Modelling the growth of plants with a uniform growth logistics.
OBJECTIVE
The increment model has previously been used to describe the growth of plants in general. Here, we examine how the same logistics enables the development of different superstructures.


METHODS
Data from the literature are analyzed with the increment model. Increments are growth-invariant molecular clusters, treated as heuristic particles. This approach formulates the law of mass action for multi-component systems, describing the general properties of superstructures which are optimized via relaxation processes.


RESULTS
The daily growth patterns of hypocotyls can be reproduced implying predetermined growth invariant model parameters. In various species, the coordinated formation and death of fine roots are modeled successfully. Their biphasic annual growth follows distinct morphological programs but both use the same logistics. In tropical forests, distributions of the diameter in breast height of trees of different species adhere to the same pattern. Beyond structural fluctuations, competition and cooperation within and between the species may drive optimization.


CONCLUSIONS
All superstructures of plants examined so far could be reproduced with our approach. With genetically encoded growth-invariant model parameters (interaction with the environment included) perfect morphological development runs embedded in the uniform logistics of the increment model.
Abteilung Experimentelle Physik, Universität Ulm, Albert-Einstein Allee 11, 89069 Ulm, Germany. Electronic address: hanns-georg.kilian@uni-ulm.de.
H G
HG
Kilian
Klinik für Strahlentherapie, Universitätsklinikum Ulm, Albert-Einstein-Allee 23, 89081 Ulm, Germany. Electronic address: detlef.bartkowiak@uniklinik-ulm.de.
D
D
Bartkowiak
Institut für Systematische Botanik und Ökologie, Universität Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany. Electronic address: marian.kazda@uni-ulm.de.
M
M
Kazda
Institut für Humangenetik, Universitätsklinikum Ulm, Albert-Einstein-Allee 11, 89081 Ulm, Germany. Electronic address: dieter.h.kaufmann@uni-ulm.de.
D
D
Kaufmann
D017360:Arabidopsis / Q000254:growth & development; D029964:Fagus / Q000254:growth & development; D065928:Forests; D018546:Hypocotyl / Q000254:growth & development; D008954:Models, Biological; D028222:Picea / Q000254:growth & development; D063245:Plant Development; D018517:Plant Roots / Q000254:growth & development; D027861:Prunus / Q000254:growth & development; D014329:Tropical Climate
Differentiation; Increment model; Law of mass action; Optimization; Superstructure