Floral development in the androdioecious tree Tapiscia sinensis: Implications for the evolution to androdioecy

The evolutionary pathway between hermaphroditism and dioecy (females and males in a single population) draws widespread interests, and androdioecy (bisexuals and males in a single population) is rarely achieved as an intermediate state between the two breeding systems. Flower bud differentiations in the pistils of hermaphrodites and the pistillodes of males in androdioecious Tapiscia sinensis Oliv. are investigated by routine paraffin section technology, light microscopy, and scanning electron microscopy. A phylogenetic approach is used to analyze the origin of androdioecy. In T. sinensis, hermaphroditic flowers (HF) and male flowers (MF) experienced a similar development pattern in early flower bud differentiation, including the initiation of tepals and stamens. However, the carpel differentiation of MF and HF proceed in different patterns. In HF, the central zone bulges out and produces a ring meristem on which two to three carpel primordia emerge, which eventually developed into a normal pistil with a stigma, a style, and an ovary. However, in most MF, vestigial pistils are stem‐like (type I), and very few have an empty ovary (type II) or a sterile ovule (type III). Moreover, the evolution of sexual systems within the Huerteales indicates that hermaphroditism is the primitive character of T. sinensis. Tapiscia sinensis shows different degrees of reduction between male flowers and bisexual ones in the evolution to dioecy. Functional androdioecy originated from a hermaphroditic ancestor in T. sinensis and, as an intermediate sexual system, involves evolution from hermaphrodites to dioecy.     

Male flowers in Tulipa pumila Moench (Liliaceae) potentially originate from gender diphasy

We found functionally male individuals in an otherwise hermaphroditic population of Tulipa pumila (Liliaceae) located in Tuscany (central Italy). We investigated the sex ratio of this population, followed by morphometric analyses of the scape, leaves and flowers, and tests on pollen germinability and seed number and mass, in order to infer which sexual strategy produced the observed co-occurrence of male and hermaphrodite individuals. We found that sex ratio deviated from 1:1, and functionally male individuals showed a smaller plant size and a reduced pollen fitness (germinability and siring ability) compared to hermaphrodites. These findings point to a resource-dependent sexual allocation strategy, probably associated with gender diphasy.     

Do inbreeding depression and relative male fitness explain the maintenance of androdioecy in white mangrove, Laguncularia racemosa (Combretaceae)?

Mathematical models predict that to maintain androdioecious populations, males must have at least twice the fitness of male function in hermaphrodites. To understand how androdioecy is maintained in Laguncularia racemosa (white mangrove), outcrossing, inbreeding depression, and relative male fitness were estimated in two androdioecious populations and one hermaphroditic population. Outcrossing was estimated based on length of pollinator foraging bout and pollen carryover assumptions. Inbreeding depression was measured at three life stages: fruit set, seedling emergence, and seedling survivorship. The relative fitnesses of males and the male component of hermaphrodites were compared at these three stages and at the pollen production stage. Male frequency predictions generated by Lloyd's model were compared with observed frequencies in two androdioecious subpopulations. Outcrossing estimates were moderate for all populations (0.29-0.66). Inbreeding depression varied among populations (-0.03-0.86), but the strength of inbreeding depression did not increase with male frequency. Males produced significantly more flowers/inflorescence than hermaphrodites, but pollen production/flower did not differ. Male and hermaphroditic progeny did not differ significantly at other life stages. Populations of white mangrove with male plants were functionally androdioecious. Lloyd's model accurately predicted male frequency in one androdioecious subpopulation, but underestimated male frequency in the second subpopulation.     

雄全异株植物瘿椒树(省沽油科)的传粉生物学

从开花动态、传粉昆虫、花的形态结构、繁育系统、花粉活力和柱头可授性等方面研究了我国特有珍稀植物瘿椒树(Tapiscia sinensis Oliv.)的传粉生物学特性。瘿椒树是典型的雄全异株植物,两性花中含有功能性花粉,且自交亲和,但雄花花粉活力和萌发力是两性花的10倍以上。雄株和两性植株具有相同开花物候期,花期均为5月下旬至6月上旬,单花期为4-5天,雄花和两性花的5枚花药开裂的不同步性明显延长了散粉时间。两性花雌蕊先熟,柱头可授性较长。具有适应风媒和虫媒传粉的花部特征。传粉昆虫主要为蜜蜂科(Apidae)和食蚜蝇科(Syrphidae)昆虫,访花高峰期为8:30-10:30。维持瘿椒树雄全异株的可能机制是:雄株总体上增加了异交花粉的数量和质量;两性花的雄蕊为该物种提供了繁殖保障,同时为传粉者提供了报酬。     

