Fibonacci Series

Figure 5.7. The phyllotactic morphospace of Niklas (1997b). The two morphological-trait dimensions are the width/length ratio of leaves (y-axis of the morphospace), and the divergence angle between leaves arranged along a branch (x-axis). The vertical axis is the light-interception efficiency (z-axis) of the geometric permutations of leaf shape and arrangement in the morphospace. At the top of the figure are given the various leaf-divergence angles produced by a series of phyllotactic fractions; note that the higher fractions converge on the Fibonacci angle of 137.5°. Narrow, slender leaves arranged in Fibonacci angles along branches have the highest light-interception efficiencies; leaves with a nearly circular outline have much lower efficiencies, even arranged in Fibonacci angles, due to overlapping leaf outlines leading to shading.

Source: Artwork courtesy of K. J. Niklas. From Niklas (1997b); copyright © 1997 by the University of Chicago Press and reprinted with the permission of the publisher.

Divergence Angle, 6

Figure 5.7. The phyllotactic morphospace of Niklas (1997b). The two morphological-trait dimensions are the width/length ratio of leaves (y-axis of the morphospace), and the divergence angle between leaves arranged along a branch (x-axis). The vertical axis is the light-interception efficiency (z-axis) of the geometric permutations of leaf shape and arrangement in the morphospace. At the top of the figure are given the various leaf-divergence angles produced by a series of phyllotactic fractions; note that the higher fractions converge on the Fibonacci angle of 137.5°. Narrow, slender leaves arranged in Fibonacci angles along branches have the highest light-interception efficiencies; leaves with a nearly circular outline have much lower efficiencies, even arranged in Fibonacci angles, due to overlapping leaf outlines leading to shading.

Source: Artwork courtesy of K. J. Niklas. From Niklas (1997b); copyright © 1997 by the University of Chicago Press and reprinted with the permission of the publisher.

both leaf arrangement and leaf shape on light-interception efficiency. Using this morphospace of hypothetical leaf geometries, Niklas (1997b) demonstrated that leaves arranged in Fibonacci angles to one another along a branch do indeed produce the maximum light-interception efficiency — but only if those leaves are long and slender (Fig. 5.7).

In contrast, hypothetical plants with circular leaves may have leaf arrangements which deviate significantly from the Fibonacci angle, as leaf divergence angles of 137.5° convey only a slight increase in light-interception efficiency (Fig. 5.7).

In summary, both Figure 5.6 and Figure 5.7 illustrate actual adaptive landscapes, created using the analytical techniques of theoretical morphology. The theoretical morphospace in Figure 5.6 is one for branching geometries, and in Figure 5.7 is one for leaf geometries, but both have been converted to adaptive landscapes by adding the dimension of light-interception efficiency to the two morphological dimensions.

Simpson (1944, 1953) made the conceptual jump of modelling macro-evolutionary phenomena in geological time on adaptive landscapes, as discussed in Chapter 3. In the next chapter we shall actually analyse such phenomena through the usage of theoretical morphospaces.

Was this article helpful?

0 0

Post a comment