of androdioecy. Claimed cases of androdioecy are reviewed. All of the species in question appear to be functionally dioecious, with females retaining substantial anther vestiges. It is argued that this morphological androdioecy is in no way indicative of a previous functionally androdioecious state. The details of the reproductive biology of many of these species seem rather to be consistent with their having evolved dioecy via gynodioecy.
The rarity of androdioecy, as a route to the evolution of dioecy, suggests that re-allocation of reproductive resources is unlikely to be the sole factor of importance, and supports an important role for inbreeding avoidance. The fact that females in some dioecious species retain anthers of substantial size, containing considerable quantities of pollen, gives further support to the view that male-sterility mutations can sometimes be favoured even when little or no resources are re-allocated to male functions. This is impossible without substantial selfing and inbreeding. It is therefore concluded that inbreeding avoidance is generally important in the evolution of dioecy, though reallocation of reproductive resources is also necessary.     

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.     

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.     

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.     

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.     

Brooding and the evolution of hermaphroditism

It has been suggested that hermaphroditism may evolve when the resources that females can profitably allocate to ova is limited by factors such as lack of brooding space. Spare resources could then be allocated to produce male gametes in a hermaphrodite. A model is developed to investigate the conditions under which this will occur. Hermaphrodites will displace males (and females) if the hermaphrodites produce at least half as many male gametes as a male. If the hermaphrodite produces less than half the number of gametes produced by a male then a stable equilibrium arises where males and hermaphrodites coexist. In this situation the frequency of males is determined by the ratio of the numbers of male gametes produced by hermaphrodites to the numbers produced by males.     

Effects of reproductive compensation, gamete discounting and reproductive assurance on mating-system diversity in hermaphrodites

Hermaphroditism allows considerable scope for contributing genes to subsequent generations through various mixtures of selfed and outcrossed offspring. The fitness consequences of different family compositions determine the evolutionarily stable mating strategy and depend on the interplay of genetic features, the nature of mating, and factors that govern offspring development. This theoretical article considers the relative contributions of these influences and their interacting effects on mating-system evolution, given a fixed genetic load within a population. Strong inbreeding depression after offspring gain independence selects for exclusive outcrossing, regardless of the intensity of predispersal inbreeding depression, unless insufficient mating limits offspring production. The extent to which selfing evolves under weak postdispersal inbreeding depression depends on predispersal inbreeding depression and the opportunity for resource limitation of offspring production. Mixed selfing and outcrossing is an evolutionarily stable strategy (ESS) if selfed zygotes survive poorly, but selfed offspring survive well, and maternal individuals produce enough "extra" eggs that deaths of unviable outcrossed embryos do not impact offspring production (reproductive compensation). Mixed mating can also be an ESS, despite weak lifetime inbreeding depression, if self-mating reduces the number of male gametes available for outcrossing (male-gamete discounting). Reproductive compensation and male-gamete discounting act largely independently on mating-system evolution. ESS mating systems always involve either complete fertilization or fertilization of enough eggs to induce resource competition among embryos, so although reproductive assurance is adaptive with insufficient mating, it is never an ESS. Our results illustrate the theoretical importance of different constraints on offspring production (availability of male gametes, egg production, and maternal resources) for both the course and outcome of mating-system evolution, whereas unequal competition between selfed and outcrossed embryos has limited effect. These results also underscore the significance of heterogeneity in the nature and intensity of inbreeding depression during the life cycle for the evolution of hermaphrodite mating systems.     

The evolution of phally polymorphism in Bulinus truncatus (Gastropoda,Planorbidae): the cost of male function analysed through life-history traits and sex allocation

In the hermaphrodite freshwater snail Bulinus truncatus, two sexual morphs, euphallic (regular hermaphrodites) and aphallic individuals without a male copulatory organ, co-occur at various ratios in natural populations. Both aphallic and euphallic individuals can reproduce by selfing, but when outcrossing aphallic individuals can only play the female role. A comparison of life-history traits and sex allocation in these two forms provides the opportunity to investigate the evolution and maintenance of sexual polymorphisms. This study was performed to test whether a reallocation of resources from the lost male function to the female function occurs in aphallic snails at the level of both sex organs (sex allocation) and life-history traits. In a first experiment we compared life-history traits over a whole life-cycle under selfing between the two sexual morphs. In a second experiment, the sex organs were weighed to test for a difference in sex allocation between the two morphs. No difference in resource allocation to female function between the two morphs was observed in either experiment. This is in contrast to patterns frequently observed in sexually polymorphic plants, and in a previous study performed on aphally in the same snail species. We discuss the genetic and physiological hypotheses that could explain these results, and their consequences for the evolution and maintenance of phally polymorphism in B. truncatus.     