Self-Incompatibility and Male Fertilization Success in Phillyrea angustifolia (Oleaceae)

Androdioecy is a rare breeding system in which low male frequency is expected in populations because males require a strong increase in their fertility to be maintained by selection. Phillyrea angustifolia L. has previously been reported as possibly functionally androdioecious. However, 1&rcolon;1 sex ratios have been reported and suggest functional dioecy. In this article, we compared both pollen tube growth and siring success of male and hermaphrodite pollen in two single-donor pollination experiments. We verified at both pre- and postzygotic levels that hermaphrodites produce functional pollen. Self-incompatibility was also clearly established. However, pollen from hermaphrodites was less efficient than male pollen. The probability of a pollen tube growing through the style was higher for male than for hermaphrodite pollen donors, and males sired twice as many fruits as hermaphrodites. The twofold male advantage in relative fecundity was mainly because of lower pollen fertility of hermaphrodites and possible cross-incompatibility among hermaphrodites.     

雄全异株植物瘿椒树（省沽油科）的传粉生物学

从开花动态、传粉昆虫、花的形态结构、繁育系统、花粉活力和柱头可授性等方面研究了我国特有珍稀植物瘿椒树（Tapiscia sinensis Oliv.）的传粉生物学特性。瘿椒树是典型的雄全异株植物,两性花中含有功能性花粉,且自交亲和,但雄花花粉活力和萌发力是两性花的10倍以上。雄株和两性植株具有相同开花物候期,花期均为5月下旬至6月上旬,单花期为4-5天,雄花和两性花的5枚花药开裂的不同步性明显延长了散粉时间。两性花雌蕊先熟,柱头可授性较长。具有适应风媒和虫媒传粉的花部特征。传粉昆虫主要为蜜蜂科（Apidae）和食蚜蝇科（Syrphidae）昆虫,访花高峰期为8：30-10：30。维持瘿椒树雄全异株的可能机制是：雄株总体上增加了异交花粉的数量和质量;两性花的雄蕊为该物种提供了繁殖保障,同时为传粉者提供了报酬。     

The unexpected mating system of the androdioecious barnacle Chelonibia testudinaria (Linnaeus 1758)

Androdioecy was first described by Darwin in his seminal work on barnacle diversity; he identified males and hermaphrodites in the same reproductive population. Today, we realize that many androdioecious plants and animals share astonishing similarities, particularly with regard to their evolutionary history and mating system. Notably, these species were ancestrally dioecious, and their mating system has the following characteristics: hermaphrodites self‐fertilize frequently, males are more successful in large mating groups, and males have a mating advantage. A male mating advantage makes androdioecy more likely to persist over evolutionary times. Androdioecious barnacles, however, appear to persist as an outlier with a different evolutionary trajectory: they originate from hermaphroditic species. Although sexual systems of androdioecious barnacles are known, no information on the mating system of androdioecious barnacles is available. This study assessed the mating system of the androdioecious barnacle Chelonibia testudinaria. In contrast to other androdioecious species, C. testudinaria does not self‐fertilize, males do not have a mating advantage over hermaphrodites, and the average mating group is quite small, averaging only three individuals. Mating success is increased by proximity to the mate and penis length. Taken together, the mating system of C. testudinaria is unusual in comparison with other androdioecious plants and animals, and the lack of a male mating advantage suggests that the mating system alone does not provide an explanation for the maintenance of androdioecy in this species. Instead, we propose that sex‐specific life history equalizes male and hermaphroditic overall fitness.     

