Species-dependent appearance of spiral pentamery and whorled trimery
For five-tepaled flowers, almost all flowers underwent a unique aestivation type (n = 20,286 among 20,287 five-tepaled Anemone flowers). That is, the flowers were quincuncial type 5-I (Fig. 3a), which is consistent with spiral initiation of organ primordia during floral development (Ren et al. 2010). For flowers with six tepals, we examined the frequency of aestivation types. The most frequent aestivation type was type 6-II, except for the A. × hybrida pale pink form, which exhibited the type 6-IV arrangement most frequently (Fig. 3a, b), as reported previously (Kitazawa and Fujimoto 2016b). Notably, whether pentamerous, quincuncial (type 5-I), or trimerous double whorls (type 6-II) was more frequent was species-dependent: quincuncial in A. nikoensis, A. flaccida, and A. × hybrida deep pink and pale pink and trimerous double whorls in A. hepatica, A. soyensis, and Pulsatilla cernua (Fig. 3a). The frequencies of quincuncial and type 6-II were nearly equivalent in A. × hybrida white. The normalized frequency of pentamerous quincuncial further varied among the four observed plant types: A. × hybrida deep pink (99%), A. nikoensis (78%), A. flaccida (59%), and A. × hybrida pale pink (37%).
Limited aestivation in six-tepaled flowers
In species showing higher frequency of type 6-II than quincuncial (A. soyensis, A. hepatica, and P. cernua), the frequency of type 6-II normalized to that of six-tepaled flowers was more than 90%, indicating outstanding robustness of type 6-II (Fig. 3a). On the other hand, in those showing equal or higher frequency of quincuncial (type 5-I) than type 6-II (A. flaccida, A. nikoensis, and A. × hybrida), types 6-I and 6-IV also appeared at comparable frequency to type 6-II, whereas the other two aestivation types (types 6-III and 6-V) were rare as reported previously (Kitazawa and Fujimoto 2016b; Fig. 3a, b). We confirmed the constrained appearance to three aestivation types of six-tepaled flowers by measuring a four times larger sample size (~ 9 × 103 six-tepaled flowers in all populations of observed species; Fig. 1) than in the previous report. These three types (types 6-I, 6-II, and 6-IV) dominated 99.3% of the six tepaled-flowers in all the observed species and forms (Fig. 3b). The frequency rank of the three types was type 6-II, type 6-IV, and type 6-I in ascending order for A. nikoensis and A. × hybrida white, whereas this order was types 6-II, 6-I, and 6-IV for A. flaccida and types 6-IV, 6-II, and 6-I for A. × hybrida pale pink. Therefore, six-tepaled flowers of pentamerous species (A. flaccida, A. nikoensis, and A. × hybrida) exhibited limited variation of three aestivation types in a species- and form-dependent manner, while five-tepaled flowers of trimerous species (A. soyensis, A. hepatica, and P. cernua) were uniquely quincuncial.
Limited aestivation in seven-tepaled flowers
As a consequence of limited aestivation of flowers with six tepals, we analyzed the aestivation of seven-tepaled flowers that co-exist with the five- and six-tepaled flowers in wild populations (Fig. 3c). Geometrically, there are ten possible aestivation types for seven-tepaled flowers (Fig. 1 lower row and Fig. S1). Even when we assume that the flowers with seven tepals are generated by adding two tepals to the inside of the quincuncial aestivation of five-tepaled flowers, six possible aestivation types remain (lower row in Fig. 1). Intriguingly, we found that two aestivation types (types 7-II and 7-V) appeared much more frequently than the other four types, dominating 98.3% of the seven-tepaled flowers in all observed species and forms (Fig. 3d). In addition, the frequency ratio of type 7-II to type 7-V was greater than 5, indicating outstanding robustness of type 7-II in all species and forms, except for A. nikoensis, where this frequency ratio was approximately 1.5, indicating similar robustness of the two aestivation types.
