Hybrid Evolutionary Algorithm HEA Research Articles

Dissolved organic nitrogen, dinoflagellates and cyanobacteria in two eutrophic lakes: Analysis by inferential modelling

The Lake Suwa (Japan) has a history of non-N-fixing Microcystis blooms. Lake Kinneret (Israel) experienced multiannual periods of sole domination by the dinoflagellate Peridinium gatunense and periods dominated seasonally by P. gatunense or cyanobacteria. Extensive studies have been carried out in both lakes regarding the role of dissolved inorganic nitrogen and phosphorus as drivers of primary productivity. There is growing evidence that dissolved organic nitrogen (DON) compounds also influence not only biomass and structure of phytoplankton communities but also microcystin production. This study focuses on relationships of DON with: (1) population dynamics of Microcystis spp. and concentrations of microcystins in Lake Suwa, and (2) population dynamics of P. gatunense as well as N- and non-N-fixing cyanobacteria in Lake Kinneret. Modelling results for historical data of Lake Suwa by means of the hybrid evolutionary algorithm HEA revealed that the prediction of abundances of four Microcystis species and concentrations of cyanotoxins achieved higher coefficients of correlation when DON/DIN-ratios were included as drivers. Population dynamics of P. gatunense in Lake Kinneret appeared to have a strong inverse relationships with DON/DIN-ratios reflected by inferential models of HEA with higher coefficients of correlation when driven by DON/DIN-ratios. When DON/DIN-ratios were included as drivers, models of Microcystis spp. in Lake Kinneret performed higher coefficients of determination compared to models of N-fixing cyanobacteria. The study highlights the need to consider DON for improved understanding and management of population dynamics of cyanobacteria and dinoflagellates in freshwater lakes.

Relationships of otter populations with fish, macroinvertebrates and water quality across three Korean rivers revealed by inferential modelling based on evolutionary computation

Depending on the life cycles of trophic biota, cascades of biological transition are established between top-down and bottom-up relationship. In South Korea, flows of the large rivers have been regulated with large weirs and estuary barrages construction. The Eurasian otter Lutra lutra is a semi-aquatic carnivore and top predator in freshwater systems. In order to understand the aquatic community variability under the impact of river modifications, we assessed the strengths of otter populations in relation to limnological data monitored between 2014 and 2016 at 250 sites of the Nakdong River, 92 sites of the Yeongsan River and 81 sites of the Seumjin River. The habitat preference and resource use of otter populations have been measured for each of the 423 river sites by the number of spraint (= otters' feces) per 600 m. The limnological data included water quality parameters, abundances of Mollusca, Anthropoda, Annelida, Nematomorpha, and Platyhelminthes as well as abundances of benthivore, herbivore, planktivore and piscivore fish. The hybrid evolutionary algorithm HEA has been applied to model relationships of otter with water quality, the benthic invertebrates and fish to determine habitat and food preferences of otter across the three rivers.Despite the stochastic noise of the data, the modelling results addressed well relationships between spraint densities and densities of fish and macroinvertebrate communities. Threshold conditions of the IF-THEN-ELSE-models discovered by HEA revealed otter responses to changing habitats and aquatic communities across the river sites but also between the three rivers. In addition, sensitivity analysis suggested possible relationships between the otter and aquatic communities. According to the results of sensitivity analysis, otter populations seemed not to control the piscivorous fish densities by showing a negative relationship, but preyed preferably on benthivorous and planktivorous fishes. Water quality parameters and benthic macro-invertebrates correlated well with otter populations suggesting favorable habitat and food-web structures. There is evidence that river flow regulation measures have a negative impact on otter populations, and that growing otter populations will alter future food web structures of the three rivers.

