Aberrant phyllotactic patterns in cones of some conifers: a quantitative study

Veronika Fierz


The scale patterns of 6000 cones from one single tree of Pinus nigra Arn. have been examined. Apart from the main Fibonacci pattern with 8 and 13 parastichies, nine aberrant spiral patterns with Fibonacci-type sequences have been found. They are quite rare and occur with different frequencies. The parastichy quotient 8/13 of the prevalent pattern is very close to the golden ratio 0.618. In case of the black pine  it appeared that the greater the deviation of the parastichy quotient m/n from 0.618, the rarer the pattern. Similar results obtained for the sample of 1506 cones collected from three individual trees of larch (Larix decidua Mill.) suggest a true correlation between the frequency of a pattern and the deviation of its parastichy quotient from the golden ratio.


phyllotaxis; phyllotactic diversity; Pinus nigra Arn.; Larix decidua Mill.; rare cone patterns; Fibonacci-type sequences; golden ratio

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Jean RV. Phyllotaxis: a systemic study in plant morphogenesis. Cambridge: Cambridge University Press; 1994. http://dx.doi.org/10.1017/CBO9780511666933

Zagórska-Marek B. Phyllotactic diversity in Magnolia flowers. Acta Soc Bot Pol. 1994;63(2):117–137. http://dx.doi.org/10.5586/asbp.1994.017

Gola E. Phyllotaxis diversity in Lycopodium clavatum L. and Lycopodium annotinum L. Acta Soc Bot Pol. 1996;65(3–4):235–247. http://dx.doi.org/10.5586/asbp.1996.036

Szpak M, Zagórska-Marek B. Phyllotaxis instability – exploring the depths of first available space. Acta Soc Bot Pol. 2011;80(4):279–284. http://dx.doi.org/10.5586/asbp.2011.043

Wiss D, Zagórska-Marek B. Geometric patterns of the apical meristem and the quality of phyllotactic patterns in Magnolia flowers. Acta Soc Bot Pol. 2012;81(3):203–216. http://dx.doi.org/10.5586/asbp.2012.029

Braun A. Vergleichende Untersuchung über die Ordnung der Schuppen an den Tannenzapfen als Einleitung zur Untersuchung der Blattstellung überhaupt. Bonn: Thormann; 1831. http://dx.doi.org/10.5962/bhl.title.69200

Zagórska-Marek B. Phyllotactic patterns and transitions in Abies balsamea. Can J Bot 1985;63(10):1844–1854. http://dx.doi.org/10.1139/b85-259

Vakarelov II. Changes in phyllotactic pattern structure in Pinus L. due to changes in altitude. In: Jean RV, Barabé D, editors. Symmetry in plants. Singapore: World Scient. Press; 1998. p. 213–230. http://dx.doi.org/10.1142/9789814261074_0009

Reinhardt D, Pesce ER, Stieger P, Mandel T, Baltensperger K, Bennett M, et al. Regulation of phyllotaxis by polar auxin transport. Nature. 2003;426,255–260. http://dx.doi.org/10.1038/nature02081

Traas J. Phyllotaxis. Development. 2013;140:249–253. http://dx.doi.org/10.1242/dev.074740

Besnard F, Refahi Y, Morin V, Marteaux B, Brunoud G, Chambrier P, et al. Cytokinin signalling inhibitory fields provide robustness to phyllotaxis. Nature. 2014;505:417–421. http://dx.doi.org/10.1038/nature12791

Zagórska-Marek B, Szpak M. Virtual phyllotaxis and real plant model cases. Funct Plant Biol. 2008;35(10):1025–1033. http://dx.doi.org/10.1071/FP08076

Gola E. Phyllotactic spectra in cacti: Mammillaria species and some genera from Rebutia group. Acta Soc Bot Pol. 1997;66(3–4):237–257. http://dx.doi.org/10.1071/FP08076

Rutishauser R. Plastochrone ratio and leaf arc as parameters of a quantitative phxllotaxis analysis in vascular plants. In: Jean RV, Barabé D, editors. Symmetry in plants. Singapore: World Scient. Press; 1998. p. 171–212. http://dx.doi.org/10.1142/9789814261074_0009

DOI: https://doi.org/10.5586/asbp.2015.025

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