A model for spiral phyllotaxis with stochasticity reproduced limited variation of Anemone tepal arrangements
To understand the developmental mechanisms of the limited positions of sixth and seventh tepals, we first examined the arrangements of the six tepals at the time when the sixth tepal appeared after the quincuncial arrangement in a phyllotaxis model using computational analysis (Fig. 2). The simplest case includes a divergence angle φ = 144° and no growth (VT = 0; Fig. 4a), since the first five tepals are placed in the regular pentagon. The computational simulation was consistent with intuitive expectation. That is, the five possible arrangements of the six tepals appeared with equal probability (φ = 144° in Fig. 4a). The dependency on φ without growth was also consistent with a previous theoretical study based on the energy landscape (Eq. 2; Kitazawa and Fujimoto 2016b). Three of the arrangements (types 6-I, 6-II, and 6-IV) observed in Anemone (Fig. 3a, b) appeared when φ < 144°, whereas the other two (types 6-III and 6-V) appeared when φ > 144° (Fig. 4a). Next, we checked the position of the seventh tepal for each arrangement and found that the seventh tepal position was also limited. Two arrangements (types 7-II and 7-V) that were dominant in Anemone (Fig. 3c, d), occupied nearly all the arrangements at φ < 144°, despite the six possible arrangements of seven tepals initiating from the quincuncial arrangement (Fig. 1, bottom row). At φ > 144°, the two arrangements decrease in frequency, and type 7-III, which was virtually not observed for Anemone (Fig. 3c, d), becomes dominant, increasing in frequency as φ gets larger (Fig. 4a). Type 7-IV (rank 3 except for A. hepatica) appeared and increased to a frequency of up to 6% when φ was approximately 144° (maximum value at φ = 146°) but decreased as φ was further increased. Type 7-I (rank 3 in A. hepatica and rank 4 in A. nikoensis) appeared at a very low frequency (maximum 1.4% at φ = 126°), decreased as φ neared 144, and then increased again (0.8% when φ = 156°). Type 7-VI (not observed in Anemone) was consistently nearly absent (0.4% at φ = 154° was the maximum) throughout the parameter range examined. Therefore, we conclude that the dominant frequency of types 7-II and 7-V for seven-tepaled flowers as well as types 6-I, 6-II, and 6-IV for six-tepaled flowers is a natural consequence of spiral phyllotaxis with φ < 144°.
Next, we examined the dependency of centrifugal displacement due to growth VT (Fig. 4b). For the sixth tepal arrangements, as VT gets larger, the fraction of type 6-II increased until VT = 4 and then decreased as VT increased further. At the same time, the fraction of type 6-III increased, while the fraction of type 6-IV did not change and the fraction of type 6-I decreased to 10–20% at VT = 1. The position of the seventh tepal showed higher variation than for the case when VT = 0. For example, the position of the seventh tepal subsequent to the arrangement type 6-IV converged to two arrangements (types 7-II and 7-V), but another arrangement (type 7-IV) also appeared when VT was larger than 4 (Fig. 4b). Overall, as VT increased, a higher degree of variation in the arrangements with seven-tepaled flowers was observed. Therefore, the arrangements with seven tepals were limited to two dominant types (types 7-II and 7-V) at small VT but were more varied as VT increased.
Finally, we examined the dependency of arrangements on another parameter, α representing thedifference of inhibitory effect due to growth progression on pre-existing organs (Fig. 4c; see “Materials and Methods” for definition of α). The limitation to three types (types 6-I, 6-II, and 6-IV) in Anemone flowers with six tepals and two types (types 7-II and 7-V) in those with seven tepals was reproduced for 0.05 ≲ α ≲ 0.1. As α represents a bias of inhibitory effect according to the tepal indices (Eq. 2), negative α had an effect similar to that of VT: For the flowers with six tepals, as α decreased, the fraction of type 6-III increased, similar to the case when VT increased, while rank of types 6-II, 6-IV, and 6-I in six-tepaled arrangements remained at 1, 2, and 3, respectively (Fig. 4c), The arrangements with seven tepals were more variable when α was small, as in the case when VT was larger. On the other hand, as α increased, the fraction of type 6-I increased, changing its rank among arrangements of six tepals from 3 to 2 and 1 (see α > − 0.2 in Fig. 4c), consistent with a previous study (Kitazawa and Fujimoto 2016b). In the arrangement with the seventh tepal, type 7-V was most dominant above a positive threshold value of α ~ 0.1, whereas the fraction of type 7-I subsequently increased to be the most dominant arrangement as α further increased. Of the parameter range examined, a positive α is the only condition for which the arrangement type 7-I appeared. In summary, a larger VT and smaller negative α cause greater variation in arrangements; therefore, the arrangements are not limited to a small number of types. A larger space between primordia caused by larger VT and a decrease of inhibition due to negative α both decrease the roughness of the energy landscape, resulting in gently sloping probability density over the edge of the floral meristem. Hence, limitation to small number of arrangement types implies that the development proceeds in compact packing of organ primordia.