Rule-based agents for forecasting algal population dynamics in freshwater lakes discovered by hybrid evolutionary algorithms
Introduction
Predictive agents for specific algal populations can be powerful tools for early warning and operational control of harmful algal blooms in lakes and drinking water reservoirs. One way of developing predictive agents for algal populations is the extraction of generic rules from ecological time-series data by means of evolutionary algorithms as suggested by Recknagel (2003).
This study demonstrates the development of rule-based agents from merged time-series data of lakes belonging to the same lake category by means of a hybrid evolutionary algorithm (HEA) and a rigorous k-fold cross-validation framework.
Three rule-based agents will be discussed and validated which are applicable for forecasting 5 to 7-days-ahead the concentration of chlorophyll-a in the warm monomictic and mesotrophic reservoirs Myponga and Happy Valley (Australia), the abundance of Microcystis in the shallow polymictic hypertrophic lakes Kasumigaura and Suwa (Japan) as well as the abundance of Oscillatoria in the shallow polymictic and hypertrophic lakes Veluwemeer and Wolderwijd (The Netherlands).
The resulting rule-based agents proved to be both explanatory and predictive. It has been demonstrated that the interpretation of the rules can be brought into the context of empirical and causal understanding of chlorophyll-a dynamics as well as population dynamics of Microcystis and Oscillatoria under specific water quality conditions. The k-fold cross-validation of the agents based on measured data of each year of two similar lakes revealed good forecasting accuracy resulting in r2 values ranging between 0.39 and 0.63.
Section snippets
Study sites and data
Myponga and Happy Valley reservoirs are located in South Australia and used for drinking water storage. Both reservoirs are classified as warm monomictic and mesotrophic, which experience in summer blue-green algal blooms. Efforts to control algal bloom events in both reservoirs include implementation of artificial mixing and aeration in summer, and operational application of copper sulphate (CuSO4).
The Japanese lakes Kasumigaura and Suwa are classified as shallow polymictic and hypertrophic.
Results and discussion
As a result of applying HEA within the framework of rigorous k-fold cross-validation according to Fig. 1, Fig. 2, Fig. 3 to time-series data of three pairs of lakes belonging to the same lake category, three rule-based agents have been developed. A rule-based chlorophyll-a agent was discovered for the two warm monomictic and mesotrophic reservoirs Myponga and Happy Valley. A rule-based Microcystis agent was developed for the two shallow polymictic and hypertrophic lakes Kasumigaura and Suwa. A
Conclusions
In the context of this study two concepts have been applied for the development of rule-based agents of algal populations: (1) rule discovery by means of a hybrid evolutionary algorithms (HEA) and rigorous k-fold cross-validation, and (2) rule generalisation by means of merged time-series data of lakes belonging to the same lake category.
The rule-based agents that have been discovered as an outcome of this study proved to be both explanatory and predictive. It has been demonstrated that the
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