Pollen Production in the Androdioecious Datisca glomerata (Datiscaceae): Implications for Breeding System Equilibrium

Abstract Androdioecy (the presence of males and hermaphrodites in a breeding population) is a rare reproductive system in plants, with Datisca glomerata (Datiscaceae) representing the only well-documented example. Recent reports of high outcrossing rates, inbreeding depression, and high male pollen production satisfy theoretical predictions for the continued maintenance of androdioecy in populations of this species. However, in prior studies pollen production was measured indirectly in terms of numbers of anthers per flower—based on the assumption that male and hermaphroditic plant have equal numbers of flowers and that anthers from the two sexual morphs produce equivalent amounts of pollen. Herein, we demonstrate that male and hermaphrodite plants do not differ significantly in terms of flower number, but that pollen production in anthers from hermaphroditic plants is 12.6% higher than in anthers from male plants, thus refining the estimate of relative pollen fecundity of male versus hermaphrodite plants. The differential lowers the frequency of males predicted by theory, but is still consistent with the maintenance of androdioecy in this species.     

INBREEDING DEPRESSION IN ANDRODIOECIOUS POPULATIONS OF DATISCA GLOMERATA (DATISCACEAE)

Several workers have suggested that the rarity of androdioecy (the presence of males and hermaphrodites in a breeding population) in nature is due to the large fitness gain required by male plants in order to be maintained by selection. As part of an ongoing investigation of this hypothesis, we tested the effects of selfing on fitness in functionally androdioecious populations of Datisca glomerata. We compared progeny from self-fertilizations, cross-fertilizations with pollen from male plants only, cross-fertilizations with pollen from hermaphrodite plants only, and open-pollinated flowers for several measures of progeny fitness including seed weight, germination rate, and seedling weight. Significant inbreeding depression was observed for androdioecious populations of D. glomerata for both seed and seedling weights. However, no significant differences were observed across treatments for seed germination percentages. The observation of significant levels of inbreeding depression in this study, combined with prior evidence of threefold greater pollen production by males, may at least partially account for the large fitness increase required by males to be maintained by selection.     

Female sterility associated with increased clonal propagation suggests a unique combination of androdioecy and asexual reproduction in populations of Cardamine amara (Brassicaceae)

Background and Aims The coexistence of hermaphrodites and female-sterile individuals, or androdioecy, has been documented in only a handful of plants and animals. This study reports its existence in the plant species Cardamine amara (Brassicaceae), in which female-sterile individuals have shorter pistils than seed-producing hermaphrodites.Methods Morphological analysis, in situ manual pollination, microsatellite genotyping and differential gene expression analysis using Arabidopsis microarrays were used to delimit variation between female-sterile individuals and hermaphrodites.Key Results Female sterility in C. amara appears to be caused by disrupted ovule development. It was associated with a 2.4- to 2.9-fold increase in clonal propagation. This made the pollen number of female-sterile genets more than double that of hermaphrodite genets, which fulfils a condition of co-existence predicted by simple androdioecy theories. When female-sterile individuals were observed in wild androdioecious populations, their ramet frequencies ranged from 5 to 54 %; however, their genet frequencies ranged from 11 to 29 %, which is consistent with the theoretically predicted upper limit of 50 %.Conclusions The results suggest that a combination of sexual reproduction and increased asexual proliferation by female-sterile individuals probably explains the invasion and maintenance of female sterility in otherwise hermaphroditic populations. To our knowledge, this is the first report of the coexistence of female sterility and hermaphrodites in the Brassicaceae.     

Males outcompete hermaphrodites for seed siring success in controlled crosses in the polygamous Fraxinus excelsior (Oleaceae)

Polygamy (including trioecy and subdioecy), the co-occurrence of males, hermaphrodites, and females in natural populations, is a rare and poorly studied breeding system expressed in Fraxinus excelsior L. (Oleaceae), a wind-pollinated tree. Here we investigate siring ability of pollen from male vs. hermaphrodite individuals to better understand this sex polymorphism. We conducted single-donor and two-donor pollination experiments and compared both fruit set and seed siring success, assessed with polymorphic microsatellite markers, of male and hermaphrodite individuals. Single pollen donor crosses allowed us to verify the male function of hermaphrodites. However, pollen from hermaphrodites was much less proficient than male pollen, with males siring 10 times as many fruits in single donor pollination treatments. This result was strengthened by the surprisingly low reproductive success of hermaphrodites in pollen competition conditions: of the 110 seedlings analyzed three were selfed and only one was sired by the hermaphrodite donor. The remaining 106 were sired by the male pollen donor. These results raise the question of the maintenance of male fertility in hermaphrodites in Fraxinus excelsior. Male function of hermaphrodites in this species now needs to be assessed under field conditions.     

