Application of the Fourier Method to Differentiate Biological Rhythms from Stochastic Processes in the Growth of Selenastrum capricornutum Printz: Implications for Model Development

The biological rhythms of microalgal growth within a hydraulically integrated serial turbidostat algal reactor (HISTAR) were examined after comparison of a simple mechanistic productivity model with actual data yielded a standard error of prediction (SEP) of 62%. The data used for this study were taken on cultures of Selenastrum capricornutum grown under continuous 400-watt metal halide lighting. Fourier series analysis (up to five harmonics) was used to model the biorhythms and differentiate them from stochastic processes. Regression analyses revealed that the best Fourier series fit for the data was a three harmonic summation. Regression analyses on additional harmonic summations did not increase r2 by more than 1%. The three harmonics were summed and incorporated into the growth term of the simple model, and the resultant full model was calibrated. The mechanistic HISTAR productivity model was greatly enhanced by the addition of the biological rhythm component, resulting in a SEP of