Primary longitudinal resin canals in lodgepole pine occur in Fibonacci numbers

Abstract

Primary (nontraumatic) longitudinal resin canals (RCs) in immature (expanding) and mature stems of lodgepole pine (Pinus contorta Dougl. ex Loud. var. latifolia Engelm.) were found to occur in Fibonacci (F) numbers (specifically 5, 8, 13, and 21). The most commonly observed number of RCs in immature stem circumferences was 13 (53% of all immature stems surveyed), but 8, 21, and 5 were also observed in decreasing order of prevalence, respectively. In general, the greater the immature stem diameter, the higher the F number of the RCs. However, branch order appeared to have the greatest effect on the number of RCs. Specifically, the leader (1° axis) generally had 21 RCs in the terminal bud and 13 in the lateral buds. All other terminal axes (i.e., 2°, 3°, 4°) tended to 13, while associated lateral axes tended to 8. The same general relationships between number of RCs, stem diameter, and branch order were also observed for mature (woody) branchlets of lodgepole pine, for example, 13 RCs were also the most prevalent F number observed (i.e., in 48% of the observed branchlets). The phyllotactic chirality was also assessed for mature branch samples. A tree tends to retain a phyllotactic chirality (or handedness) as branch order increases, despite decreases in the number of RCs from 21 to 5 from low to high branch orders. The implication of these findings to helical phyllotactic development in conifers is discussed.Key words: Fibonacci numbers, resin canals, lodgepole pine, Pinus contorta var. latifolia, phyllotaxis.