Towards 3D basic theories of plant forms

Abstract

Allometric, metabolic, and biomechanical theories are the critical foundations for scientifically deciphering plant forms. Their concrete laws, however, are found to deviate for plenty of plant specimens. This phenomenon has not been extensively studied, due to technical restrictions. This bottleneck now can be overcome by the state-of-the-art three-dimensional (3D) mapping technologies, such as fine-scale terrestrial laser scanning. On these grounds, we proposed to reexamine the basic theories regarding plant forms, and then, we case validated the feasibility of upgrading them into 3D modes. As an in-time enlightening of 3D revolutionizing the related basic subject, our theoretical prospect further sorted out the potential challenges as the cutting points for advancing its future exploration, which may enable 3D reconstruction of the basic theories of plant forms and even boost life science.

Fig. 1. The background of inspiring a rethink of the basic theories of plant forms.

Illustration of (a) the TLS-collected point cloud and (b) characterized 3D structure of a woody plant, with the high potential for boosting reexaminations of the deviations from its related (c) allometric scaling laws, (d) metabolic scaling laws, and (e) biomechanical laws. Note that (a) and (b) were generated based on published TLS data and Quantitative Structure Model software, (c) was generated based on the published formulas of allometric scaling, (d) was generated by following the published formulas of metabolic scaling, i.e., scaling exponent = 1.131 for gross primary productivity, scaling exponent = 0.602 for gross photosynthesis ability, and scaling exponent = 3/4 ~ 1 as derived from the adapted WBE model, and (e) was generated in accordance to the published formulas of biomechanics (in terms of lean angle) before and after tree thinning. The integration of the five images that reflect the kernel aspects of 3D reexamining the basic theories of plant forms draws the schematic framework to guide future studies.

Fig. 2. The 3D mode transition for reexamining the basic theories of plant forms.

Illustration of the potential of proposing 3D allometric scaling for plants, via comparing, in principle, the effects of the (a) scalar—(length: A, B, C, and D) and (b) vector-parameter-based (length and orientation: A, B, C, and D) allometric scaling (s and s) characterizations that are based on the traditional and 3D-mode plant mapping technologies, respectively. The latter can open a new way for 3D upgrading the traditional allometric theory to adapt to the ecological analyses with the, in essence, vector-mode environmental forces such as solar radiance (R) and wind fields (W). Enabled by the proposed 3D theoretical framework, we found that the diameters of the trunk below branches are more correlated with the horizontal components of the first-level branches than themselves (c) vs. (d), for the samples of Sycamore (Acer pseudoplatanus, 180 first-level branches for all of its trees) and Beech (Fagus sylvatica, 104) tree species in the Wytham Woods, UK, as characterized by a comparison of the performance in terms of R².

Fig. 3. The principle feasibility of going towards 3D basic theories of plant forms.

Illustration of the principle framework for supportively advancing 3D basic theories of plant forms, after finding their laws with deviations (Fig. 1) and proposing vector parameters for characterizing the form-related functional traits and their driving forces (Fig. 2). In terms of carbon that is the basic element of composing plant forms and the coherent inner scaling relationships between their allometric, metabolic, and biomechanical aspects, exploring 3D growth space leads to branches growing in the form of vector, branches growing in the form of vector means 3D allometric scaling, 3D allometric scaling brings about 3D metabolic scaling, 3D metabolic scaling causes asymmetrical carbon allocating, asymmetrical carbon allocating gives rise to 3D biomechanical coordinating, and in the end back to where this cycle starts, 3D biomechanical coordinating alters growth vectors. Under this framework ranging from physical demand (left) to mechanism foundation (right), new 3D basic theories of plant forms can be comprehensively and systematically explored and developed.