Phyllotaxy, Magnolia, Fibonacci numbers, Magnolia x soulangiana 'Verbana', Fibonacci sequence
Spiral patterns in the arrangement of plant organs have interested scientists and mathematicians for centuries, but many gaps still remain in our understanding of these patterns' establishment. These spiral patterns can be quantified by counting the number of parallel spirals called parastichies wrapping clockwise and counter-clockwise around the shoot, and they have long been of interest because the number of parastichies in each direction are often successive members of the Fibonacci sequence which begins 1, 1, 2, 3, 5, 8, 13, 21. At different stages in plant development, these patterns can transition, resulting in changes to the parastichy numbers. While the geometry behind gradual transitions between pairs of parastichy numbers such as from (3, 5) to (5, 8) can be modeled successfully, more rapid transitions remain cannot be accommodated by existing models. In this work, I attempt to model rapid phyllotactic transitions as they appear in Magnolia x soulangiana 'Verbanica'. This species shows a clear and consistent transition from (3, 3) parastichies in the tepals to (8, 13) in the stamens immediately above. My model piles discs on a rectangular field to represent the placement of primordia in the peripheral zone of the meristem. To explore this, I ran sweeps across ranges of values for parameters representing the size of tepal primordia in relation to the width of the field, the difference in size between the tepal primordia and stamen primordia, and the amount of overlap in the tepal primordia. The model was able to produce rapid non-Fibonacci transitions such as (3,3) to (9,12) and somewhat rapid Fibonacci transitions such as (3,3) to (5,8) but could not produce the jump to (8,13). This reflects a need for modifications to the model.
Franz, Madeline Christine, "Modeling rapid phyllotactic transitions in Magnolia x soulangiana 'Verbanica'" (2015). Honors Project, Smith College, Northampton, MA.
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