Evolutionary transitions among dioecy,androdioecy and hermaphroditism in limnadiid clam shrimp (Branchiopoda: Spinicaudata)

Examinations of breeding system transitions have primarily concentrated on the transition from hermaphroditism to dioecy, likely because of the preponderance of this transition within flowering plants. Fewer studies have considered the reverse transition: dioecy to hermaphroditism. A fruitful approach to studying this latter transition can be sought by studying clades in which transitions between dioecy and hermaphroditism have occurred multiple times. Freshwater crustaceans in the family Limnadiidae comprise dioecious, hermaphroditic and androdioecious (males + hermaphrodites) species, and thus this family represents an excellent model system for the assessment of the evolutionary transitions between these related breeding systems. Herein we report a phylogenetic assessment of breeding system transitions within the family using a total evidence comparative approach. We find that dioecy is the ancestral breeding system for the Limnadiidae and that a minimum of two independent transitions from dioecy to hermaphroditism occurred within this family, leading to (1) a Holarctic, all‐hermaphrodite species, Limnadia lenticularis and (2) mixtures of hermaphrodites and males in the genus Eulimnadia. Both hermaphroditic derivatives are essentially females with only a small amount of energy allocated to male function. Within Eulimnadia, we find several all‐hermaphrodite populations/species that have been independently derived at least twice from androdioecious progenitors within this genus. We discuss two adaptive (based on the notion of ‘reproductive assurance’) and one nonadaptive explanations for the derivation of all‐hermaphroditism from androdioecy. We propose that L. lenticularis likely represents an all‐hermaphrodite species that was derived from an androdioecious ancestor, much like the all‐hermaphrodite populations derived from androdioecy currently observed within the Eulimnadia. Finally, we note that the proposed hypotheses for the dioecy to hermaphroditism transition are unable to explain the derivation of a fully functional, outcrossing hermaphroditic species from a dioecious progenitor.     

Dioecy inHonkenya peploides var.major (Caryophyllaceae)

Sexual difference and pollination system inHonkenya peploides var.major were investigated. The present analyses indicate that sex expression of this plant is functionally dioecious, rather than androdioecious, as described previously. Its flowers are largely pollinated by small bees, hover-flies, flies, and ants. Female flowers were morphologically characterized by conspicuously longer styles and smaller petals, and had no pollen grains, while male flowers had shorter styles, larger petals, and longer filaments, and produced viable pollen grains. Although the male flowers possess many ovules in an ovary, they set fruits at a very low frequency in natural conditions and did not produce fruits by pollination experiments. We suggest that the dioecy of this species has been derived from hermaphrodite through gynodioecy, and not directly from hermaphrodite.     

FUNCTIONAL DIOECY AND ANDROMONOECY IN SOLANUM

Field and laboratory studies of 19 diclinous species endemic to Australia help to clarify the nature and evolution of andromonoecy, androdioecy, and dioecy in the genus Solanum. Ten species are andromonoecious; typically these species bear inflorescences with a single, large basal hermaphroditic flower and 12–60 distal, smaller staminate flowers. We suggest that the andromonoecious condition was derived from hermaphroditic-flowered ancestors in part by hemisterilization of flowers but largely by addition of staminate flowers. The resultant larger inflorescences are hypothesized to serve both to attract and to entrain pollinators, yielding more or higher-quality seed set in hermaphroditic flowers and/or greater dispersion of pollen from staminate flowers. We suggest that andromonoecy may also serve to reduce selling. Nine other species are morphologically androdioecious but functionally dioecious. In these species, staminate flowers, like those of the andromonoecious species, bear anthers with copious tricolporate pollen and a highly reduced gynoecium. The morphologically hermaphroditic flowers are functionally pistillate and borne singly in inflorescences, and they bear anthers with inaperturate pollen. The inaperturate pollen, although viable, never germinates and is hypothesized to be retained in pistillate flowers as a reward to pollinators in the nectarless Solanum flowers. All other species of Solanum studied with pollen dimorphism in which one pollen morph is inaperturate are also best treated as functionally dioecious. We conclude that there is no evidence for androdioecy in Solanum. A review of other families suggests that there is little support for this unusual breeding system in any other angiosperm group either. Preliminary analyses suggest that andromonoecy and dioecy are polyphyletic in Solanum. Furthermore, dioecy is as likely to have arisen from hermaphroditic as from andromonoecious ancestors.     

