Petiole length in Boerhavia (Nyctaginaceae) approximates the golden ratio phi

  • Justin K. Williams Department of Biological Sciences, Sam Houston State University
Keywords: Boerhavia, Nyctaginaceae, Anisophylly, Anisoclady, C4, Golden Ratio, phi

Abstract

The leaves of Boerhavia exhibit anisophylly. It is here hypothesized that the scale of the uneven leaves exhibits a determined pattern, rather than an arbitrary difference in size. To test for this, the opposite petioles of Boerhavia diffusa and B. erecta from both regional and local populations were measured, and the ratio of the measurements were compared to the Golden Ratio. One-paired t-tests for a critical mean indicate that the ratios of paired petioles for both species are not statically different from the value 1.6180339887…. These tests indicate that petiole length in Boerhavia approximates the Golden Ratio. The significance of this observation is that the Golden Ratio is here expressed as a line segment rather than as a spiral, which is how the Golden Ratio has been previously observed and reported in plant growth.

References

Ajao, A.A., M.A. Jimoh, & S.A. Saheed. 2017. Studies on anatomical characters indicating C3 and C4 photosynthetic metabolism in the genus Boerhavia L. (Nyctaginaceae). Taiwania 62:265–271.

Cooke, T.J. 2006. Do Fibonacci numbers reveal the involvement of geometrical imperatives or biological interactions in phyllotaxis? Bot. J. Linn. Soc. 150:3–24. doi: 10.1111/j.1095-8339.2006.00490.x

Dengler, N.G. 1983. The developmental basis of anisophylly in Selaginella martensii. II. Histogenesis. Amer. J. Bot. 70(2):193–206. doi: 10.1002/j.1537-2197.1983.tb07858.x

Ekern, P.C. 1968. Phyllotaxy of pineapple plant and fruit. Bot. Gaz. 129:92–94. doi: 10.1086/336419

Fujita, H., K. Toyokura, K. Okada, & M. Kawaguchi. 2011. Reaction-diffusion pattern in shoot apical meristem of plants. PloS One 6(3):e18243. doi: 10.1371/journal.pone.0018243.

Heath, T.L. 1956. Euclid: The thirteen books of the elements. Dover Publications, New York, U.S.A.

Heimerl, A. 1901. Studien über einige Nyctaginaceen des Herbarium Delessert. Annuaire du Conservatoire et du Jardin botaniques de Genève. 5:177–197.

Hepworth, J. & M. Lenhard. 2014. Regulation of plant lateral-organ growth by modulating cell number and size. Curr. Opin. Plant Biol. 17:36–42. doi: 10.1016/j.pbi.2013.11.005

Keller, R. 2004. Identification of tropical woody plants in the absence of flowers and fruits: A field guide (2nd ed.). Birkhäuser Verlag, Basel, Boston, Berlin, Germany.

King, S., F. Beck, & U. Lüttge. 2004. On the mystery of the golden angle in phyllotaxis. Plant, Cell and Environ. 27:685–695. doi: 10.1111/j.1365-3040.2004.01185.x

Livio, M. 2003. The golden ratio: The story of phi, the world's most astonishing number. Broadway Books, New York, U.S.A.

Muelbert, A.E., I.G. Varassin, M.R. Torres Boeger, & R. Goldenberg. 2010. Incomplete lateral anisophylly in Miconia and Leandra (Melastomataceae): Inter- and intraspecific patterns of variation in leaf dimensions. J. Torrey Bot. Soc. 137:214–219. doi: 10.3159/09-RA-063R.1

Niklas, K.J. 1988. The role of phyllotatic pattern as a" developmental constraint" on the interception of light by leaf surfaces. Evolution 42:1–16. doi: 10.2307/2409111

Phillips, B.G. 1976. Anatomy and developmental morphology of Allionia L. (Nyctaginaceae). Ph.D. Dissertation, University of Arizona, U.S.A.

Powell, A. & M. Lenhard. 2012. Control of organ size in plants. Curr. Biol. 22:R360–R367. doi: 10.1016/j.cub.2012.02.010

Pratt, D.B. & L.G. Clark. 2010. Occurrence of anisophylly and anisoclady within the Amaranthaceae. J. Bot. Res. Inst. Texas 4:271–279.

Procher, R.D. 1978. Boerhavia diffusa L. (B. coccinea Mill.) (Nyctaginaceae) in the Carolinas. Castanea 43:172–174.

Okabe, T. 2015. Extraordinary accuracy in floret position of Helianthus annuus. Acta Societatis Botanicorum Poloniae 84:79–85. doi: 10.5586/asbp.2015.007

Turing, A.M. 1952. The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. 237:37–72. doi: 10.1098/rstb.1952.0012

Woodson, R.E., Jr., R.W. Schery, & H.J. Kidd. 1961. Nyctaginaceae. In: Flora of Panama. Ann. Missouri Bot. Gard. 48:51–65.

Published
2018-11-20
How to Cite
Williams, J. K. (2018). Petiole length in Boerhavia (Nyctaginaceae) approximates the golden ratio phi. Journal of the Botanical Research Institute of Texas, 12(2), 667-682. Retrieved from https://journals.brit.org/jbrit/article/view/967