Abstract
It has been said that response of plants to environment is irregular and complicated. We have intuitively attributed the reason to complexity of living systems. In nonlinear systems, however, complex phenomena can be generated by simple rules. They are called chaos. So we examined whether irregular response of photosynthetic rate and growth rate are chaos. To measure accurately as many data as possible, six environmental factors were controlled in a small growth chamber. Air temperature, humidity, CO2 concentration and air pressure were changed by a computer while PAR (photosynthetically active radiation) and wind speed were kept constant. Photosynthetic rate and growth rate (measured by the diameter of the stem) were recorded as a function of time and chaotic nature of the time series data were analyzed. By calculating the correlation dimension, response of photosynthetic rate was identified as chaos. The correlation dimension of photosynthetic rate was 2.7±0.4 and that of growth rate was larger than -4.5.
Moreover to examine the chaotic nature of photosynthetic rate, predictions by four different models were compared. Two of the models are nonlinear models developed with neural networks and two are linear regression models. The models predict photosynthetic rate using four different environmental factors. One linear model and one nonlinear model included a factor of delay, which is represented by a variable of actual photosynthetic rate in one past step. Only the nonlinear model which included the factor of delay could predict unknown test samples well. No other models generated irregular patterns of photosynthetic rate. Therefore we concluded that photosynthetic rate behaves chaotically. Although we cannot forecast plants' response far into the future because of the chaotic nature, we can expect to control the growth by very few energy based on orbital instability of chaos.