Sex‐biased oviposition by a nursery pollinator on a gynodioecious host plant: Implications for breeding system evolution and evolution of mutualism

Dioecy, a breeding system where individual plants are exclusively male or female, has evolved repeatedly. Extensive theory describes when dioecy should arise from hermaphroditism, frequently through gynodioecy, where females and hermaphrodites coexist, and when gynodioecy should be stable. Both pollinators and herbivores often prefer the pollen‐bearing sex, with sex‐specific fitness effects that can affect breeding system evolution. Nursery pollination, where adult insects pollinate flowers but their larvae feed on plant reproductive tissues, is a model for understanding mutualism evolution but could also yield insights into plant breeding system evolution. We studied a recently established nursery pollination interaction between native Hadena ectypa moths and introduced gynodioecious Silene vulgaris plants in North America to assess whether oviposition was biased toward females or hermaphrodites, which traits were associated with oviposition, and the effect of oviposition on host plant fitness. Oviposition was hermaphrodite‐biased and associated with deeper flowers and more stems. Sexual dimorphism in flower depth, a trait also associated with oviposition on the native host plant (Silene stellata), explained the hermaphrodite bias. Egg‐receiving plants experienced more fruit predation than plants that received no eggs, but relatively few fruits were lost, and egg receipt did not significantly alter total fruit production at the plant level. Oviposition did not enhance pollination; egg‐receiving flowers usually failed to expand and produce seeds. Together, our results suggest that H. ectypa oviposition does not exert a large fitness cost on host plants, sex‐biased interactions can emerge from preferences developed on a hermaphroditic host species, and new nursery pollination interactions can arise as negative or neutral rather than as mutualistic for the plant.     

Is Phillyrea angustifolia L. (Oleaceae) an androdioecious species?

LEPART, J. & DOMMEE B., 1992. Is Phillyrea angustifolia L. (Oleaceae) an androdioecious species? Observations during two or three years on three natural populations of Phillyrea angustifolia growing in contrasting environments in southern France show that two distinct phenotypes occur in approximately equal proportions: hermaphrodites, which produce pollen and seeds, and males, which produce pollen only. The populations studied are thus morphologically androdioecious. Biometric investigation of the two morphs shows that they are clearly distinguished by (1) the shape of the stigma and (2) the ovary which is well developed in hermaphrodites and aborted in males. Neither size of anthers and corolla, nor pollen germination, differ between the two sexes. In the Camargue, where P. angustifolia is presently an invader, controlled crosses between hermaphrodites (selfing and inter-individual) are partially successful. In contrast, such crosses are sterile in the well-established population of the La Gardiole. Hence the Camargue population appears to be functionally androdioecious and La Gardiole functionally dioecious. This breeding system is particularly puzzling, since the occurrence of anemogamy and possible selfing do not fit classical explanations of androdioecy. The ability of hermaphrodites to be functionally male and female could be particularly adaptive in founding populations. Since functional hermaphroditism occurs in expanding populations of the Camargue population, we consider that the androdioecy of P. angustifolia could be a kind of leaky dioecism.     

Pollen limitation and the evolution of androdioecy from dioecy

Androdioecy is an unusual breeding system in which populations consist of separate male and hermaphrodite individuals. The evolution of androdioecy is still poorly understood; however, there is evidence from several androdioecious species that the breeding system may have evolved from dioecy (males and females). This article presents a simple deterministic model showing that androdioecy can evolve from dioecy under a broad range of realistic conditions. For the evolution of androdioecy from dioecy, hermaphrodites must be able to invade the dioecious population. Then, males must be maintained, while females are eliminated. Hermaphrodite invasion is favored when females are pollen limited and hermaphrodites have high overall fertility and are self-fertile. Male maintenance is favored when hermaphrodites resemble females, having high seed production and low pollen fitness, and when the selfing rate is not too high. These conditions were satisfied over a broad and realistic range of parameter values, suggesting that the evolution of androdioecy from dioecy is highly plausible.     

