A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling

Abstract

As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. Scenedesmus obliquus, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.

Interaction among Hydrological, Environmental, and Ecological Processes in Aquatic Ecosystems

“…However, this method depends on prior knowledge of the nominal values of the model parameters and largely ignores the uncertainty associated with the nominal values. Li and Zhang [3] designed a new method that coupled the traditional uniform and non-uniform sampling schedules by adopting the D-optimal design and Monte Carlo simulations. The new method could be effective for sampling schedule design in algae research.…”

Cumulative Effects of Physical, Chemical, and Biological Measures on Algae Growth Inhibition

“…In practice, measures for controlling HABs can be accomplished by manipulating various physical, chemical, and biological factors [11]. The effects of physical and chemical measures on algae growth have been primarily studied, and their applications are relatively broader [12,13]. The most direct physical method is separating out and harvesting the microalgal biomass [14].…”