雌雄同花植物的性分配

性分配理论假定雌雄功能之间存在着trade-off,对一种性别的投入增多必然会减少对另一性别的投入。雌雄功能投入的适合度曲线的形状决定了哪种繁育系统是进化稳定的。因此,性分配理论可以解释植物繁育系统的进化,尤其被认为是雌雄异株进化的选择机制之一。目前的实验研究分别在物种间、种群间、个体间及花间四个层次上进行:自交率的程度对物种和种群的性分配都有影响;虫媒和风媒植物的性分配是个体大小依赖的;而且花序内花的性分配模式受昆虫访花行为的影响。相对于理论,性分配的实验研究明显滞后,随着分子标记技术的普及,性分配理论将会获得更大的发展。繁殖分配需要进一步与性分配理论结合,尤其在空间尺度上资源分配与繁育系统变化的研究是很有意义的。     

Sexual conflicts along gradients of density and predation risk: insights from an egg-trading fish

In principle, the intensity of sexual conflict is best measured as a loss of fitness associated with the expression of conflict-related traits. But because the relevant traits may be difficult to manipulate and fitness difficult to assess, proxy variables linked to conflict intensity may provide important tools for empirical measurement. Here we identify two common types of sexual conflict—one within mating pairs over the less expensive male role, and one between mating pairs and intruders seeking to obtain fertilizations—and consider how they vary in intensity along gradients of population density and predation risk. To do this, we develop and analyze a model of mating dynamics in the chalk bass, an egg-trading simultaneous hermaphrodite that lives on Caribbean coral reefs. In this species, within-pair sexual conflict leads each female-role partner to provide in each mating episode only a subset (parcel) of its egg clutch to its mate for fertilization. Pair-intruder sexual conflict (i.e., sperm competition) increases the proportion of the gonad allocated to male function. In the model, more parceling and greater male allocation both resulted in lower fitness at the ESS, our measure of conflict intensity. Male allocation increased along the density gradient but decreased along the predation-risk gradient, reflecting shifts in intrusion frequency. Parcel number sharply increased and then decreased more gradually along a gradient of increasing local density, initially responding to increased availability of alternative mates across low densities and then to diminishing clutch size toward higher densities. Parcel number decreased with predation risk as each mating episode became more dangerous. Conflict intensities were usually greatest at intermediate positions along the two environmental gradients, and each conflict ameliorated the intensity of the other. Overall, parceling and sex allocation may be good though imperfect proxies for intensities of within-pair and pair-intruder sexual conflicts among chalk bass.     

Sex allocation in a simultaneously hermaphroditic marine shrimp

Two fundamental questions dealing with simultaneous hermaphrodites are how resources are optimally allocated to the male and female function and what conditions determine shifts in optimal sex allocation with age or size. In this study, I explored multiple factors that theoretically affect fitness gain curves (that depict the relationship between sex-specific investment and fitness gains) to predict and test the overall and size-dependent sex allocation in a simultaneously hermaphroditic brooding shrimp with an early male phase. In Lysmata wurdemanni, sperm competition is absent as hermaphrodites reproducing in the female role invariably mated only once with a single other shrimp. Shrimps acting as females preferred small over large shrimps as male mating partners, male mating ability was greater for small compared to large hermaphrodites, and adolescent males were predominant in the population during the breeding season. In addition, brooding constraints were not severe and varied linearly with body size whereas the ability to acquire resources increased markedly with body size. Using sex allocation theory as a framework, the findings above permitted to infer the shape of the male and female fitness gain curves for the hermaphrodites. The absence of sperm competition and the almost unconstrained brooding capacity imply that both curves saturate, however the male curve levels off much more quickly than the female curve with increasing level of investment. In turn, the predominance of adolescent males in the population implies that the absolute gain of the female curve is greater than that of the male curve. Last, the size-dependent female preference and male mating ability of hermaphrodites determines that the absolute gain of the male curve is greater for small than for large hermaphrodites. Taking into consideration the inferred shape of the fitness gain curves, two predictions with respect to the optimal sex allocation were formulated. First, overall sex allocation should be female biased; it permits hermaphrodites to profit from the female function that provides a greater fitness return than the male function. Second, sex allocation should be size-dependent with smaller hermaphrodites allocating more than proportionally resources to male reproduction than larger ones. This size-dependent sex allocation permits hermaphrodites to profit from male mating opportunities that are the greatest at small body sizes. Size-dependent sex allocation is also expected because the male fitness gain curve decelerates more quickly than the female gain curve and experiments indicated that resources are greater for large than small hermaphrodites. These two predictions were tested when determining the sex allocation of hermaphrodites by dissecting their gonad and quantifying ovaries versus testes mass. Supporting the predictions above, hermaphrodites allocated, on average, 118 times more to the female than to the male gonad and the proportion of resources devoted to male function was higher in small than in large hermaphrodites. A trade-off between male and female allocation is assumed by theory but no negative correlation between male and female reproductive investment was observed. In L. wurdemanni, the relationship between sex-specific investment and fitness changes during ontogeny in a way that is consistent with an adjustment of sex allocation to improve size-specific reproductive success.     

