Bayesian modelling of algal mass occurrences - using adaptive MCMC methods with a lake water quality model

Our study aims to estimate confounded effects of nutrients and grazing zooplankton (Crustacea) on phytoplankton groupsdspecifically on nitrogen-fixing Cyanobacteriadin the shallow, mesotrophic Lake Pyhäjärvi in the northern hemisphere (Finland, northern Europe, lat. 60 54 0e 61 06 0, long. 22 09 0e22 22 0). Phytoplankton is modelled with a non-linear dynamic model which describes the succession of three dominant algae groups (Diatomophyceae, Chrysophyceae, nitrogen-fixing Cyanobacteria) and minor groups summed together as a function of total phosphorus, total nitrogen, temperature, global irradiance and crustacean zooplankton grazing. The model is fitted using 8 years of in situ observations and adaptive Markov chain Monte Carlo (MCMC) methods for estimation of model parameters. The approach offers a way to deal with noisy data and a large number of weakly identifiable parameters in a model. From our posterior simulations we calculate the lower limit for zooplankton carbon mass concentration (45 mgC L ) and the upper limit for total phosphorus concentration (16 mg L ) that satisfy with 0.95 probability our predefined water quality criteria (Cyanobacteria concentration during late summer period does not exceed the value 0.86 mg L ). Within the observational range total phosphorus has marginal effect on Cyanobacteria compared to the zooplankton grazing effect, which is temperature-dependent. Extensive fishing efforts are needed to attain the criteria. 2006 Elsevier Ltd. All rights reserved.