Causal relationships of Raphidiopsis (formerly Cylindrospermopsis) dynamics with water temperature and N:P-ratios: A meta-analysis across lakes with different climates based on inferential modelling

Raphidiopsis raciborskii is a tropical toxic cyanobacterium that is rapidly expanding to diverse lake habitats in different climate zones by sophisticated adaptation mechanisms.This meta-analysis investigated correlations of R. raciborskii with water temperature and N:P (nitrogen to phosphorus)-ratios across four lakes with different climates and trophic states by means of long-term time series and the hybrid evolutionary algorithm HEA. The results have shown that in the lakes with temperate and Mediterranean climate, R. raciborskii is strongly correlated with water temperature since germination and growth rely on rising water temperatures in spring. In contrast, there was a weaker correlation with water temperature in subtropical and tropical lakes where pelagic populations of R. raciborskii are overwintering, and are present all year round. However, the highest abundances of R. raciborskii coincided with highest water temperature for the Mediterranean, subtropical and tropical lakes, whilst in the temperate Langer See the highest abundances of R. raciborskii occurred at 24.1 °C, even though temperatures of up to 27 °C were recorded in 2013 and 2014. The correlation of R. raciborskii with N:P-ratios proved to be strongest for the meso- to eutrophic Lake Kinneret (r2 = 0.8) and lowest for the eutrophic Lake Paranoa (r2 = 0.16). However, the assumption has been confirmed that R. raciborskii is growing fastest when waters are N-limited regardless of trophic states. In terms of phenology, the temperate and Mediterranean lakes displayed “fastest growth” in spring and early summer. In contrast, the growing season in subtropical and tropical lakes lasted from spring to autumn most likely because of overwintering populations, and growing importance of direct and indirect biotic regulating factors such as competition, grazing, remineralisation of nutrients along warming climate. In order to carry out a meta-analysis of time series across four different lakes, HEA served as powerful tool resulting in inferential models with predictive capacity for population dynamics of R. raciborskii just driven by water temperature or N:P-ratios, whilst coefficients of determination r2 served as criteria for hypotheses testing.

Early warning of limit-exceeding concentrations of cyanobacteria and cyanotoxins in drinking water reservoirs by inferential modelling

An early warning scheme is proposed that runs ensembles of inferential models for predicting the cyanobacterial population dynamics and cyanotoxin concentrations in drinking water reservoirs on a diel basis driven by in situ sonde water quality data. When the 10- to 30-day-ahead predicted concentrations of cyanobacteria cells or cyanotoxins exceed pre-defined limit values, an early warning automatically activates an action plan considering in-lake control, e.g. intermittent mixing and ad hoc water treatment in water works, respectively. Case studies of the sub-tropical Lake Wivenhoe (Australia) and the Mediterranean Vaal Reservoir (South Africa) demonstrate that ensembles of inferential models developed by the hybrid evolutionary algorithm HEA are capable of up to 30days forecasts of cyanobacteria and cyanotoxins using data collected in situ. The resulting models for Dolicospermum circinale displayed validity for up to 10days ahead, whilst concentrations of Cylindrospermopsis raciborskii and microcystins were successfully predicted up to 30days ahead. Implementing the proposed scheme for drinking water reservoirs enhances current water quality monitoring practices by solely utilising in situ monitoring data, in addition to cyanobacteria and cyanotoxin measurements. Access to routinely measured cyanotoxin data allows for development of models that predict explicitly cyanotoxin concentrations that avoid to inadvertently model and predict non-toxic cyanobacterial strains.

Variations on memetic algorithms for graph coloring problems

Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem. The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm. This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA from Galinier and Hao (1999). The proposed algorithm, denoted HEAD - for HEA in Duet - works with a population of only two individuals. Moreover, a new way of managing diversity is brought by HEAD. These two main differences greatly improve the results, both in terms of solution quality and computational time. HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for , 81-colorings for and even 47-colorings for and 82-colorings for .

Threshold quantification and short-term forecasting of Anabaena, Aphanizomenon and Microcystis in the polymictic eutrophic Lake Müggelsee (Germany) by inferential modelling using the hybrid evolutionary algorithm HEA

