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On the Structure-Bounded Growth Processes in Plant Populations

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Abstract

If growing cells in plants are considered to be composed of increments (ICs) an extended version of the law of mass action can be formulated. It evidences that growth of plants runs optimal if the reaction–entropy term (entropy times the absolute temperature) matches the contact energy of ICs. Since these energies are small, thermal molecular movements facilitate via relaxation the removal of structure disturbances. Stem diameter distributions exhibit extra fluctuations likely to be caused by permanent constraints. Since the signal–response system enables in principle perfect optimization only within finite-sized cell ensembles, plants comprising relatively large cell numbers form a network of size-limited subsystems. The maximal number of these constituents depends both on genetic and environmental factors. Accounting for logistical structure–dynamics interrelations, equations can be formulated to describe the bimodal growth curves of very different plants. The reproduction of the S-bended growth curves verifies that the relaxation modes with a broad structure-controlled distribution freeze successively until finally growth is fully blocked thus bringing about “continuous solidification”.

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Authors and Affiliations

  1. Abteilung Experimentelle Physik, Universität Ulm, Albert-Einstein Allee 11, 89069, Ulm, Germany

    H. G. Kilian

  2. Institut für Systematische Botanik und Ökologie, Universität Ulm, Albert-Einstein Allee 11, 89069, Ulm, Germany

    M. Kazda

  3. Institut für Reine Mathematik, Universität Ulm, Helmholtzstraße 18, 89081, Ulm, Germany

    F. Király

  4. Institut für Humangenetik, Universitätsklinik, Albert-Einstein Allee 11, 89081, Ulm, Germany

    D. Kaufmann

  5. Max-Planck-Institut für Metallforschung, Heisenbergstr. 3, 70569, Stuttgart, Germany

    R. Kemkemer

  6. Klinik für Strahlentherapie und Radioonkologie, Universitätsklinikum, Albert-Einstein-Allee 23, 89081, Ulm, Germany

    D. Bartkowiak

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  1. H. G. Kilian
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  6. D. Bartkowiak
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Correspondence to H. G. Kilian.

Appendix

Appendix

Growth curves are calculated with Eq. 10. For biomass the parameter p was set equal to 3 while height was characterized by p = 1. All parameters except from p were assigned their values by educated guess and subsequent manual optimization.

To describe dbh or height distributions, Eq. 1 was subjected to an iterative non-linear fit procedure (Excel Solver). During iterations at constant values for ξ and y min the parameters p and βΔu 0 were modified until the deviation reduction converged towards 0.0001. These fits incorporate aberrant data points. To quantify this, we use the parameter γ which relates all deviations from the ideal size-distribution to the total plant mass.

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Kilian, H.G., Kazda, M., Király, F. et al. On the Structure-Bounded Growth Processes in Plant Populations. Cell Biochem Biophys 57, 87–100 (2010). https://doi.org/10.1007/s12013-010-9087-y

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