An economic principle for regulating rhythms of plants

Supposing that rhythms as biological events must be teleologically regulated, the phase relations of the rhythms in the leaf movement of Canavalia ensiformis, exposed to periodical light-darkness changes, are investigated. Pergressive Fourier analysis is applied because it is especially suitable for such analyses. In order to understand the demonstration, a short description of this method is given. It is a variant of the Schuster method, developing at the end of the last century. It is demonstrated in particular that the three parameters of a sine function can be calculated. The key for this calculation is a parallel effect in the phase diagram by which it is possible to calculate the period T of a sine even if the analysis interval p is not a whole-numbered multiple of the period T. Because this parallel effect occurs even if the parameters of a sine have more or less great random oscillations, a heuristic principle is defined for revealing sine-like rhythms hidden in a curve or data. Its approximation to the analyzed curve or data can be calculated by an application of the method of the error squares of Gauss or by drawing. By applying this method it is demonstrated that the leaf movement of Canavalia ensiformis follows an economic principle if the plant is exposed to artificial changes of light and darkness of different periods. The rhythm with the weaker amplitude is so regulated by the stronger rhythm that extreme values coincide as much as possible. By such movement of the leaves the plant applies the smallest amount of mechanical energy, to produce the weaker rhythm simultaneously with the stronger.