Forecasting models for Anabaena, Aphanizomenon and Microcystis have been developed for the hypertrophic phase from 1979 to 1990 and the eutrophic phase from 1997 to 2012 of the polymictic Lake Muggelsee by means of the hybrid evolutionary algorithm HEA. Comparisons of limnological parameters of the two phases revealed not only a distinct seasonal extension of N-limitation but also higher water temperatures that rose earlier and lasted longer between spring and autumn from 1997 to 2012. These differences were reflected by threshold conditions and sensitivity functions of the cyanobacteria-specific models evolved by HEA for the two phases. Seven-day-ahead forecasts matched well timings of peaking biomass observed for the three cyanobacteria but partially failed to predict accurate magnitudes, whereby coefficients of determination r 2 ranged between 0.48 and 0.76 for models in Phase I and between 0.42 and 0.69 in Phase II. The threshold conditions of the models quantified ranges of key predictor variables such as water temperature and transparency, concentrations of NO3-N and PO4-P that were symptomatic for sudden outbreaks of high biomass of the three cyanobacteria. Sensitivity functions extracted from 20 best performing models for each of the three cyanobacteria in both phases indicated different abundances between N-fixing Anabaena and Aphanizomenon compared to non-N-fixing Microcystis in response to strengthened N-limitation in Phase II.

Modelling and forecasting the heterogeneous distribution of picocyanobacteria in the tropical Lajes Reservoir (Brazil) by evolutionary computation

Five years of water quality data from six stations across the mesotrophic and oligomictic Lajes Reservoir (Brazil) were utilized to develop 7-day ahead forecasting models for the picocyanobacteria Cyanodictyon imperfectum, Cyanogranis ferruginea and Synechococcus sp. by means of the hybrid evolutionary algorithm HEA. The data included physical and chemical water quality parameters as well as abundance data of the three picocyanobacteria. Models based on site-specific data of six monitoring stations forecasted population dynamics of Synechococcus with coefficients of determination (r2) between 0.58 for and 0.88, of Cyanodictyon with r2 between 0.5 and 0.89 and of Cyanogranis with r2 between 0.53 and 0.77. Despite phosphorus limiting conditions the sensitivity analysis revealed that the three picocyanobacteria responded much stronger to nitrate rather than to phosphate concentrations throughout the Lajes Reservoir suggesting that cyanobacteria may have adopted the sulphur-for-phosphorus strategy by utilizing sulfolipids instead. Cyanogranis displayed a negative relationship with increasing water temperature indicating its higher competitiveness at internal nutrient supply and low light levels during winter turnover. The resulting models will inform operational intervention and prevention of fast growth and dispersal of picocyanobacteria in Lajes Reservoir, and reveal environmental thresholds for outbreaks of such events.

Hybrid evolutionary computation quantifies environmental thresholds for recurrent outbreaks of population density

Identification of thresholds as indicators for sudden shifts in the community composition has proven difficult. Evolutionary computation learns inferential models from data. We investigated the hypothesis that models built from data of largely different lakes by evolutionary computation reveal similar thresholds for outbreaks of cyanobacteria densities. Here we show that IF–THEN–ELSE models inferred by the hybrid evolutionary algorithm HEA from multidimensional data of the hypertrophic polymictic Lake Taihu (China) and the mesotrophic warm-monomictic Lake Kinneret (Israel) perform fairly good 5-day-ahead forecasting of density outbreaks and indicate thresholds referring to the same environmental factors, such as nitrate and water temperature. The discovered thresholds suggest that hypereutrophic lakes may reach N-limitation at nitrate concentrations that are orders of magnitude higher than in a mesotrophic lake, and that cyanobacteria may grow at much lower water temperatures and within a much wider temperature range at phosphorus sufficiency in a hypereutrophic lake than under phosphorus deficiency in a stratified mesotrophic lake.

Model ensemble for the simulation of plankton community dynamics of Lake Kinneret (Israel) induced from in situ predictor variables by evolutionary computation

This study addresses the need for operational models in view of rapidly advancing in situ sensor technology that puts lakes into online surveillance mode. A model ensemble for simulating plankton community dynamics in Lake Kinneret (Israel) from 1988 to 1999 has been induced from electronically-measurable predictor variables (EMPV) such as water temperature, pH, turbidity, electrical conductivity and dissolved oxygen by the hybrid evolutionary algorithm HEA. It cascade wise predicts the total nitrogen to total phosphorus ratios TN/TP, concentrations of chlorophyta, baccilariophyta, cyanophyta and dinophyta, as well as densities of rotifera, cladocera and copepoda solely from EMPV. The best coefficients of determination (r2) have been achieved with 0.6 by the dinophyta model, 0.45 by the rotifera model and 0.44 by the bacillariophyta model. The worst coefficients of determination (r2) have been produced by the cladocera model with 0.24 and by the TN/TP model with 0.28. Despite the differences in the r2 values and apart from the cladocera model, the remaining models matched reasonably well seasonal and interannual plankton dynamics observed over 11 years in Lake Kinneret.The model ensemble developed by HEA also revealed ecological thresholds and relationships determining plankton community dynamics in Lake Kinneret solely based on in situ predictor variables.

