Mathematical modeling is one of the techniques used by botanists to understand the developmental processes of plants.
It can also be a tool in taxonomy. Scientists from Poland and Great Britain have created a proprietary mathematical model that allows the analysis of changes in the shape of leaves with parallel nerve.
To create the model, the results of experimental studies conducted on several species of orchids of the Epipactis genus growing naturally in Poland were used.
Mathematical modeling is a technique that allows you to reflect the studied object in the form, often simplified, in which it actually occurs. The model is therefore nothing more than a set of information about the properties of an object, expressed in the form of a mathematical notation – note the authors of the work, Dr. Anna Jakubska-Busse from the Faculty of Biological Sciences at the University of Wrocław and dr hab. Maciej Janowicz from the Warsaw University of Life Sciences.
As they add, this technique has long been used in natural sciences. Some scientists believe that the greatest advances in this area have come from careful analysis of simple models. This group also includes the outstanding theoretical physicist, Nobel laureate Albert Einstein, who used to say that the models should be as simple as possible, but not more.
As part of the cooperation, prof. Anna Jakubska-Busse with dr Jo Ashbourn from the University of Oxford (Great Britain) and dr hab. Maciej Janowicz, Dr. Luiza Ochnio, Dr. Beata Jackowska-Zduniak from the Warsaw University of Life Sciences, an original mathematical model was developed that allows the analysis of changes in the shape of leaves with parallel nerve.
The shape of leaves in plants is a variable feature, but in some systematic groups, incl. in orchids of the genus Epipactis, it is considered a diagnostic feature that allows the species to be identified. As this identification is not always easy, scientists set out to see if it was possible to verify the determinations made by researchers using an objective tool such as a mathematical model.
The model is based on the assumption that a leaf – like any other macroscopic natural object – can be the subject of research for continuum mechanics. Thus, from the point of view of its physical properties, a leaf can be treated in the same way as, for example, a piece of paper or a piece of clothing, regardless of its morphogenesis. This type of approach to the problems of statics and morphology of long leaves was proposed, among others, by Lakshminarayanan Mahadevan (Harvard University) with colleagues, who considered the leaf as a two-dimensional flexible shell, described by the so-called von Karman equations. Mahadevan’s method including differs from L-system modeling (Lindenmayer systems) in that it is directly related to basic physical properties of leaves, such as Young’s modulus or Poisson’s ratios, we read in a press release sent to PAP.
The method of describing leaves, developed by a team of scientists from the University of Wrocław, Warsaw University of Life Sciences and the University of Oxford, is also in line with the continuum mechanics. It differs from Mahadevan’s approach in that it directly takes into account both the anisotropy and the heterogeneity of long leaves, especially leaves with parallel nerve. This is achieved by using a model of coupled flexible rods instead of an isotropic coating. The fact that the physical properties of the leaves along the veins are different from their “cross” properties is built into the model from the very beginning, which is its novelty.