The Possible and the Actual in Phyllotaxis: Bridging the Gap between Empirical Observations and Iterative Models

Hotton, Scott; Johnson, Valerie; Wilbarger, Jessica; Zwieniecki, Kajetan; Atela, Pau; Golé, Christophe; Dumais, Jacques

doi:10.1007/s00344-006-0067-9

Cited by 43 publications

(55 citation statements)

References 26 publications

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“…Other authors observed similar concordance using different plant model systems (Couder 1998;Hotton et al 2006;Smith et al 2006b;Hellwig et al 2008). The new development in our model application is that, sometimes, there is more than one initiation site available for an emerging primordium.…”

Section: Conclusion and Future Goalssupporting

confidence: 52%

Virtual phyllotaxis and real plant model cases

Zagórska‐Marek

Szpak

2008

Functional Plant Biol.

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Abstract. Phyllotactic pattern results from genetic control of lateral primordia size (physiological or physical) relative to the size of organogenic lateral surface of shoot apical meristem (SAM). In order to understand the diversity of patterns and ontogenetic transitions of phyllotaxis we have developed a geometric model allowing changes of the above proportion in a computer simulation of SAM's growth. The results of serial simulations confirmed that many phyllotactic patterns (including most esoteric ones) and ontogenetic transitions known from real plant model cases can be easily obtained in silico. Properties of virtual patterns often deviated from those of ideal mathematical lattices but closely resembled those of the natural ones. This proved the assumptions of the model, such as initiation in the first available space or ontogenetic changes in primordia size, to be quite realistic. Confrontation of simulation results with some sequences of real phyllotactic patterns (case study Verbena) questions the autonomy of SAM in its organogenic activity and suggests the involvement of unknown signal positioning primordia in a non-random manner in the first available space.

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Section: Conclusion and Future Goalssupporting

confidence: 52%

Virtual phyllotaxis and real plant model cases

Zagórska‐Marek

Szpak

2008

Functional Plant Biol.

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“…In our model, the sizes of the fields are visualized by the geometric sizes of primordia packed on the shoot apical meristem's surface. This simple representation already used by other authors [55] allowed us to analyze the longrange effects of the changes in the field size for phyllotaxis. We have obtained a whole palette of possible transformations of phyllotaxis including those associated in many plant species with the developmental phase shift.…”

Section: Discussionmentioning

confidence: 99%

The significance of γ-and λ-dislocations in transient states of phyllotaxis: how to get more from less – sometimes!

Zagórska‐Marek

Szpak

2016

Acta Soc Bot Pol

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In some plants, developmental changes of phyllotaxis are so frequent that the whole spectrum of phyllotactic patterns becomes available for investigation and thus many unknown subtleties of phyllotaxis come to light. Among these, Magnolia acuminata is the most prominent. In a series of experiments performed in silico with application of a simple geometric model of phyllotaxis, we were able to confront the empirical data on phyllotactic transitions occurring in magnolia flowers with the results of computer simulations. They revealed that in addition to the ratio between the sizes of plant organs, the history of developing pattern was also important, especially for the direction of ontogenetic changes. The parameters of size tolerance and vertical tolerance in positioning a new element in the first available space, brought the effects of simulations closer to the real patterns. They helped especially to resolve the enigma of multiplication of parastichies (γ-dislocations) observed sometimes during determined growth of magnolia floral axes. We conclude that ontogenetic changes in phyllotaxis result mainly from changing sizes of organs in the course of development and that the changes do not always occur with mathematical accuracy.

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“…To analyze the phyllotactic patterns and their transitions, we make use of the concept of primordia fronts, which can be seen as the latest layer of primordia formed in the peripheral zone of the meristem [6,22]. These fronts can be represented by the zigzagging lines joining the centers of disk-shaped primordia (Fig.…”

Section: Developmental Dynamics Behind Phyllotactic Patternsmentioning

confidence: 99%

“…Informally, a front is the ring formed by the most recent primordia around the apical meristem at a given instant of the growth [22]. It includes all the necessary information for the positioning of the next primordium, and not more.…”

Section: Fronts and Their Parastichy Numbersmentioning

confidence: 99%

Fibonacci or quasi-symmetric phyllotaxis. Part I: why?

2016

Self Cite

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The study of phyllotaxis has focused on seeking explanations for the occurrence of consecutive Fibonacci numbers in the number of helices paving the stems of plants in the two opposite directions. Using the disk-accretion model, first introduced by Schwendener and justified by modern biological studies, we observe two distinct types of solutions: the classical Fibonacci-like ones, and also more irregular configurations exhibiting nearly equal number of helices in a quasi-square packing, the quasi-symmetric ones, which are a generalization of the whorled patterns. Defining new geometric tools allowing to work with irregular patterns and local transitions, we provide simple explanations for the emergence of these two states within the same elementary model. A companion paper will provide a wide array of plant data analyses that support our view.

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The Possible and the Actual in Phyllotaxis: Bridging the Gap between Empirical Observations and Iterative Models

Cited by 43 publications

References 26 publications

Virtual phyllotaxis and real plant model cases

Virtual phyllotaxis and real plant model cases

The significance of γ-and λ-dislocations in transient states of phyllotaxis: how to get more from less – sometimes!

Fibonacci or quasi-symmetric phyllotaxis. Part I: why?

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