Inductive reasoning and forecasting of population dynamics of Cylindrospermopsis raciborskii in three sub-tropical reservoirs by evolutionary computation

Seven-day-ahead forecasting models of Cylindrospermopsis raciborskii in three warm-monomictic and mesotrophic reservoirs in south-east Queensland have been developed by means of water quality data from 1999 to 2010 and the hybrid evolutionary algorithm HEA. Resulting models using all measured variables as inputs as well as models using electronically measurable variables only as inputs forecasted accurately timing of overgrowth of C. raciborskii and matched well high and low magnitudes of observed bloom events with 0.45≤r2>0.61 and 0.4≤r2>0.57, respectively. The models also revealed relationships and thresholds triggering bloom events that provide valuable information on synergism between water quality conditions and population dynamics of C. raciborskii. Best performing models based on using all measured variables as inputs indicated electrical conductivity (EC) within the range of 206–280mSm−1 as threshold above which fast growth and high abundances of C. raciborskii have been observed for the three lakes. Best models based on electronically measurable variables for the Lakes Wivenhoe and Somerset indicated a water temperature (WT) range of 25.5–32.7°C within which fast growth and high abundances of C. raciborskii can be expected. By contrast the model for Lake Samsonvale highlighted a turbidity (TURB) level of 4.8 NTU as indicator for mass developments of C. raciborskii.Experiments with online measured water quality data of the Lake Wivenhoe from 2007 to 2010 resulted in predictive models with 0.61≤r2>0.65 whereby again similar levels of EC and WT have been discovered as thresholds for outgrowth of C. raciborskii. The highest validity of r2=0.75 for an in situ data-based model has been achieved after considering time lags for EC by 7 days and dissolved oxygen by 1 day. These time lags have been discovered by a systematic screening of all possible combinations of time lags between 0 and 10 days for all electronically measurable variables. The so-developed model performs seven-day-ahead forecasts and is currently implemented and tested for early warning of C. raciborskii blooms in the Wivenhoe reservoir.

Generic limnological models on the touchstone: Testing the lake simulation library SALMO-OO and the rule-based Microcystis agent for warm-monomictic hypertrophic lakes in South Africa

Generic models are required to share models for the same category of ecosystems in order to facilitate comparative scenario analyses and forecasting, and classify ecosystem health. However, generality is the most often neglected one of the three criteria for model validation: reality, precision and generality. The paper suggests to validate models for lake ecosystem categories defined by (a) circulation types of lakes that to some degree reflect climate and morphometry, and (b) trophic states of lakes that to some degree reflect community structures and habitat properties. Two models are tested for South African lakes belonging to the category of warm-monomictic and hypertrophic lakes: the deterministic simulation library SALMO-OO and a rule-based agent for Microcystis discovered by evolutionary computation. SALMO-OO is an object-oriented implementation of mass balance equations for a typical pelagic food web (diatoms, green algae, blue-green algae, and cladocerans) and nutrient cycles (PO 4-P, NO 3-N, detritus) as well as alternative process models for algal growth and grazing, zooplankton growth and mortality. During validation the best performing model structure is determined for a number of lakes belonging to the same category. SALMO-OO is implemented in JAVA providing an interactive user-interface. The rule-based Microcystis agent has been discovered by the hybrid evolutionary algorithm HEA after training by merged time series data of three lakes belonging to the same category and 14-fold cross-validation for data of all 14 years of each lake. The agent allows 7-days-ahead forecasting of Microcystis abundance for any of the three lakes. It can be concluded that the design and validation of models for ecosystem categories improves the generality of models, and promotes both model as well as data sharing. Future work will focus on distinctive ecological features of ecosystem categories to be considered in informed structure design and validation of category models.