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

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Abstract

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 r 2 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 <24.8 %. The period of the first harmonic was 13.4 days, which is very close to a circasemilunar rhythm (14.8 days). In summary, the predictive power of productivity models for continuous microalgal cultures can be dramatically improved with the inclusion of a biorhythm analysis.

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Abbreviations

μmax :

Maximum specific growth rate (day−1)

μn :

Specific growth rate in reactor n (day−1)

μs :

Hypothetical average system growth rate (day−1)

aI :

Coefficient of the cosine component of the kth harmonic (k = 1, 2, 3)

bI :

Coefficient of the sine component of the kth harmonic (k = 1, 2, 3)

CFSTR:

continuous-flow, stirred-tank reactors

Dn :

Local dilution rate for CFSTR n (day−1)

Ds :

System dilution rate (day−1)

En :

Elevation of the light source over CFSTRn (cm)

FD :

Factor representing the effect of Ds on growth rate

HISTAR:

Hydraulically integrated serial turbidostat algal reactor

Ia n(PAR):

Average scalar irradiance in CFSTR n (μmol photons m−2 s−1)

Iopt(PAR):

Optimal scalar irradiance (μmol photons m−2 s−1)

k:

Number of the harmonics

ken :

Decay rate in reactor n (day−1)

n:

Numerical position of the specific CFSTR in the series

N:

Total number of CFSTRs in HISTAR

ηt :

Residual daily biomass concentration unaccounted for by harmonics (g dry wt m−3)

P:

Periodic function that describes biorhythms

Pa :

Areal productivity of HISTAR (g m−2 day−1)

Padj :

Proportional influence of the biorhythms on microalgal growth

RI :

Residual biomass concentration at time t (g dry wt m−3)

\( \overline{R}\) :

Mid-point of the oscillations or mean of the residuals

t:

Time (days)

tadj :

Adjustment required to synchronize minimum p value with spring tide

T:

Total time (days)

Tp :

Period (days)

Vn :

Volume of CFSTRn (m3)

W(t):

Mass loading per time period

X8a :

Actual biomass concentration in CFSTR8 (g dry wt m–3)

X8p :

Predicted biomass concentration in CFSTR8 (g dry wt m–3)

Xn :

Concentration of biomass in CFSTR n (g dry wt m–3)

Yo :

Mid-point of the oscillations or mean

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Authors and Affiliations

  1. Department of Renewable Resources, University of Louisiana at Lafayette, Lafayette, LA, 70504, USA

    Barbara C. Benson

  2. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA, 70803, USA

    Maria T. Gutierrez-Wing & Kelly A. Rusch

Authors
  1. Barbara C. Benson
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  2. Maria T. Gutierrez-Wing
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  3. Kelly A. Rusch
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Correspondence to Barbara C. Benson.

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Benson, B.C., Gutierrez-Wing, M.T. & Rusch, K.A. Application of the Fourier Method to Differentiate Biological Rhythms from Stochastic Processes in the Growth of Selenastrum capricornutum Printz: Implications for Model Development. J Appl Phycol 20, 103–111 (2008). https://doi.org/10.1007/s10811-007-9187-2

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