Size-dependent variation in plant form Karl J. Niklas, Edward D. Cobb  Current Biology  Volume 27, Issue 17, Pages R900-R905 (September 2017) DOI: 10.1016/j.cub.2017.02.007 Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 1 Effects of geometry and shape on the performance of biological functions. (A,B) Bivariate plots of log10-transformed data for cell surface area and carbon content versus cell volume (for data, Niklas 2015). (A) Cell surface area versus volume of heterotrophs (n = 159), autotrophs (algae, n = 308), and the filamentous green alga Spirogyra (n = 10). (B) Cell carbon content versus the volume of unicellular heterotrophs (n = 21) and autotrophs (algae, n = 125). Dashed black lines indicate a one-to-one correspondence between the variables of interest (i.e., the scaling exponent α = 1/1); solid black lines denote regression curves; dashed blue line (in A) denotes the scaling relationship when size increases but neither geometry nor shape change (α = 2/3). The numerical values for the scaling exponents for the data are shown as numbers rather than fractions. The data are taken from the primary literature. (C–F) Bivariate plots of the quotient of projected surface area Sp and total surface area S versus the degree of incident light θ for different geometries and shapes. (C) Sp/S versus θ for oblate spheroids. (D) Sp/S versus θ for prolate spheroids. (E) Sp/S versus θ for cylinders differing in shape. (F) Bivariate plot of light interception LI versus differing aspect ratios for oblate and prolate spheroids and cylinders. LI is computed by integrating the area under Sp/S versus θ. Current Biology 2017 27, R900-R905DOI: (10.1016/j.cub.2017.02.007) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 2 Convergent evolution on light interception using spheroids and cylinders. Two examples of plants composed of light intercepting spheroids attached to circular columns or beams. (A) The unicellular (coenocytic) marine alga Caulerpa racemosa. (B,C) The angiosperms Sedum hernandezii and Senecio rowleyanus, respectively. Bar scales = 1 cm. Current Biology 2017 27, R900-R905DOI: (10.1016/j.cub.2017.02.007) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 3 Predicting the best arrangements for leaves on a stem. The results of computer simulations using six parameters (A) predicting the amount of light energy (expressed in Watt-hrs.) intercepted by stems differing in intermodal length (B) or the same stem elevating leaves differing in morphology (C–E). The six parameters are leaf lamina width W and length L, petiole length l, the distance between successive leaves d (internode distance), the leaf deflection angle from the vertical ϕ, and the rotational angle between successive leaves θ (the phylotactic or divergence angle). Total leaf areas are equivalent in all simulations. Although changes in any of the six parameters can yield nearly comparable capacities for light interception, the optimal leaf rotational angle θ is approximately 137.5° (shown as a line running along the ‘crest’ in each simulation). Current Biology 2017 27, R900-R905DOI: (10.1016/j.cub.2017.02.007) Copyright © 2017 Elsevier Ltd Terms and Conditions

Figure 4 Simulations of early land plant forms. The results of computer simulations using six parameters (A) predicting the phenotypes that optimize intercepting light, maintaining mechanical stability, conserving water, and dispersing windborne spores simultaneously. (B) Phenotypes with equal branching are simulated using only three parameters: the probability of branching P, the bifurcation angle ϕ, and the rotation angle γ. Phenotypes with unequal branching require six parameters (e.g., f1 and f2). An additional two (or four) parameters are required to simulate axes of different length and diameter (not shown). The results of these and other simulations indicate that the number of optimal phenotypes exceeds that of the phenotypes that can maximize the performance of any one of the four functional obligations (see Niklas 1994). Current Biology 2017 27, R900-R905DOI: (10.1016/j.cub.2017.02.007) Copyright © 2017 Elsevier Ltd Terms and Conditions