On sex allocation and selfing in higher plants

Summary Sex allocation (male allocation/female allocation) as a function of selfing rate is studied in the wild riceOryza perennis. Using dry weight measures, the male/female ratio is linearly related to the selfing rate. This linear relationship may have a fairly radical interpretation in terms of current sex allocation theory. It suggests that the intermediate selfing rates are themselves maintained by a form of frequency dependence. In particular, the linearity suggests: (i) the relative fitness of a selfed versus outcrossed offspring decreases with increased selfing; (ii) in equilibrium, a selfed offspring is approximately half as fit as an outcrossed offspring; (iii) the frequency dependence, being the opposite of that proposed in most selfing models, may result from the same forces thought to be involved in the maintenance of sex itself, and (iv) the position of the fitted line contains information about the plant's use of wind pollination for male reproduction. It suggests that wind shows much less mixing of pollen than previously assumed, and/or that there are severe morphological constraints on pollen presentation. The above interpretations are clearly speculative and tentative. Possible problems in the analysis, and some alternatives for data interpretation are discussed.     

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.     

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.     

Sex allocation in clonal plants: might clonal expansion enhance fitness gains through male function?

The returns on investment in sexual reproduction are described by fitness gain curves and the shapes of these curves affect, among other things, the evolutionary stability of reproductive systems. The available evidence indicates that gain curves for male function decelerate, corresponding to diminishing fitness returns on investment in pollen. In contrast, the gain curve for female function is thought to decelerate less strongly than it does for male function (e.g., if seed fertility is limited by more by resources than by mating opportunities). Here we suggest that when the shapes of the female and male gain curves differ, clonality alters the rates of return on investment via the two sex functions. In particular, we propose that clonal expansion might increase fitness gains through male function because the subdivision of reproductive effort among ramets allows each ramet to take advantage of the steepest parts of the male gain curve. We examined the interaction between clonal expansion and fitness gains using numerical analysis of a model of sex allocation in which we assumed that there is no mating interference among ramets. We found that clonal expansion led to substantial increases in fitness through male function, but to decreases in fitness through female function. Under intermediate investment in clonal growth, marginal fertility gains through the two sex functions did not intersect over a broad range of sex allocation patterns, suggesting that clonality could favor the evolution of separate sexes. Finally, we suggest an alternative explanation for the common observation of male-biased sex ratios in clonal dioecious plants. If male function fitness is maximized under higher rates of clonal expansion than for female function, greater frequencies of male ramets might reflect the outcome of fertility selection, rather than constraints on clonal expansion imposed by greater costs of reproduction for females.     

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.     

SEX CHANGE WITH INBREEDING: EXPERIMENTS ON SEPARATE VERSUS COMBINED SEXES

Ipomopsis rubra plants grown in the laboratory initially produced hermaphrodite flowers, but some self- or sib-mated individuals switched to produce large numbers of pistillate (male sterile) flowers. The sex change did not occur with outcrossing. Plants with extreme male sterility were also observed in natural populations, usually in smaller individuals. Male sterility may be compensated by more seeds (resource reallocation), better seeds (avoidance of selfing), or both. Pistillate flowers were smaller, so savings could be used for additional seeds. Selfed seeds had reduced survival and fecundity, so avoidance of selfing could produce better quality offspring. We explored costs and benefits of sex change with two fitness models. The first assumes randomoutcross matings. Estimates of resource reallocation and inbreeding (selfing) depression are sufficient for pistillate inflorescences to have equal or greater fitness than hermaphrodite inflorescences if the selfing rate is high. Frequencies of sex change with intensive self-pollination were consistent with this model. The second model assumes all nonself matings are between sibs in “local mating” groups. Parents may benefit by male sterility in offspring, but gains would be higher if sex change occurred earlier and at higher than observed frequencies.