How organisms determine particular organ numbers is a fundamental key to the development of precise body structures; however, the developmental mechanisms underlying organ-number determination are unclear. In many eudicot plants, the primordia of sepals and petals (the floral organs) first arise sequentially at the edge of a circular, undifferentiated region called the floral meristem, and later transition into a concentric arrangement called a whorl, which includes four or five organs. The properties controlling the transition to whorls comprising particular numbers of organs is little explored. We propose a development-based model of floral organ-number determination, improving upon earlier models of plant phyllotaxis that assumed two developmental processes: the sequential initiation of primordia in the least crowded space around the meristem and the constant growth of the tip of the stem. By introducing mutual repulsion among primordia into the growth process, we numerically and analytically show that the whorled arrangement emerges spontaneously from the sequential initiation of primordia. Moreover, by allowing the strength of the inhibition exerted by each primordium to decrease as the primordium ages, we show that pentamerous whorls, in which the angular and radial positions of the primordia are consistent with those observed in sepal and petal primordia in Silene coeli-rosa, Caryophyllaceae, become the dominant arrangement. The organ number within the outmost whorl, corresponding to the sepals, takes a value of four or five in a much wider parameter space than that in which it takes a value of six or seven. These results suggest that mutual repulsion among primordia during growth and a temporal decrease in the strength of the inhibition during initiation are required for the development of the tetramerous and pentamerous whorls common in eudicots.

Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning.

The bilateral symmetry of flowers is a striking morphological achievement during floral evolution, providing high adaptation potential for pollinators. The symmetry can appear when floral organ primordia developmentally initiate. Primordia initiation at the ventral and dorsal sides of the floral bud is differentially regulated by several factors, including external organs of the flower and CYCLOIDEA (CYC) gene homologues, which are expressed asymmetrically on the dorso-ventral axis. It remains unclear how these factors control the diversity in the number and bilateral arrangement of floral organs. Here, we propose a mathematical model demonstrating that the relative strength of the dorsal-to-ventral inhibitions and the size of the floral stem cell region (meristem) determines the number and positions of the sepal and petal primordia. The simulations reproduced the diversity of monocots and eudicots, including snapdragon Antirrhinum majus and its cyc mutant, with respect to organ number, arrangement and initiation patterns, which were dependent on the inhibition strength. These theoretical results suggest that diversity in floral symmetry is primarily regulated by the dorso-ventral inhibitory field and meristem size during developmental evolution.

Merosity, indicating the basic number of floral organs such as sepals and petals, has been constrained to specific and stable numbers during the evolution of angiosperms. The ancestral flower is considered to have a spiral arrangement of perianth organs, as in phyllotaxis, the arrangement of leaves. How has the ancestral spiral evolved into flowers with specific merosities? To address this question, we studied perianth organ arrangement in the Anemone genus of the basal eudicot family Ranunculaceae, because various merosities are found in this genus. In three species, A. flaccida, A. scabiosa, and A. nikoensis that are normally pentamerous, we found positional arrangement of the excessive sixth perianth organ indicating the possibility of a transition from pentamerous to trimerous arrangement. Arrangement was intraspecifically stochastic, but constrained to three of five types, where trimerous arrangement was the most frequent in all species except for a form of A. scabiosa. The rank of frequency of the other two types was species-dependent. We connect these observations with classical theories of spiral phyllotaxis. The phyllotaxis model for initiation of the sixth organ showed that the three arrangements occur at a divergence angle <144°, indicating the spiral nature of floral phyllotaxis rather than a perfect penta-radial symmetry of 144°. The model further showed that selective occurrence of trimerous arrangement is mainly regulated by the organ growth rate. Differential organ growth as well as divergence angle may regulate transitions between pentamerous and trimerous flowers in intraspecific variation as well as in species evolution.

Stabilization and variation of floral structures are indispensable for plant reproduction and evolution; however, the developmental mechanism regulating their structural robustness is largely unknown. To investigate this mechanism, we examined positional arrangement (aestivation) of excessively produced perianth organs (tepals) of six- and seven-tepaled (lobed) flowers in six Anemone species (Ranunculaceae). We found that the tepal arrangement that occurred in nature varied intraspecifically between spiral and whorled arrangements. Moreover, among the studied species, variation was commonly limited to three types, including whorls, despite five geometrically possible arrangements in six-tepaled flowers and two types among six possibilities in seven-tepaled flowers. A spiral arrangement, on the other hand, was unique to five-tepaled flowers. A spiral phyllotaxis model with stochasticity on initiating excessive primordia accounted for these limited variations in arrangement in cases when the divergence angle between preexisting primordia was less than 144°. Moreover, interspecific differences in the frequency of the observed arrangements were explained by the change of model parameters that represent meristematic growth and differential organ growth. These findings suggest that the phyllotaxis parameters are responsible for not only intraspecific stability but interspecific difference of floral structure. Decreasing arrangements from six-tepaled to seven-tepaled Anemone flowers demonstrate that the stabilization occurs as development proceeds to increase the component (organ) number, in contrast from the intuition that the variation will be larger due to increasing number of possible states (arrangements).Electronic supplementary materialThe online version of this article (10.1007/s10265-018-1025-x) contains supplementary material, which is available to authorized users.

The representative phenotype is, in most cases, unique to the species or genus level, despite intraspecific differences of average phenotype among populations. The type of variation shown by the statistical quantities indicates not only the robustness of the morphologies but also how flowering plants changed during evolution among representative phenotypes that eventually led to phylogenetic diversification.

We thank the Kuwagata family, S. Maeda and K. Horibe for their support in field work.

Floral phyllotaxis is a relatively robust phenotype; trimerous and pentamerous arrangements are widely observed in monocots and core eudicots. Conversely, it also shows variability in some angiosperm clades such as ‘ANA’ grade (Amborellales, Nymphaeales, and Austrobaileyales), magnoliids, and Ranunculales. Regardless of the phylogenetic relationship, however, phyllotactic pattern formation appears to be a common process. What are the causes of the variability in floral phyllotaxis and how has the variation of floral phyllotaxis contributed to floral diversity? In this review, I summarize recent progress in studies on two related fields to develop answers to these questions. First, it is known that molecular and cellular stochasticity are inevitably found in biological systems, including plant development. Organisms deal with molecular stochasticity in several ways, such as dampening noise through gene networks or maintaining function through cellular redundancy. Recent studies on molecular and cellular stochasticity suggest that stochasticity is not always detrimental to plants and that it is also essential in development. Second, studies on vegetative and inflorescence phyllotaxis have shown that plants often exhibit variability and flexibility in phenotypes. Three types of phyllotaxis variations are observed, namely, fluctuation around the mean, transition between regular patterns, and a transient irregular organ arrangement called permutation. Computer models have demonstrated that stochasticity in the phyllotactic pattern formation plays a role in pattern transitions and irregularities. Variations are also found in the number and positioning of floral organs, although it is not known whether such variations provide any functional advantages. Two ways of diversification may be involved in angiosperm floral evolution: precise regulation of organ position and identity that leads to further specialization of organs and organ redundancy that leads to flexibility in floral phyllotaxis.