Photo-sensitive “flip-flop” characteristics of the developing Narcissus plant (daffodil phototropism)

Abstract

Main conclusion

The developing Narcissus pseudonarcissus plant (daffodil) is shown to face towards a preferential direction (east, south, west, or north, in that order) before flowering. Said directionality is accomplished by stem bending, a phototropic response mechanism, which is sensitive to partial blocking of the available sunlight from the local environmental.

Abstract

Polar distribution diagrams show that with partial environmental shading from the north, east, south, or west, the developing daffodil plant always excludes facing in that direction, to absorb maximum available sunlight. Stem buckling experiments, equivalent to stem bending, are presented measuring the Euler buckling exponent n =  − 2.1 for daffodil flower stems, in good agreement with theory, r = 0.99. Individual flower stems are capable of generating 2–3 lbf of vertical force, which explains the plants ability to penetrate frozen ground cover. Results from 193 daffodil flower stems are presented, showing that 61.7% face East [95% CI 54–70%], 17.1% face South, 15.0% face West, and only 6.2% face North [95% CI 2–10%], depending strongly on the partial shading effect of the surrounding environment.

Appendix 1: Euler stem buckling experiments and equations

For a column of length L, Young’s modulus E, cross-sectional moment of inertia I, uniform properties along column length (i.e. uniform modulus and cross-section) the critical unclamped buckling load F_crit is given by (Greene and Greene 2017):

$$ F_{{{\text{crit}}}} = \pi^{2} \times EI/(L^{2} ), $$

(1)

where F_crit  is the axial buckling force, E  is the Young's modulus of elasticity, I  is the  moment of inertia, and L  is the column length.

For columns that are tapered along the length ( the entasis factor) (as is the situation with Narcissus flower stems) the mechanics are considerably more complicated, beyond the scope of this report.

The moment of inertia I for bending and buckling of a hollow column is given by:

$$ I = \pi \times (R^{3} )\Delta R, $$

(2)

where I is the  moment of inertia of the tube, R  is the  average tube radius, ΔR  is the  tube wall thickness.

Experimental data from three daffodil flower stalks yields the force–length curve shown in Fig. 2. Euler buckling load F_crit is graphed vs. column length L, units of [inches], Euler exponent n =  − 2.1, correlation r = 0.99.

In a previous report (Greene and Greene 2017), we measured an Euler buckling exponent of − 1.9 to − 2.2 for the Taraxacum plant (dandelion), in excellent agreement with the Euler exponent n =  2.0 (Eq. 1). Experimental data from the tapered daffodil stems indicate an Euler exponent of n =  − 2.1 (Fig. 2), somewhat greater than the classical result of  − 2.0, perhaps as a result of column tapering along the length. Variable column tapering in cross-section is referred to as entasis.