Sex determination in the androdioecious barnacle Scalpellum scalpellum (Crustacea: Cirripedia)

How androdioecy (coexistence of hermaphrodites and males) is maintained is still poorly understood. Therefore, sex determination was studied in the androdioecious barnacle Scalpellum scalpellum L. First, 247 cypris larvae from seven broods were investigated for sexual dimorphism in larval morphology and found to be all identical. Second, experiments with cyprids showed that males and hermaphrodites differ distinctly in morphology as soon as 4–5 days after settlement. Third, 14 252 cyprids were allowed to settle on the bottom of their culture cages, and all surviving larvae developed into hermaphrodites and none into dwarf males. Fourth, larvae settled in hermaphrodite receptacles (i.e. future males) were removed at increasing intervals after settlement to study if the male and hermaphrodite sexual expressions are fixed or plastic. All larvae became dwarf males if allowed to stay there for more than 8 h after settlement. But if removed within 3 h after settlement, half of them developed into hermaphrodites. We conclude that an environmental sex determination mechanism operates in S. scalpellum. Together with a 1:1 hermaphrodite/male ratio observed in previously reported experiments offering a free choice of settlement, we suggest that all larvae are potential hermaphrodites, but only 50% can settle in hermaphrodite receptacles and yield males.     

Selective nectar robbing in a gynodioecious plant (Glechoma longituba) enhances female advantage

Nectar robbing not only affects the reproductive fitness of the plant but it may also potentially affect the pollination dynamics of the associated coflowering individuals. In this study, we established that the nectar robber Xylocopa sinensis robs nectar only from the hermaphrodite ramets of the gynodioecious plant Glechoma longituba but not from the female ramets. In populations with high rates of nectar robbing, this results in hermaphrodite ramets having reduced seed set whereas the female ramets have a slightly increased seed set. We hypothesize that selective nectar robbing confers an advantage to female individuals and thus ensures their maintenance in gynodioecious populations. Results of controlled experiments indicated that the reduction in the amounts of nectar available occasioned by nectar robbing resulted in some legitimate pollinators switching to visiting flowers on female rather than hermaphrodite ramets. This resulted in lower pollination rates and seed set for hermaphrodites and higher pollination rates and seed set for females. This study presents a previously unreported mechanism causing female advantage in gynodioecious plants.     

Floral biology and pollination mechanisms of four Mexico-endemic Fuchsia species with contrasting reproductive systems

Aims The evolution of the outstanding variation of reproductive systems in angiosperms has been considered an important driver of lineage diversification. Closely related hermaphroditic and dioecious species with biotic pollination provide the opportunity to study and compare traits related to pollinator attraction and their consequences on reproductive components. A higher predictability of pollination syndromes is expected in dioecious species, which are dependent on pollinators, than in self-compatible hermaphroditic taxa. Dioecious species may suffer pollen limitation depending on the quality of floral rewards and the kind and abundance of pollinators, whereas no pollen limitation is expected in hermaphroditic species with autonomous self-pollination. Additionally, in the absence of pollen limitation, more or better seeds are expected in dioecious species, according to the sexual specialization hypothesis.Methods In natural populations of the hermaphroditic Fuchsia fulgens and Fuchsia arborescens and dioecious Fuchsia parviflora and Fuchsia obconica, all endemic to Mexico, we first described flower phenology, flower production and longevity and nectar volume and concentration. Then, we evaluated the correspondence between floral visitors and pollination syndromes. In hermaphrodite plants, we determined the level of herkogamy and the potential for autonomous self-pollination. Finally, we evaluated the effect of pollen limitation on fruit set and seed number and assessed seed germination for all species.Important findings In contrast to our prediction, dioecious species did not show a higher correspondence between pollination syndromes and floral visitors than did hermaphrodites; however, male flowers exhibited a higher correspondence than female flowers. No pollen limitation was detected in dioecious species, for which visitation rate did not differ between male and female flowers. The hermaphroditic F. fulgens showed pollen limitation for seed number, despite the presence of autonomous selfing. Fruit set from autonomous pollination was higher in F. arborescens, which showed a lower level of herkogamy compared with F. fulgens. Finally, dioecious species produced fewer but heavier seeds compared with hermaphrodite species. Although Fuchsia is classified as an outcrossing genus, both hermaphroditic species showed autonomous self-pollination. The heavier but lower number of seeds per fruit in dioecious species may be related to the more efficient resource allocation expected from sexual specialization. This could play an important role in the evolution of dioecy; however, a comparative phylogenetic approach is required to confirm this hypothesis.