Summary
1.A safe, clean water supply is critical for sustaining many important ecosystem services provided by freshwaters. The development of cyanobacterial blooms in lakes and reservoirs has a major impact on the provision of these services, particularly limiting their use for recreation and water supply for drinking and spray irrigation. Nutrient enrichment is thought to be the most important pressure responsible for the widespread increase in cyanobacterial blooms in recent decades. Quantifying how nutrients limit cyanobacterial abundance in lakes is, therefore, a key need for setting robust targets for the management of freshwaters. 2. Using a data set from over 800 European lakes, we highlight the use of quantile regression modelling for understanding the maximum potential capacity of cyanobacteria in relation to total phosphorus (TP) and the use of a range of quantile responses, alongside World Health Organisation (WHO) health alert thresholds for recreational waters, for setting robust phosphorus targets for lake management in relation to water use. 3. The analysis shows that cyanobacteria exhibit a nonlinear response to phosphorus with the sharpest increase in cyanobacterial abundance occurring in the TP range from about 20 lg L À1 up to about 100 lg L À1 .4. The likelihood of exceeding the World Health Organisation (WHO) 'low health alert' threshold increases from about 5% exceedance at 16 lg L À1 to 40% exceedance at 54 lg L À1 . About 50% of the studied lakes remain below this WHO health alert threshold, irrespective of high summer TP concentrations, highlighting the importance of other factors affecting cyanobacteria population growth and loss processes, such as high flushing rate. 5. Synthesis and applications. Developing a more quantitative understanding of the effect of nutrients on cyanobacterial abundance in freshwater lakes provides important knowledge for restoring and sustaining a safe, clean water supply for multiple uses. Our models can be used to set nutrient targets to sustain recreational services and provide different levels of precaution that can be chosen dependent on the importance of the service provision.Key-words: algal bloom, blue-green algae, ecosystem services, freshwater, lake, nutrient, quantile regression, WHO *Correspondence author. E-mail: laca@ceh.ac.uk † On secondment from CEH 2 to JRC 1 .